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Refactored Ppg for frequency based algorithm. (#1486)

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New implementation of the heart rate sensor data processing using a frequency based PPG algorithm.
The HRS3300 settings are fine-tuned for better signal to noise at 10Hz.
The measurement delay is now set to 100ms.
Enable and use the ambient light sensor.
FFT implementation based on ArduinoFFT (https://github.com/kosme/arduinoFFT, GPLv3.0).
This commit is contained in:
Ceimour 2023-04-30 08:50:18 -05:00 committed by GitHub
parent 40f7e1c7be
commit c22e30a4a6
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GPG key ID: 4AEE18F83AFDEB23
26 changed files with 2675 additions and 210 deletions
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12
src/CMakeLists.txt
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@ -488,10 +488,8 @@ list(APPEND SOURCE_FILES
drivers/TwiMaster.cpp
heartratetask/HeartRateTask.cpp
components/heartrate/Ppg.cpp
components/heartrate/Biquad.cpp
components/heartrate/Ptagc.cpp
components/heartrate/HeartRateController.cpp
components/heartrate/Ppg.cpp
buttonhandler/ButtonHandler.cpp
touchhandler/TouchHandler.cpp
@ -552,8 +550,7 @@ list(APPEND RECOVERY_SOURCE_FILES
components/heartrate/HeartRateController.cpp
heartratetask/HeartRateTask.cpp
components/heartrate/Ppg.cpp
components/heartrate/Biquad.cpp
components/heartrate/Ptagc.cpp
components/motor/MotorController.cpp
components/fs/FS.cpp
buttonhandler/ButtonHandler.cpp
@ -666,9 +663,10 @@ set(INCLUDE_FILES
drivers/TwiMaster.h
heartratetask/HeartRateTask.h
components/heartrate/Ppg.h
components/heartrate/Biquad.h
components/heartrate/Ptagc.h
components/heartrate/HeartRateController.h
libs/arduinoFFT-develop/src/arduinoFFT.h
libs/arduinoFFT-develop/src/defs.h
libs/arduinoFFT-develop/src/types.h
components/motor/MotorController.h
buttonhandler/ButtonHandler.h
touchhandler/TouchHandler.h

26
src/components/heartrate/Biquad.cpp
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@ -1,26 +0,0 @@
/*
SPDX-License-Identifier: LGPL-3.0-or-later
Original work Copyright (C) 2020 Daniel Thompson
C++ port Copyright (C) 2021 Jean-François Milants
*/
#include "components/heartrate/Biquad.h"
using namespace Pinetime::Controllers;
/** Original implementation from wasp-os : https://github.com/daniel-thompson/wasp-os/blob/master/wasp/ppg.py */
Biquad::Biquad(float b0, float b1, float b2, float a1, float a2) : b0 {b0}, b1 {b1}, b2 {b2}, a1 {a1}, a2 {a2} {
}
float Biquad::Step(float x) {
auto v1 = this->v1;
auto v2 = this->v2;
auto v = x - (a1 * v1) - (a2 * v2);
auto y = (b0 * v) + (b1 * v1) + (b2 * v2);
this->v2 = v1;
this->v1 = v;
return y;
}

22
src/components/heartrate/Biquad.h
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@ -1,22 +0,0 @@
#pragma once
namespace Pinetime {
namespace Controllers {
/// Direct Form II Biquad Filter
class Biquad {
public:
Biquad(float b0, float b1, float b2, float a1, float a2);
float Step(float x);
private:
float b0;
float b1;
float b2;
float a1;
float a2;
float v1 = 0.0f;
float v2 = 0.0f;
};
}
}

339
src/components/heartrate/Ppg.cpp
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@ -1,107 +1,292 @@
/*
SPDX-License-Identifier: LGPL-3.0-or-later
Original work Copyright (C) 2020 Daniel Thompson
C++ port Copyright (C) 2021 Jean-François Milants
*/
#include "components/heartrate/Ppg.h"
#include <vector>
#include <nrf_log.h>
#include <vector>
using namespace Pinetime::Controllers;
/** Original implementation from wasp-os : https://github.com/daniel-thompson/wasp-os/blob/master/wasp/ppg.py */
namespace {
int Compare(int8_t* d1, int8_t* d2, size_t count) {
int e = 0;
for (size_t i = 0; i < count; i++) {
auto d = d1[i] - d2[i];
e += d * d;
float LinearInterpolation(const float* xValues, const float* yValues, int length, float pointX) {
if (pointX > xValues[length - 1]) {
return yValues[length - 1];
} else if (pointX <= xValues[0]) {
return yValues[0];
}
return e;
int index = 0;
while (pointX > xValues[index] && index < length - 1) {
index++;
}
float pointX0 = xValues[index - 1];
float pointX1 = xValues[index];
float pointY0 = yValues[index - 1];
float pointY1 = yValues[index];
float mu = (pointX - pointX0) / (pointX1 - pointX0);
return (pointY0 * (1 - mu) + pointY1 * mu);
}
int CompareShift(int8_t* d, int shift, size_t count) {
return Compare(d + shift, d, count - shift);
}
int Trough(int8_t* d, size_t size, uint8_t mn, uint8_t mx) {
auto z2 = CompareShift(d, mn - 2, size);
auto z1 = CompareShift(d, mn - 1, size);
for (int i = mn; i < mx + 1; i++) {
auto z = CompareShift(d, i, size);
if (z2 > z1 && z1 < z) {
return i;
float PeakSearch(float* xVals, float* yVals, float threshold, float& width, float start, float end, int length) {
int peaks = 0;
bool enabled = false;
float minBin = 0.0f;
float maxBin = 0.0f;
float peakCenter = 0.0f;
float prevValue = LinearInterpolation(xVals, yVals, length, start - 0.01f);
float currValue = LinearInterpolation(xVals, yVals, length, start);
float idx = start;
while (idx < end) {
float nextValue = LinearInterpolation(xVals, yVals, length, idx + 0.01f);
if (currValue < threshold) {
enabled = true;
}
z2 = z1;
z1 = z;
if (currValue >= threshold and enabled) {
if (prevValue < threshold) {
minBin = idx;
} else if (nextValue <= threshold) {
maxBin = idx;
peaks++;
width = maxBin - minBin;
peakCenter = width / 2.0f + minBin;
}
}
prevValue = currValue;
currValue = nextValue;
idx += 0.01f;
}
return -1;
if (peaks != 1) {
width = 0.0f;
peakCenter = 0.0f;
}
return peakCenter;
}
float SpectrumMean(const std::array<float, Ppg::spectrumLength>& signal, int start, int end) {
int total = 0;
float mean = 0.0f;
for (int idx = start; idx < end; idx++) {
mean += signal.at(idx);
total++;
}
if (total > 0) {
mean /= static_cast<float>(total);
}
return mean;
}
float SignalToNoise(const std::array<float, Ppg::spectrumLength>& signal, int start, int end, float max) {
float mean = SpectrumMean(signal, start, end);
return max / mean;
}
// Simple bandpass filter using exponential moving average
void Filter30to240(std::array<float, Ppg::dataLength>& signal) {
// From:
// https://www.norwegiancreations.com/2016/03/arduino-tutorial-simple-high-pass-band-pass-and-band-stop-filtering/
int length = signal.size();
// 0.268 is ~0.5Hz and 0.816 is ~4Hz cutoff at 10Hz sampling
float expAlpha = 0.816f;
float expAvg = 0.0f;
for (int loop = 0; loop < 4; loop++) {
expAvg = signal.front();
for (int idx = 0; idx < length; idx++) {
expAvg = (expAlpha * signal.at(idx)) + ((1 - expAlpha) * expAvg);
signal[idx] = expAvg;
}
}
expAlpha = 0.268f;
for (int loop = 0; loop < 4; loop++) {
expAvg = signal.front();
for (int idx = 0; idx < length; idx++) {
expAvg = (expAlpha * signal.at(idx)) + ((1 - expAlpha) * expAvg);
signal[idx] -= expAvg;
}
}
}
float SpectrumMax(const std::array<float, Ppg::spectrumLength>& data, int start, int end) {
float max = 0.0f;
for (int idx = start; idx < end; idx++) {
if (data.at(idx) > max) {
max = data.at(idx);
}
}
return max;
}
void Detrend(std::array<float, Ppg::dataLength>& signal) {
int size = signal.size();
float offset = signal.front();
float slope = (signal.at(size - 1) - offset) / static_cast<float>(size - 1);
for (int idx = 0; idx < size; idx++) {
signal[idx] -= (slope * static_cast<float>(idx) + offset);
}
for (int idx = 0; idx < size - 1; idx++) {
signal[idx] = signal[idx + 1] - signal[idx];
}
}
// Hanning Coefficients from numpy: python -c 'import numpy;print(numpy.hanning(64))'
// Note: Harcoded and must be updated if constexpr dataLength is changed. Prevents the need to
// use cosf() which results in an extra ~5KB in storage.
// This data is symetrical so just using the first half (saves 128B when dataLength is 64).
static constexpr float hanning[Ppg::dataLength >> 1] {
0.0f, 0.00248461f, 0.00991376f, 0.0222136f, 0.03926189f, 0.06088921f, 0.08688061f, 0.11697778f,
0.15088159f, 0.1882551f, 0.22872687f, 0.27189467f, 0.31732949f, 0.36457977f, 0.41317591f, 0.46263495f,
0.51246535f, 0.56217185f, 0.61126047f, 0.65924333f, 0.70564355f, 0.75f, 0.79187184f, 0.83084292f,
0.86652594f, 0.89856625f, 0.92664544f, 0.95048443f, 0.96984631f, 0.98453864f, 0.99441541f, 0.99937846f};
}
Ppg::Ppg()
: hpf {0.87033078, -1.74066156, 0.87033078, -1.72377617, 0.75754694},
agc {20, 0.971, 2},
lpf {0.11595249, 0.23190498, 0.11595249, -0.72168143, 0.18549138} {
Ppg::Ppg() {
dataAverage.fill(0.0f);
spectrum.fill(0.0f);
}
int8_t Ppg::Preprocess(float spl) {
spl -= offset;
spl = hpf.Step(spl);
spl = agc.Step(spl);
spl = lpf.Step(spl);
auto spl_int = static_cast<int8_t>(spl);
if (dataIndex < 200) {
data[dataIndex++] = spl_int;
int8_t Ppg::Preprocess(uint32_t hrs, uint32_t als) {
if (dataIndex < dataLength) {
dataHRS[dataIndex++] = hrs;
}
return spl_int;
alsValue = als;
if (alsValue > alsThreshold) {
return 1;
}
return 0;
}
int Ppg::HeartRate() {
if (dataIndex < 200) {
if (dataIndex < dataLength) {
return 0;
}
NRF_LOG_INFO("PREPROCESS, offset = %d", offset);
auto hr = ProcessHeartRate();
dataIndex = 0;
int hr = 0;
hr = ProcessHeartRate(resetSpectralAvg);
resetSpectralAvg = false;
// Make room for overlapWindow number of new samples
for (int idx = 0; idx < dataLength - overlapWindow; idx++) {
dataHRS[idx] = dataHRS[idx + overlapWindow];
}
dataIndex = dataLength - overlapWindow;
return hr;
}
int Ppg::ProcessHeartRate() {
int t0 = Trough(data.data(), dataIndex, 7, 48);
if (t0 < 0) {
return 0;
void Ppg::Reset(bool resetDaqBuffer) {
if (resetDaqBuffer) {
dataIndex = 0;
}
int t1 = t0 * 2;
t1 = Trough(data.data(), dataIndex, t1 - 5, t1 + 5);
if (t1 < 0) {
return 0;
}
int t2 = (t1 * 3) / 2;
t2 = Trough(data.data(), dataIndex, t2 - 5, t2 + 5);
if (t2 < 0) {
return 0;
}
int t3 = (t2 * 4) / 3;
t3 = Trough(data.data(), dataIndex, t3 - 4, t3 + 4);
if (t3 < 0) {
return (60 * 24 * 3) / t2;
}
return (60 * 24 * 4) / t3;
avgIndex = 0;
dataAverage.fill(0.0f);
lastPeakLocation = 0.0f;
alsThreshold = UINT16_MAX;
alsValue = 0;
resetSpectralAvg = true;
spectrum.fill(0.0f);
}
void Ppg::SetOffset(uint16_t offset) {
this->offset = offset;
dataIndex = 0;
// Pass init == true to reset spectral averaging.
// Returns -1 (Reset Acquisition), 0 (Unable to obtain HR) or HR (BPM).
int Ppg::ProcessHeartRate(bool init) {
std::copy(dataHRS.begin(), dataHRS.end(), vReal.begin());
Detrend(vReal);
Filter30to240(vReal);
vImag.fill(0.0f);
// Apply Hanning Window
int hannIdx = 0;
for (int idx = 0; idx < dataLength; idx++) {
if (idx >= dataLength >> 1) {
hannIdx--;
}
vReal[idx] *= hanning[hannIdx];
if (idx < dataLength >> 1) {
hannIdx++;
}
}
// Compute in place power spectrum
ArduinoFFT<float> FFT = ArduinoFFT<float>(vReal.data(), vImag.data(), dataLength, sampleFreq);
FFT.compute(FFTDirection::Forward);
FFT.complexToMagnitude();
FFT.~ArduinoFFT();
SpectrumAverage(vReal.data(), spectrum.data(), spectrum.size(), init);
peakLocation = 0.0f;
float threshold = peakDetectionThreshold;
float peakWidth = 0.0f;
int specLen = spectrum.size();
float max = SpectrumMax(spectrum, hrROIbegin, hrROIend);
float signalToNoiseRatio = SignalToNoise(spectrum, hrROIbegin, hrROIend, max);
if (signalToNoiseRatio > signalToNoiseThreshold && spectrum.at(0) < dcThreshold) {
threshold *= max;
// Reuse VImag for interpolation x values passed to PeakSearch
for (int idx = 0; idx < dataLength; idx++) {
vImag[idx] = idx;
}
peakLocation = PeakSearch(vImag.data(),
spectrum.data(),
threshold,
peakWidth,
static_cast<float>(hrROIbegin),
static_cast<float>(hrROIend),
specLen);
peakLocation *= freqResolution;
}
// Peak too wide? (broad spectrum noise or large, rapid HR change)
if (peakWidth > maxPeakWidth) {
peakLocation = 0.0f;
}
// Check HR limits
if (peakLocation < minHR || peakLocation > maxHR) {
peakLocation = 0.0f;
}
// Reset spectral averaging if bad reading
if (peakLocation == 0.0f) {
resetSpectralAvg = true;
}
// Set the ambient light threshold and return HR in BPM
alsThreshold = static_cast<uint16_t>(alsValue * alsFactor);
// Get current average HR. If HR reduced to zero, return -1 (reset) else HR
peakLocation = HeartRateAverage(peakLocation);
int rtn = -1;
if (peakLocation == 0.0f && lastPeakLocation > 0.0f) {
lastPeakLocation = 0.0f;
} else {
lastPeakLocation = peakLocation;
rtn = static_cast<int>((peakLocation * 60.0f) + 0.5f);
}
return rtn;
}
void Ppg::Reset() {
dataIndex = 0;
void Ppg::SpectrumAverage(const float* data, float* spectrum, int length, bool reset) {
if (reset) {
spectralAvgCount = 0;
}
float count = static_cast<float>(spectralAvgCount);
for (int idx = 0; idx < length; idx++) {
spectrum[idx] = (spectrum[idx] * count + data[idx]) / (count + 1);
}
if (spectralAvgCount < spectralAvgMax) {
spectralAvgCount++;
}
}
float Ppg::HeartRateAverage(float hr) {
avgIndex++;
avgIndex %= dataAverage.size();
dataAverage[avgIndex] = hr;
float avg = 0.0f;
float total = 0.0f;
float min = 300.0f;
float max = 0.0f;
for (const float& value : dataAverage) {
if (value > 0.0f) {
avg += value;
if (value < min)
min = value;
if (value > max)
max = value;
total++;
}
}
if (total > 0) {
avg /= total;
} else {
avg = 0.0f;
}
return avg;
}

74
src/components/heartrate/Ppg.h
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@ -3,29 +3,77 @@
#include <array>
#include <cstddef>
#include <cstdint>
#include "components/heartrate/Biquad.h"
#include "components/heartrate/Ptagc.h"
// Note: Change internal define 'sqrt_internal sqrt' to
// 'sqrt_internal sqrtf' to save ~3KB of flash.
#define FFT_SPEED_OVER_PRECISION
#include "libs/arduinoFFT-develop/src/arduinoFFT.h"
namespace Pinetime {
namespace Controllers {
class Ppg {
public:
Ppg();
int8_t Preprocess(float spl);
int8_t Preprocess(uint32_t hrs, uint32_t als);
int HeartRate();
void SetOffset(uint16_t offset);
void Reset();
void Reset(bool resetDaqBuffer);
static constexpr int deltaTms = 100;
// Daq dataLength: Must be power of 2
static constexpr uint16_t dataLength = 64;
static constexpr uint16_t spectrumLength = dataLength >> 1;
private:
std::array<int8_t, 200> data;
size_t dataIndex = 0;
float offset;
Biquad hpf;
Ptagc agc;
Biquad lpf;
// The sampling frequency (Hz) based on sampling time in milliseconds (DeltaTms)
static constexpr float sampleFreq = 1000.0f / static_cast<float>(deltaTms);
// The frequency resolution (Hz)
static constexpr float freqResolution = sampleFreq / dataLength;
// Number of samples before each analysis
// 0.5 second update rate at 10Hz
static constexpr uint16_t overlapWindow = 5;
// Maximum number of spectrum running averages
// Note: actual number of spectra averaged = spectralAvgMax + 1
static constexpr uint16_t spectralAvgMax = 2;
// Multiple Peaks above this threshold (% of max) are rejected
static constexpr float peakDetectionThreshold = 0.6f;
// Maximum peak width (bins) at threshold for valid peak.
static constexpr float maxPeakWidth = 2.5f;
// Metric for spectrum noise level.
static constexpr float signalToNoiseThreshold = 3.0f;
// Heart rate Region Of Interest begin (bins)
static constexpr uint16_t hrROIbegin = static_cast<uint16_t>((30.0f / 60.0f) / freqResolution + 0.5f);
// Heart rate Region Of Interest end (bins)
static constexpr uint16_t hrROIend = static_cast<uint16_t>((240.0f / 60.0f) / freqResolution + 0.5f);
// Minimum HR (Hz)
static constexpr float minHR = 40.0f / 60.0f;
// Maximum HR (Hz)
static constexpr float maxHR = 230.0f / 60.0f;
// Threshold for high DC level after filtering
static constexpr float dcThreshold = 0.5f;
// ALS detection factor
static constexpr float alsFactor = 2.0f;
int ProcessHeartRate();
// Raw ADC data
std::array<uint16_t, dataLength> dataHRS;
// Stores Real numbers from FFT
std::array<float, dataLength> vReal;
// Stores Imaginary numbers from FFT
std::array<float, dataLength> vImag;
// Stores power spectrum calculated from FFT real and imag values
std::array<float, (spectrumLength)> spectrum;
// Stores each new HR value (Hz). Non zero values are averaged for HR output
std::array<float, 20> dataAverage;
uint16_t avgIndex = 0;
uint16_t spectralAvgCount = 0;
float lastPeakLocation = 0.0f;
uint16_t alsThreshold = UINT16_MAX;
uint16_t alsValue = 0;
uint16_t dataIndex = 0;
float peakLocation;
bool resetSpectralAvg = true;
int ProcessHeartRate(bool init);
float HeartRateAverage(float hr);
void SpectrumAverage(const float* data, float* spectrum, int length, bool reset);
};
}
}

29
src/components/heartrate/Ptagc.cpp
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@ -1,29 +0,0 @@
/*
SPDX-License-Identifier: LGPL-3.0-or-later
Original work Copyright (C) 2020 Daniel Thompson
C++ port Copyright (C) 2021 Jean-François Milants
*/
#include "components/heartrate/Ptagc.h"
#include <cmath>
using namespace Pinetime::Controllers;
/** Original implementation from wasp-os : https://github.com/daniel-thompson/wasp-os/blob/master/wasp/ppg.py */
Ptagc::Ptagc(float start, float decay, float threshold) : peak {start}, decay {decay}, boost {1.0f / decay}, threshold {threshold} {
}
float Ptagc::Step(float spl) {
if (std::abs(spl) > peak) {
peak *= boost;
} else {
peak *= decay;
}
if ((spl > (peak * threshold)) || (spl < (peak * -threshold))) {
return 0.0f;
}
spl = 100.0f * spl / (2.0f * peak);
return spl;
}

17
src/components/heartrate/Ptagc.h
View file

@ -1,17 +0,0 @@
#pragma once
namespace Pinetime {
namespace Controllers {
class Ptagc {
public:
Ptagc(float start, float decay, float threshold);
float Step(float spl);
private:
float peak;
float decay;
float boost;
float threshold;
};
}
}

24
src/drivers/Hrs3300.cpp
View file

@ -16,6 +16,8 @@ using namespace Pinetime::Drivers;
/** Driver for the HRS3300 heart rate sensor.
* Original implementation from wasp-os : https://github.com/daniel-thompson/wasp-os/blob/master/wasp/drivers/hrs3300.py
*
* Experimentaly derived changes to improve signal/noise (see comments below) - Ceimour
*/
Hrs3300::Hrs3300(TwiMaster& twiMaster, uint8_t twiAddress) : twiMaster {twiMaster}, twiAddress {twiAddress} {
}
@ -26,19 +28,21 @@ void Hrs3300::Init() {
Disable();
vTaskDelay(100);
// HRS disabled, 12.5 ms wait time between cycles, (partly) 20mA drive
WriteRegister(static_cast<uint8_t>(Registers::Enable), 0x60);
// HRS disabled, 50ms wait time between ADC conversion period, current 12.5mA
WriteRegister(static_cast<uint8_t>(Registers::Enable), 0x50);
// (partly) 20mA drive, power on, "magic" (datasheet says both
// "reserved" and "set low nibble to 8" but 0xe gives better results
// and is used by at least two other HRS3300 drivers
WriteRegister(static_cast<uint8_t>(Registers::PDriver), 0x6E);
// Current 12.5mA and low nibble 0xF.
// Note: Setting low nibble to 0x8 per the datasheet results in
// modulated LED driver output. Setting to 0xF results in clean,
// steady output during the ADC conversion period.
WriteRegister(static_cast<uint8_t>(Registers::PDriver), 0x2f);
// HRS and ALS both in 16-bit mode
WriteRegister(static_cast<uint8_t>(Registers::Res), 0x88);
// HRS and ALS both in 15-bit mode results in ~50ms LED drive period
// and presumably ~50ms ADC conversion period.
WriteRegister(static_cast<uint8_t>(Registers::Res), 0x77);
// 8x gain, non default, reduced value for better readings
WriteRegister(static_cast<uint8_t>(Registers::Hgain), 0xc);
// Gain set to 1x
WriteRegister(static_cast<uint8_t>(Registers::Hgain), 0x00);
}
void Hrs3300::Enable() {

35
src/heartratetask/HeartRateTask.cpp
View file

@ -26,10 +26,11 @@ void HeartRateTask::Process(void* instance) {
void HeartRateTask::Work() {
int lastBpm = 0;
while (true) {
auto delay = portMAX_DELAY;
Messages msg;
uint32_t delay;
if (state == States::Running) {
if (measurementStarted) {
delay = 40;
delay = ppg.deltaTms;
} else {
delay = 100;
}
@ -37,8 +38,7 @@ void HeartRateTask::Work() {
delay = portMAX_DELAY;
}
Messages msg;
if (xQueueReceive(messageQueue, &msg, delay) == pdTRUE) {
if (xQueueReceive(messageQueue, &msg, delay)) {
switch (msg) {
case Messages::GoToSleep:
StopMeasurement();
@ -70,12 +70,28 @@ void HeartRateTask::Work() {
}
if (measurementStarted) {
ppg.Preprocess(static_cast<float>(heartRateSensor.ReadHrs()));
auto bpm = ppg.HeartRate();
int8_t ambient = ppg.Preprocess(heartRateSensor.ReadHrs(), heartRateSensor.ReadAls());
int bpm = ppg.HeartRate();
// If ambient light detected or a reset requested (bpm < 0)
if (ambient > 0) {
// Reset all DAQ buffers
ppg.Reset(true);
// Force state to NotEnoughData (below)
lastBpm = 0;
bpm = 0;
} else if (bpm < 0) {
// Reset all DAQ buffers except HRS buffer
ppg.Reset(false);
// Set HR to zero and update
bpm = 0;
controller.Update(Controllers::HeartRateController::States::Running, bpm);
}
if (lastBpm == 0 && bpm == 0) {
controller.Update(Controllers::HeartRateController::States::NotEnoughData, 0);
controller.Update(Controllers::HeartRateController::States::NotEnoughData, bpm);
}
if (bpm != 0) {
lastBpm = bpm;
controller.Update(Controllers::HeartRateController::States::Running, lastBpm);
@ -87,7 +103,7 @@ void HeartRateTask::Work() {
void HeartRateTask::PushMessage(HeartRateTask::Messages msg) {
BaseType_t xHigherPriorityTaskWoken = pdFALSE;
xQueueSendFromISR(messageQueue, &msg, &xHigherPriorityTaskWoken);
if (xHigherPriorityTaskWoken == pdTRUE) {
if (xHigherPriorityTaskWoken) {
/* Actual macro used here is port specific. */
// TODO : should I do something here?
}
@ -95,11 +111,12 @@ void HeartRateTask::PushMessage(HeartRateTask::Messages msg) {
void HeartRateTask::StartMeasurement() {
heartRateSensor.Enable();
ppg.Reset(true);
vTaskDelay(100);
ppg.SetOffset(heartRateSensor.ReadHrs());
}
void HeartRateTask::StopMeasurement() {
heartRateSensor.Disable();
ppg.Reset(true);
vTaskDelay(100);
}

3
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@ -0,0 +1,3 @@
/.project
/sync.ffs_db
*.*bak

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/*
Example of use of the FFT libray
Copyright (C) 2014 Enrique Condes
Copyright (C) 2020 Bim Overbohm (header-only, template, speed improvements)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
/*
In this example, the Arduino simulates the sampling of a sinusoidal 1000 Hz
signal with an amplitude of 100, sampled at 5000 Hz. Samples are stored
inside the vReal array. The samples are windowed according to Hamming
function. The FFT is computed using the windowed samples. Then the magnitudes
of each of the frequencies that compose the signal are calculated. Finally,
the frequency with the highest peak is obtained, being that the main frequency
present in the signal.
*/
#include "arduinoFFT.h"
/*
These values can be changed in order to evaluate the functions
*/
const uint16_t samples = 64; //This value MUST ALWAYS be a power of 2
const double signalFrequency = 1000;
const double samplingFrequency = 5000;
const uint8_t amplitude = 100;
/*
These are the input and output vectors
Input vectors receive computed results from FFT
*/
double vReal[samples];
double vImag[samples];
/* Create FFT object */
ArduinoFFT<double> FFT = ArduinoFFT<double>(vReal, vImag, samples, samplingFrequency);
#define SCL_INDEX 0x00
#define SCL_TIME 0x01
#define SCL_FREQUENCY 0x02
#define SCL_PLOT 0x03
void setup()
{
Serial.begin(115200);
Serial.println("Ready");
}
void loop()
{
/* Build raw data */
double cycles = (((samples-1) * signalFrequency) / samplingFrequency); //Number of signal cycles that the sampling will read
for (uint16_t i = 0; i < samples; i++)
{
vReal[i] = int8_t((amplitude * (sin((i * (TWO_PI * cycles)) / samples))) / 2.0);/* Build data with positive and negative values*/
//vReal[i] = uint8_t((amplitude * (sin((i * (twoPi * cycles)) / samples) + 1.0)) / 2.0);/* Build data displaced on the Y axis to include only positive values*/
vImag[i] = 0.0; //Imaginary part must be zeroed in case of looping to avoid wrong calculations and overflows
}
/* Print the results of the simulated sampling according to time */
Serial.println("Data:");
PrintVector(vReal, samples, SCL_TIME);
FFT.windowing(FFTWindow::Hamming, FFTDirection::Forward); /* Weigh data */
Serial.println("Weighed data:");
PrintVector(vReal, samples, SCL_TIME);
FFT.compute(FFTDirection::Forward); /* Compute FFT */
Serial.println("Computed Real values:");
PrintVector(vReal, samples, SCL_INDEX);
Serial.println("Computed Imaginary values:");
PrintVector(vImag, samples, SCL_INDEX);
FFT.complexToMagnitude(); /* Compute magnitudes */
Serial.println("Computed magnitudes:");
PrintVector(vReal, (samples >> 1), SCL_FREQUENCY);
double x = FFT.majorPeak();
Serial.println(x, 6);
while(1); /* Run Once */
// delay(2000); /* Repeat after delay */
}
void PrintVector(double *vData, uint16_t bufferSize, uint8_t scaleType)
{
for (uint16_t i = 0; i < bufferSize; i++)
{
double abscissa;
/* Print abscissa value */
switch (scaleType)
{
case SCL_INDEX:
abscissa = (i * 1.0);
break;
case SCL_TIME:
abscissa = ((i * 1.0) / samplingFrequency);
break;
case SCL_FREQUENCY:
abscissa = ((i * 1.0 * samplingFrequency) / samples);
break;
}
Serial.print(abscissa, 6);
if(scaleType==SCL_FREQUENCY)
Serial.print("Hz");
Serial.print(" ");
Serial.println(vData[i], 4);
}
Serial.println();
}

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/*
Example of use of the FFT libray to compute FFT for several signals over a range of frequencies.
The exponent is calculated once before the excecution since it is a constant.
This saves resources during the excecution of the sketch and reduces the compiled size.
The sketch shows the time that the computing is taking.
Copyright (C) 2014 Enrique Condes
Copyright (C) 2020 Bim Overbohm (header-only, template, speed improvements)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#include "arduinoFFT.h"
/*
These values can be changed in order to evaluate the functions
*/
const uint16_t samples = 64;
const double sampling = 40;
const uint8_t amplitude = 4;
const double startFrequency = 2;
const double stopFrequency = 16.4;
const double step_size = 0.1;
/*
These are the input and output vectors
Input vectors receive computed results from FFT
*/
double vReal[samples];
double vImag[samples];
/* Create FFT object */
ArduinoFFT<double> FFT = ArduinoFFT<double>(vReal, vImag, samples, sampling);
unsigned long startTime;
#define SCL_INDEX 0x00
#define SCL_TIME 0x01
#define SCL_FREQUENCY 0x02
#define SCL_PLOT 0x03
void setup()
{
Serial.begin(115200);
Serial.println("Ready");
}
void loop()
{
Serial.println("Frequency\tDetected\ttakes (ms)");
Serial.println("=======================================\n");
for(double frequency = startFrequency; frequency<=stopFrequency; frequency+=step_size)
{
/* Build raw data */
double cycles = (((samples-1) * frequency) / sampling);
for (uint16_t i = 0; i < samples; i++)
{
vReal[i] = int8_t((amplitude * (sin((i * (TWO_PI * cycles)) / samples))) / 2.0);
vImag[i] = 0; //Reset the imaginary values vector for each new frequency
}
/*Serial.println("Data:");
PrintVector(vReal, samples, SCL_TIME);*/
startTime=millis();
FFT.windowing(FFTWindow::Hamming, FFTDirection::Forward); /* Weigh data */
/*Serial.println("Weighed data:");
PrintVector(vReal, samples, SCL_TIME);*/
FFT.compute(FFTDirection::Forward); /* Compute FFT */
/*Serial.println("Computed Real values:");
PrintVector(vReal, samples, SCL_INDEX);
Serial.println("Computed Imaginary values:");
PrintVector(vImag, samples, SCL_INDEX);*/
FFT.complexToMagnitude(); /* Compute magnitudes */
/*Serial.println("Computed magnitudes:");
PrintVector(vReal, (samples >> 1), SCL_FREQUENCY);*/
double x = FFT.majorPeak();
Serial.print(frequency);
Serial.print(": \t\t");
Serial.print(x, 4);
Serial.print("\t\t");
Serial.print(millis()-startTime);
Serial.println(" ms");
// delay(2000); /* Repeat after delay */
}
while(1); /* Run Once */
}
void PrintVector(double *vData, uint16_t bufferSize, uint8_t scaleType)
{
for (uint16_t i = 0; i < bufferSize; i++)
{
double abscissa;
/* Print abscissa value */
switch (scaleType)
{
case SCL_INDEX:
abscissa = (i * 1.0);
break;
case SCL_TIME:
abscissa = ((i * 1.0) / sampling);
break;
case SCL_FREQUENCY:
abscissa = ((i * 1.0 * sampling) / samples);
break;
}
Serial.print(abscissa, 6);
if(scaleType==SCL_FREQUENCY)
Serial.print("Hz");
Serial.print(" ");
Serial.println(vData[i], 4);
}
Serial.println();
}

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/*
Example of use of the FFT libray to compute FFT for a signal sampled through the ADC.
Copyright (C) 2018 Enrique Condés and Ragnar Ranøyen Homb
Copyright (C) 2020 Bim Overbohm (header-only, template, speed improvements)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#include "arduinoFFT.h"
/*
These values can be changed in order to evaluate the functions
*/
#define CHANNEL A0
const uint16_t samples = 64; //This value MUST ALWAYS be a power of 2
const double samplingFrequency = 100; //Hz, must be less than 10000 due to ADC
unsigned int sampling_period_us;
unsigned long microseconds;
/*
These are the input and output vectors
Input vectors receive computed results from FFT
*/
double vReal[samples];
double vImag[samples];
/* Create FFT object */
ArduinoFFT<double> FFT = ArduinoFFT<double>(vReal, vImag, samples, samplingFrequency);
#define SCL_INDEX 0x00
#define SCL_TIME 0x01
#define SCL_FREQUENCY 0x02
#define SCL_PLOT 0x03
void setup()
{
sampling_period_us = round(1000000*(1.0/samplingFrequency));
Serial.begin(115200);
Serial.println("Ready");
}
void loop()
{
/*SAMPLING*/
microseconds = micros();
for(int i=0; i<samples; i++)
{
vReal[i] = analogRead(CHANNEL);
vImag[i] = 0;
while(micros() - microseconds < sampling_period_us){
//empty loop
}
microseconds += sampling_period_us;
}
/* Print the results of the sampling according to time */
Serial.println("Data:");
PrintVector(vReal, samples, SCL_TIME);
FFT.windowing(FFTWindow::Hamming, FFTDirection::Forward); /* Weigh data */
Serial.println("Weighed data:");
PrintVector(vReal, samples, SCL_TIME);
FFT.compute(FFTDirection::Forward); /* Compute FFT */
Serial.println("Computed Real values:");
PrintVector(vReal, samples, SCL_INDEX);
Serial.println("Computed Imaginary values:");
PrintVector(vImag, samples, SCL_INDEX);
FFT.complexToMagnitude(); /* Compute magnitudes */
Serial.println("Computed magnitudes:");
PrintVector(vReal, (samples >> 1), SCL_FREQUENCY);
double x = FFT.majorPeak();
Serial.println(x, 6); //Print out what frequency is the most dominant.
while(1); /* Run Once */
// delay(2000); /* Repeat after delay */
}
void PrintVector(double *vData, uint16_t bufferSize, uint8_t scaleType)
{
for (uint16_t i = 0; i < bufferSize; i++)
{
double abscissa;
/* Print abscissa value */
switch (scaleType)
{
case SCL_INDEX:
abscissa = (i * 1.0);
break;
case SCL_TIME:
abscissa = ((i * 1.0) / samplingFrequency);
break;
case SCL_FREQUENCY:
abscissa = ((i * 1.0 * samplingFrequency) / samples);
break;
}
Serial.print(abscissa, 6);
if(scaleType==SCL_FREQUENCY)
Serial.print("Hz");
Serial.print(" ");
Serial.println(vData[i], 4);
}
Serial.println();
}

110
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/*
Example of use of the FFT libray
Copyright (C) 2018 Enrique Condes
Copyright (C) 2020 Bim Overbohm (header-only, template, speed improvements)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
/*
In this example, the Arduino simulates the sampling of a sinusoidal 1000 Hz
signal with an amplitude of 100, sampled at 5000 Hz. Samples are stored
inside the vReal array. The samples are windowed according to Hamming
function. The FFT is computed using the windowed samples. Then the magnitudes
of each of the frequencies that compose the signal are calculated. Finally,
the frequency spectrum magnitudes are printed. If you use the Arduino IDE
serial plotter, you will see a single spike corresponding to the 1000 Hz
frecuency.
*/
#include "arduinoFFT.h"
/*
These values can be changed in order to evaluate the functions
*/
const uint16_t samples = 64; //This value MUST ALWAYS be a power of 2
const double signalFrequency = 1000;
const double samplingFrequency = 5000;
const uint8_t amplitude = 100;
/*
These are the input and output vectors
Input vectors receive computed results from FFT
*/
double vReal[samples];
double vImag[samples];
ArduinoFFT<double> FFT = ArduinoFFT<double>(vReal, vImag, samples, samplingFrequency);
#define SCL_INDEX 0x00
#define SCL_TIME 0x01
#define SCL_FREQUENCY 0x02
#define SCL_PLOT 0x03
void setup()
{
Serial.begin(115200);
}
void loop()
{
/* Build raw data */
double cycles = (((samples-1) * signalFrequency) / samplingFrequency); //Number of signal cycles that the sampling will read
for (uint16_t i = 0; i < samples; i++)
{
vReal[i] = int8_t((amplitude * (sin((i * (TWO_PI * cycles)) / samples))) / 2.0);/* Build data with positive and negative values*/
//vReal[i] = uint8_t((amplitude * (sin((i * (twoPi * cycles)) / samples) + 1.0)) / 2.0);/* Build data displaced on the Y axis to include only positive values*/
vImag[i] = 0.0; //Imaginary part must be zeroed in case of looping to avoid wrong calculations and overflows
}
FFT.windowing(FFTWindow::Hamming, FFTDirection::Forward); /* Weigh data */
FFT.compute(FFTDirection::Forward); /* Compute FFT */
FFT.complexToMagnitude(); /* Compute magnitudes */
PrintVector(vReal, samples>>1, SCL_PLOT);
double x = FFT.majorPeak();
while(1); /* Run Once */
// delay(2000); /* Repeat after delay */
}
void PrintVector(double *vData, uint16_t bufferSize, uint8_t scaleType)
{
for (uint16_t i = 0; i < bufferSize; i++)
{
double abscissa;
/* Print abscissa value */
switch (scaleType)
{
case SCL_INDEX:
abscissa = (i * 1.0);
break;
case SCL_TIME:
abscissa = ((i * 1.0) / samplingFrequency);
break;
case SCL_FREQUENCY:
abscissa = ((i * 1.0 * samplingFrequency) / samples);
break;
}
if(scaleType!=SCL_PLOT)
{
Serial.print(abscissa, 6);
if(scaleType==SCL_FREQUENCY)
Serial.print("Hz");
Serial.print(" ");
}
Serial.println(vData[i], 4);
}
Serial.println();
}

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/*
Example of use of the FFT libray
Copyright (C) 2014 Enrique Condes
Copyright (C) 2020 Bim Overbohm (header-only, template, speed improvements)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
/*
In this example, the Arduino simulates the sampling of a sinusoidal 1000 Hz
signal with an amplitude of 100, sampled at 5000 Hz. Samples are stored
inside the vReal array. The samples are windowed according to Hamming
function. The FFT is computed using the windowed samples. Then the magnitudes
of each of the frequencies that compose the signal are calculated. Finally,
the frequency with the highest peak is obtained, being that the main frequency
present in the signal. This frequency is printed, along with the magnitude of
the peak.
*/
#include "arduinoFFT.h"
/*
These values can be changed in order to evaluate the functions
*/
const uint16_t samples = 64; //This value MUST ALWAYS be a power of 2
const double signalFrequency = 1000;
const double samplingFrequency = 5000;
const uint8_t amplitude = 100;
/*
These are the input and output vectors
Input vectors receive computed results from FFT
*/
double vReal[samples];
double vImag[samples];
/* Create FFT object */
ArduinoFFT<double> FFT = ArduinoFFT<double>(vReal, vImag, samples, samplingFrequency);
#define SCL_INDEX 0x00
#define SCL_TIME 0x01
#define SCL_FREQUENCY 0x02
#define SCL_PLOT 0x03
void setup()
{
Serial.begin(115200);
Serial.println("Ready");
}
void loop()
{
/* Build raw data */
double cycles = (((samples-1) * signalFrequency) / samplingFrequency); //Number of signal cycles that the sampling will read
for (uint16_t i = 0; i < samples; i++)
{
vReal[i] = int8_t((amplitude * (sin((i * (TWO_PI * cycles)) / samples))) / 2.0);/* Build data with positive and negative values*/
//vReal[i] = uint8_t((amplitude * (sin((i * (twoPi * cycles)) / samples) + 1.0)) / 2.0);/* Build data displaced on the Y axis to include only positive values*/
vImag[i] = 0.0; //Imaginary part must be zeroed in case of looping to avoid wrong calculations and overflows
}
/* Print the results of the simulated sampling according to time */
Serial.println("Data:");
PrintVector(vReal, samples, SCL_TIME);
FFT.windowing(FFTWindow::Hamming, FFTDirection::Forward); /* Weigh data */
Serial.println("Weighed data:");
PrintVector(vReal, samples, SCL_TIME);
FFT.compute(FFTDirection::Forward); /* Compute FFT */
Serial.println("Computed Real values:");
PrintVector(vReal, samples, SCL_INDEX);
Serial.println("Computed Imaginary values:");
PrintVector(vImag, samples, SCL_INDEX);
FFT.complexToMagnitude(); /* Compute magnitudes */
Serial.println("Computed magnitudes:");
PrintVector(vReal, (samples >> 1), SCL_FREQUENCY);
double x;
double v;
FFT.majorPeak(x, v);
Serial.print(x, 6);
Serial.print(", ");
Serial.println(v, 6);
while(1); /* Run Once */
// delay(2000); /* Repeat after delay */
}
void PrintVector(double *vData, uint16_t bufferSize, uint8_t scaleType)
{
for (uint16_t i = 0; i < bufferSize; i++)
{
double abscissa;
/* Print abscissa value */
switch (scaleType)
{
case SCL_INDEX:
abscissa = (i * 1.0);
break;
case SCL_TIME:
abscissa = ((i * 1.0) / samplingFrequency);
break;
case SCL_FREQUENCY:
abscissa = ((i * 1.0 * samplingFrequency) / samples);
break;
}
Serial.print(abscissa, 6);
if(scaleType==SCL_FREQUENCY)
Serial.print("Hz");
Serial.print(" ");
Serial.println(vData[i], 4);
}
Serial.println();
}

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/*
Example of use of the FFT libray to compute FFT for a signal sampled through the ADC
with speedup through different arduinoFFT options. Based on examples/FFT_03/FFT_03.ino
Copyright (C) 2020 Bim Overbohm (header-only, template, speed improvements)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
// There are two speedup options for some of the FFT code:
// Define this to use reciprocal multiplication for division and some more speedups that might decrease precision
//#define FFT_SPEED_OVER_PRECISION
// Define this to use a low-precision square root approximation instead of the regular sqrt() call
// This might only work for specific use cases, but is significantly faster. Only works for ArduinoFFT<float>.
//#define FFT_SQRT_APPROXIMATION
#include "arduinoFFT.h"
/*
These values can be changed in order to evaluate the functions
*/
#define CHANNEL A0
const uint16_t samples = 64; //This value MUST ALWAYS be a power of 2
const float samplingFrequency = 100; //Hz, must be less than 10000 due to ADC
unsigned int sampling_period_us;
unsigned long microseconds;
/*
These are the input and output vectors
Input vectors receive computed results from FFT
*/
float vReal[samples];
float vImag[samples];
/*
Allocate space for FFT window weighing factors, so they are calculated only the first time windowing() is called.
If you don't do this, a lot of calculations are necessary, depending on the window function.
*/
float weighingFactors[samples];
/* Create FFT object with weighing factor storage */
ArduinoFFT<float> FFT = ArduinoFFT<float>(vReal, vImag, samples, samplingFrequency, weighingFactors);
#define SCL_INDEX 0x00
#define SCL_TIME 0x01
#define SCL_FREQUENCY 0x02
#define SCL_PLOT 0x03
void setup()
{
sampling_period_us = round(1000000*(1.0/samplingFrequency));
Serial.begin(115200);
Serial.println("Ready");
}
void loop()
{
/*SAMPLING*/
microseconds = micros();
for(int i=0; i<samples; i++)
{
vReal[i] = analogRead(CHANNEL);
vImag[i] = 0;
while(micros() - microseconds < sampling_period_us){
//empty loop
}
microseconds += sampling_period_us;
}
/* Print the results of the sampling according to time */
Serial.println("Data:");
PrintVector(vReal, samples, SCL_TIME);
FFT.windowing(FFTWindow::Hamming, FFTDirection::Forward); /* Weigh data */
Serial.println("Weighed data:");
PrintVector(vReal, samples, SCL_TIME);
FFT.compute(FFTDirection::Forward); /* Compute FFT */
Serial.println("Computed Real values:");
PrintVector(vReal, samples, SCL_INDEX);
Serial.println("Computed Imaginary values:");
PrintVector(vImag, samples, SCL_INDEX);
FFT.complexToMagnitude(); /* Compute magnitudes */
Serial.println("Computed magnitudes:");
PrintVector(vReal, (samples >> 1), SCL_FREQUENCY);
float x = FFT.majorPeak();
Serial.println(x, 6); //Print out what frequency is the most dominant.
while(1); /* Run Once */
// delay(2000); /* Repeat after delay */
}
void PrintVector(float *vData, uint16_t bufferSize, uint8_t scaleType)
{
for (uint16_t i = 0; i < bufferSize; i++)
{
float abscissa;
/* Print abscissa value */
switch (scaleType)
{
case SCL_INDEX:
abscissa = (i * 1.0);
break;
case SCL_TIME:
abscissa = ((i * 1.0) / samplingFrequency);
break;
case SCL_FREQUENCY:
abscissa = ((i * 1.0 * samplingFrequency) / samples);
break;
}
Serial.print(abscissa, 6);
if(scaleType==SCL_FREQUENCY)
Serial.print("Hz");
Serial.print(" ");
Serial.println(vData[i], 4);
}
Serial.println();
}

674
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GNU GENERAL PUBLIC LICENSE
Version 3, 29 June 2007
Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.
Preamble
The GNU General Public License is a free, copyleft license for
software and other kinds of works.
The licenses for most software and other practical works are designed
to take away your freedom to share and change the works. By contrast,
the GNU General Public License is intended to guarantee your freedom to
share and change all versions of a program--to make sure it remains free
software for all its users. We, the Free Software Foundation, use the
GNU General Public License for most of our software; it applies also to
any other work released this way by its authors. You can apply it to
your programs, too.
When we speak of free software, we are referring to freedom, not
price. Our General Public Licenses are designed to make sure that you
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arduinoFFT
==========
# Fast Fourier Transform for Arduino
This is a fork from https://code.google.com/p/makefurt/ which has been abandoned since 2011.
~~This is a C++ library for Arduino for computing FFT.~~ Now it works both on Arduino and C projects. This is version 2.0 of the library, which has a different [API](#api). See here [how to migrate from 1.x to 2.x](#migrating-from-1x-to-2x).
Tested on Arduino 1.6.11 and 1.8.10.
## Installation on Arduino
Use the Arduino Library Manager to install and keep it updated. Just look for arduinoFFT. Only for Arduino 1.5+
## Manual installation on Arduino
To install this library, just place this entire folder as a subfolder in your Arduino installation. When installed, this library should look like:
`Arduino\libraries\arduinoFTT` (this library's folder)
`Arduino\libraries\arduinoFTT\src\arduinoFTT.h` (the library header file. include this in your project)
`Arduino\libraries\arduinoFTT\keywords.txt` (the syntax coloring file)
`Arduino\libraries\arduinoFTT\Examples` (the examples in the "open" menu)
`Arduino\libraries\arduinoFTT\LICENSE` (GPL license file)
`Arduino\libraries\arduinoFTT\README.md` (this file)
## Building on Arduino
After this library is installed, you just have to start the Arduino application.
You may see a few warning messages as it's built.
To use this library in a sketch, go to the Sketch | Import Library menu and
select arduinoFTT. This will add a corresponding line to the top of your sketch:
`#include <arduinoFTT.h>`
## API
* ```ArduinoFFT(T *vReal, T *vImag, uint_fast16_t samples, T samplingFrequency, T * weighingFactors = nullptr);```
Constructor.
The type `T` can be `float` or `double`. `vReal` and `vImag` are pointers to arrays of real and imaginary data and have to be allocated outside of ArduinoFFT. `samples` is the number of samples in `vReal` and `vImag` and `weighingFactors` (if specified). `samplingFrequency` is the sample frequency of the data. `weighingFactors` can optionally be specified to cache weighing factors for the windowing function. This speeds up repeated calls to **windowing()** significantly. You can deallocate `vReal` and `vImag` after you are done using the library, or only use specific library functions that only need one of those arrays.
```C++
const uint32_t nrOfSamples = 1024;
auto real = new float[nrOfSamples];
auto imag = new float[nrOfSamples];
auto fft = ArduinoFFT<float>(real, imag, nrOfSamples, 10000);
// ... fill real + imag and use it ...
fft.compute();
fft.complexToMagnitude();
delete [] imag;
// ... continue using real and only functions that use real ...
auto peak = fft.majorPeak();
```
* ```~ArduinoFFT()```
Destructor.
* ```void complexToMagnitude() const;```
Convert complex values to their magnitude and store in vReal. Uses vReal and vImag.
* ```void compute(FFTDirection dir) const;```
Calcuates the Fast Fourier Transform. Uses vReal and vImag.
* ```void dcRemoval() const;```
Removes the DC component from the sample data. Uses vReal.
* ```T majorPeak() const;```
Returns the frequency of the biggest spike in the analyzed signal. Uses vReal.
* ```void majorPeak(T &frequency, T &value) const;```
Returns the frequency and the value of the biggest spike in the analyzed signal. Uses vReal.
* ```uint8_t revision() const;```
Returns the library revision.
* ```void setArrays(T *vReal, T *vImag);```
Replace the data array pointers.
* ```void windowing(FFTWindow windowType, FFTDirection dir, bool withCompensation = false);```
Performs a windowing function on the values array. Uses vReal. The possible windowing options are:
* Rectangle
* Hamming
* Hann
* Triangle
* Nuttall
* Blackman
* Blackman_Nuttall
* Blackman_Harris
* Flat_top
* Welch
If `withCompensation` == true, the following compensation factors are used:
* Rectangle: 1.0 * 2.0
* Hamming: 1.8549343278 * 2.0
* Hann: 1.8554726898 * 2.0
* Triangle: 2.0039186079 * 2.0
* Nuttall: 2.8163172034 * 2.0
* Blackman: 2.3673474360 * 2.0
* Blackman Nuttall: 2.7557840395 * 2.0
* Blackman Harris: 2.7929062517 * 2.0
* Flat top: 3.5659039231 * 2.0
* Welch: 1.5029392863 * 2.0
## Special flags
You can define these before including arduinoFFT.h:
* #define FFT_SPEED_OVER_PRECISION
Define this to use reciprocal multiplication for division and some more speedups that might decrease precision.
* #define FFT_SQRT_APPROXIMATION
Define this to use a low-precision square root approximation instead of the regular sqrt() call. This might only work for specific use cases, but is significantly faster. Only works if `T == float`.
See the `FFT_speedup.ino` example in `Examples/FFT_speedup/FFT_speedup.ino`.
# Migrating from 1.x to 2.x
* The function signatures where you could pass in pointers were deprecated and have been removed. Pass in pointers to your real / imaginary array in the ArduinoFFT() constructor. If you have the need to replace those pointers during usage of the library (e.g. to free memory) you can do the following:
```C++
const uint32_t nrOfSamples = 1024;
auto real = new float[nrOfSamples];
auto imag = new float[nrOfSamples];
auto fft = ArduinoFFT<float>(real, imag, nrOfSamples, 10000);
// ... fill real + imag and use it ...
fft.compute();
fft.complexToMagnitude();
delete [] real;
// ... replace vReal in library with imag ...
fft.setArrays(imag, nullptr);
// ... keep doing whatever ...
```
* All function names are camelCase case now (start with lower-case character), e.g. "windowing()" instead of "Windowing()".
## TODO
* Ratio table for windowing function.
* Document windowing functions advantages and disadvantages.
* Optimize usage and arguments.
* Add new windowing functions.
* ~~Spectrum table?~~

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02/22/20 v1.9.2
Fix compilation on AVR systems.
02/22/20 v1.9.1
Add setArrays() function because of issue #32.
Add API migration info to README and improve README.
Use better sqrtf() approximation.
02/19/20 v1.9.0
Remove deprecated API. Consistent renaming of functions to lowercase.
Make template to be able to use float or double type (float brings a ~70% speed increase on ESP32).
Add option to provide cache for window function weighing factors (~50% speed increase on ESP32).
Add some #defines to enable math approximisations to further speed up code (~40% speed increase on ESP32).
01/27/20 v1.5.5
Lookup table for constants c1 and c2 used during FFT comupting. This increases the FFT computing speed in around 5%.
02/10/18 v1.4
Transition version. Minor optimization to functions. New API. Deprecation of old functions.
12/06/18 v1.3
Add support for mbed development boards.
09/04/17 v1.2.3
Finally solves the issue of Arduino IDE not correctly detecting and highlighting the keywords.
09/03/17 v1.2.2
Solves a format issue in keywords.txt that prevented keywords from being detected.
08/28/17 v1.2.1
Fix to issues 6 and 7. Not cleaning the imaginary vector after each cycle leaded to erroneous calculations and could cause buffer overflows.
08/04/17 v1.2
Fix to bug preventing the number of samples to be greater than 128. New logical limit is 32768 samples but it is bound to the RAM on the chip.
05/12/17 v1.1
Fix issue that prevented installation through the Arduino Library Manager interface.
05/11/17 v1.0
Initial commit to Arduino Library Manager.

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#######################################
# Syntax Coloring Map For arduinoFFT
#######################################
#######################################
# Datatypes (KEYWORD1)
#######################################
ArduinoFFT KEYWORD1
FFTDirection KEYWORD1
FFTWindow KEYWORD1
#######################################
# Methods and Functions (KEYWORD2)
#######################################
complexToMagnitude KEYWORD2
compute KEYWORD2
dcRemoval KEYWORD2
windowing KEYWORD2
exponent KEYWORD2
revision KEYWORD2
majorPeak KEYWORD2
setArrays KEYWORD2
#######################################
# Constants (LITERAL1)
#######################################
Forward LITERAL1
Reverse LITERAL1
Rectangle LITERAL1
Hamming LITERAL1
Hann LITERAL1
Triangle LITERAL1
Nuttall LITERAL1
Blackman LITERAL1
Blackman_Nuttall LITERAL1
Blackman_Harris LITERAL1
Flat_top LITERAL1
Welch LITERAL1

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{
"name": "arduinoFFT",
"keywords": "FFT, Fourier, FDT, frequency",
"description": "A library for implementing floating point Fast Fourier Transform calculations.",
"repository":
{
"type": "git",
"url": "https://github.com/kosme/arduinoFFT.git"
},
"authors":
[
{
"name": "Enrique Condes",
"email": "enrique@shapeoko.com",
"maintainer": true
},
{
"name": "Didier Longueville",
"url": "http://www.arduinoos.com/",
"email": "contact@arduinoos.com"
},
{
"name": "Bim Overbohm",
"url": "https://github.com/HorstBaerbel",
"email": "bim.overbohm@googlemail.com"
}
],
"version": "1.9.2",
"frameworks": ["arduino","mbed","espidf"],
"platforms": "*"
}

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name=arduinoFFT
version=1.9.2
author=Enrique Condes <enrique@shapeoko.com>
maintainer=Enrique Condes <enrique@shapeoko.com>
sentence=A library for implementing floating point Fast Fourier Transform calculations on Arduino.
paragraph=With this library you can calculate the frequency of a sampled signal.
category=Data Processing
url=https://github.com/kosme/arduinoFFT
architectures=*
includes=arduinoFFT.h

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/arduinoFFT.h.gch

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/*
FFT library
Copyright (C) 2010 Didier Longueville
Copyright (C) 2014 Enrique Condes
Copyright (C) 2020 Bim Overbohm (header-only, template, speed improvements)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#ifndef ArduinoFFT_h /* Prevent loading library twice */
#define ArduinoFFT_h
#ifdef ARDUINO
#if ARDUINO >= 100
#include "Arduino.h"
#else
#include "WProgram.h" /* This is where the standard Arduino code lies */
#endif
#else
#include <stdlib.h>
#include <stdio.h>
#ifdef __AVR__
#include <avr/io.h>
#include <avr/pgmspace.h>
#endif
#include <math.h>
#include "defs.h"
#include "types.h"
#endif
// Define this to use reciprocal multiplication for division and some more speedups that might decrease precision
//#define FFT_SPEED_OVER_PRECISION
// Define this to use a low-precision square root approximation instead of the regular sqrt() call
// This might only work for specific use cases, but is significantly faster. Only works for ArduinoFFT<float>.
//#define FFT_SQRT_APPROXIMATION
#ifdef FFT_SQRT_APPROXIMATION
#include <type_traits>
#else
#define sqrt_internal sqrtf
#endif
enum class FFTDirection
{
Reverse,
Forward
};
enum class FFTWindow
{
Rectangle, // rectangle (Box car)
Hamming, // hamming
Hann, // hann
Triangle, // triangle (Bartlett)
Nuttall, // nuttall
Blackman, //blackman
Blackman_Nuttall, // blackman nuttall
Blackman_Harris, // blackman harris
Flat_top, // flat top
Welch // welch
};
template <typename T>
class ArduinoFFT
{
public:
// Constructor
ArduinoFFT(T *vReal, T *vImag, uint_fast16_t samples, T samplingFrequency, T *windowWeighingFactors = nullptr)
: _vReal(vReal)
, _vImag(vImag)
, _samples(samples)
#ifdef FFT_SPEED_OVER_PRECISION
, _oneOverSamples(1.0 / samples)
#endif
, _samplingFrequency(samplingFrequency)
, _windowWeighingFactors(windowWeighingFactors)
{
// Calculates the base 2 logarithm of sample count
_power = 0;
while (((samples >> _power) & 1) != 1)
{
_power++;
}
}
// Destructor
~ArduinoFFT()
{
}
// Get library revision
static uint8_t revision()
{
return 0x19;
}
// Replace the data array pointers
void setArrays(T *vReal, T *vImag)
{
_vReal = vReal;
_vImag = vImag;
}
// Computes in-place complex-to-complex FFT
void compute(FFTDirection dir) const
{
// Reverse bits /
uint_fast16_t j = 0;
for (uint_fast16_t i = 0; i < (this->_samples - 1); i++)
{
if (i < j)
{
Swap(this->_vReal[i], this->_vReal[j]);
if (dir == FFTDirection::Reverse)
{
Swap(this->_vImag[i], this->_vImag[j]);
}
}
uint_fast16_t k = (this->_samples >> 1);
while (k <= j)
{
j -= k;
k >>= 1;
}
j += k;
}
// Compute the FFT
#ifdef __AVR__
uint_fast8_t index = 0;
#endif
T c1 = -1.0;
T c2 = 0.0;
uint_fast16_t l2 = 1;
for (uint_fast8_t l = 0; (l < this->_power); l++)
{
uint_fast16_t l1 = l2;
l2 <<= 1;
T u1 = 1.0;
T u2 = 0.0;
for (j = 0; j < l1; j++)
{
for (uint_fast16_t i = j; i < this->_samples; i += l2)
{
uint_fast16_t i1 = i + l1;
T t1 = u1 * this->_vReal[i1] - u2 * this->_vImag[i1];
T t2 = u1 * this->_vImag[i1] + u2 * this->_vReal[i1];
this->_vReal[i1] = this->_vReal[i] - t1;
this->_vImag[i1] = this->_vImag[i] - t2;
this->_vReal[i] += t1;
this->_vImag[i] += t2;
}
T z = ((u1 * c1) - (u2 * c2));
u2 = ((u1 * c2) + (u2 * c1));
u1 = z;
}
#ifdef __AVR__
c2 = pgm_read_float_near(&(_c2[index]));
c1 = pgm_read_float_near(&(_c1[index]));
index++;
#else
T cTemp = 0.5 * c1;
c2 = sqrt_internal(0.5 - cTemp);
c1 = sqrt_internal(0.5 + cTemp);
#endif
c2 = dir == FFTDirection::Forward ? -c2 : c2;
}
// Scaling for reverse transform
if (dir != FFTDirection::Forward)
{
for (uint_fast16_t i = 0; i < this->_samples; i++)
{
#ifdef FFT_SPEED_OVER_PRECISION
this->_vReal[i] *= _oneOverSamples;
this->_vImag[i] *= _oneOverSamples;
#else
this->_vReal[i] /= this->_samples;
this->_vImag[i] /= this->_samples;
#endif
}
}
}
void complexToMagnitude() const
{
// vM is half the size of vReal and vImag
for (uint_fast16_t i = 0; i < this->_samples; i++)
{
this->_vReal[i] = sqrt_internal(sq(this->_vReal[i]) + sq(this->_vImag[i]));
}
}
void dcRemoval() const
{
// calculate the mean of vData
T mean = 0;
for (uint_fast16_t i = 1; i < ((this->_samples >> 1) + 1); i++)
{
mean += this->_vReal[i];
}
mean /= this->_samples;
// Subtract the mean from vData
for (uint_fast16_t i = 1; i < ((this->_samples >> 1) + 1); i++)
{
this->_vReal[i] -= mean;
}
}
void windowing(FFTWindow windowType, FFTDirection dir, bool withCompensation = false)
{
// check if values are already pre-computed for the correct window type and compensation
if (_windowWeighingFactors && _weighingFactorsComputed &&
_weighingFactorsFFTWindow == windowType &&
_weighingFactorsWithCompensation == withCompensation)
{
// yes. values are precomputed
if (dir == FFTDirection::Forward)
{
for (uint_fast16_t i = 0; i < (this->_samples >> 1); i++)
{
this->_vReal[i] *= _windowWeighingFactors[i];
this->_vReal[this->_samples - (i + 1)] *= _windowWeighingFactors[i];
}
}
else
{
for (uint_fast16_t i = 0; i < (this->_samples >> 1); i++)
{
#ifdef FFT_SPEED_OVER_PRECISION
// on many architectures reciprocals and multiplying are much faster than division
T oneOverFactor = 1.0 / _windowWeighingFactors[i];
this->_vReal[i] *= oneOverFactor;
this->_vReal[this->_samples - (i + 1)] *= oneOverFactor;
#else
this->_vReal[i] /= _windowWeighingFactors[i];
this->_vReal[this->_samples - (i + 1)] /= _windowWeighingFactors[i];
#endif
}
}
}
else
{
// no. values need to be pre-computed or applied
T samplesMinusOne = (T(this->_samples) - 1.0);
T compensationFactor = _WindowCompensationFactors[static_cast<uint_fast8_t>(windowType)];
for (uint_fast16_t i = 0; i < (this->_samples >> 1); i++)
{
T indexMinusOne = T(i);
T ratio = (indexMinusOne / samplesMinusOne);
T weighingFactor = 1.0;
// Compute and record weighting factor
switch (windowType)
{
case FFTWindow::Rectangle: // rectangle (box car)
weighingFactor = 1.0;
break;
case FFTWindow::Hamming: // hamming
weighingFactor = 0.54 - (0.46 * cos(TWO_PI * ratio));
break;
case FFTWindow::Hann: // hann
weighingFactor = 0.54 * (1.0 - cos(TWO_PI * ratio));
break;
case FFTWindow::Triangle: // triangle (Bartlett)
weighingFactor = 1.0 - ((2.0 * abs(indexMinusOne - (samplesMinusOne / 2.0))) / samplesMinusOne);
break;
case FFTWindow::Nuttall: // nuttall
weighingFactor = 0.355768 - (0.487396 * (cos(TWO_PI * ratio))) + (0.144232 * (cos(FOUR_PI * ratio))) - (0.012604 * (cos(SIX_PI * ratio)));
break;
case FFTWindow::Blackman: // blackman
weighingFactor = 0.42323 - (0.49755 * (cos(TWO_PI * ratio))) + (0.07922 * (cos(FOUR_PI * ratio)));
break;
case FFTWindow::Blackman_Nuttall: // blackman nuttall
weighingFactor = 0.3635819 - (0.4891775 * (cos(TWO_PI * ratio))) + (0.1365995 * (cos(FOUR_PI * ratio))) - (0.0106411 * (cos(SIX_PI * ratio)));
break;
case FFTWindow::Blackman_Harris: // blackman harris
weighingFactor = 0.35875 - (0.48829 * (cos(TWO_PI * ratio))) + (0.14128 * (cos(FOUR_PI * ratio))) - (0.01168 * (cos(SIX_PI * ratio)));
break;
case FFTWindow::Flat_top: // flat top
weighingFactor = 0.2810639 - (0.5208972 * cos(TWO_PI * ratio)) + (0.1980399 * cos(FOUR_PI * ratio));
break;
case FFTWindow::Welch: // welch
weighingFactor = 1.0 - sq((indexMinusOne - samplesMinusOne / 2.0) / (samplesMinusOne / 2.0));
break;
}
if (withCompensation)
{
weighingFactor *= compensationFactor;
}
if (_windowWeighingFactors)
{
_windowWeighingFactors[i] = weighingFactor;
}
if (dir == FFTDirection::Forward)
{
this->_vReal[i] *= weighingFactor;
this->_vReal[this->_samples - (i + 1)] *= weighingFactor;
}
else
{
#ifdef FFT_SPEED_OVER_PRECISION
// on many architectures reciprocals and multiplying are much faster than division
T oneOverFactor = 1.0 / weighingFactor;
this->_vReal[i] *= oneOverFactor;
this->_vReal[this->_samples - (i + 1)] *= oneOverFactor;
#else
this->_vReal[i] /= weighingFactor;
this->_vReal[this->_samples - (i + 1)] /= weighingFactor;
#endif
}
}
// mark cached values as pre-computed
_weighingFactorsFFTWindow = windowType;
_weighingFactorsWithCompensation = withCompensation;
_weighingFactorsComputed = true;
}
}
T majorPeak() const
{
T maxY = 0;
uint_fast16_t IndexOfMaxY = 0;
//If sampling_frequency = 2 * max_frequency in signal,
//value would be stored at position samples/2
for (uint_fast16_t i = 1; i < ((this->_samples >> 1) + 1); i++)
{
if ((this->_vReal[i - 1] < this->_vReal[i]) && (this->_vReal[i] > this->_vReal[i + 1]))
{
if (this->_vReal[i] > maxY)
{
maxY = this->_vReal[i];
IndexOfMaxY = i;
}
}
}
T delta = 0.5 * ((this->_vReal[IndexOfMaxY - 1] - this->_vReal[IndexOfMaxY + 1]) / (this->_vReal[IndexOfMaxY - 1] - (2.0 * this->_vReal[IndexOfMaxY]) + this->_vReal[IndexOfMaxY + 1]));
T interpolatedX = ((IndexOfMaxY + delta) * this->_samplingFrequency) / (this->_samples - 1);
if (IndexOfMaxY == (this->_samples >> 1))
{
//To improve calculation on edge values
interpolatedX = ((IndexOfMaxY + delta) * this->_samplingFrequency) / (this->_samples);
}
// returned value: interpolated frequency peak apex
return interpolatedX;
}
void majorPeak(T &frequency, T &value) const
{
T maxY = 0;
uint_fast16_t IndexOfMaxY = 0;
//If sampling_frequency = 2 * max_frequency in signal,
//value would be stored at position samples/2
for (uint_fast16_t i = 1; i < ((this->_samples >> 1) + 1); i++)
{
if ((this->_vReal[i - 1] < this->_vReal[i]) && (this->_vReal[i] > this->_vReal[i + 1]))
{
if (this->_vReal[i] > maxY)
{
maxY = this->_vReal[i];
IndexOfMaxY = i;
}
}
}
T delta = 0.5 * ((this->_vReal[IndexOfMaxY - 1] - this->_vReal[IndexOfMaxY + 1]) / (this->_vReal[IndexOfMaxY - 1] - (2.0 * this->_vReal[IndexOfMaxY]) + this->_vReal[IndexOfMaxY + 1]));
T interpolatedX = ((IndexOfMaxY + delta) * this->_samplingFrequency) / (this->_samples - 1);
if (IndexOfMaxY == (this->_samples >> 1))
{
//To improve calculation on edge values
interpolatedX = ((IndexOfMaxY + delta) * this->_samplingFrequency) / (this->_samples);
}
// returned value: interpolated frequency peak apex
frequency = interpolatedX;
value = abs(this->_vReal[IndexOfMaxY - 1] - (2.0 * this->_vReal[IndexOfMaxY]) + this->_vReal[IndexOfMaxY + 1]);
}
private:
#ifdef __AVR__
static const float _c1[] PROGMEM;
static const float _c2[] PROGMEM;
#endif
static const T _WindowCompensationFactors[10];
// Mathematial constants
#ifndef TWO_PI
static constexpr T TWO_PI = 6.28318531; // might already be defined in Arduino.h
#endif
static constexpr T FOUR_PI = 12.56637061;
static constexpr T SIX_PI = 18.84955593;
static inline void Swap(T &x, T &y)
{
T temp = x;
x = y;
y = temp;
}
#ifdef FFT_SQRT_APPROXIMATION
// Fast inverse square root aka "Quake 3 fast inverse square root", multiplied by x.
// Uses one iteration of Halley's method for precision.
// See: https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Iterative_methods_for_reciprocal_square_roots
// And: https://github.com/HorstBaerbel/approx
template <typename V = T>
static inline V sqrt_internal(typename std::enable_if<std::is_same<V, float>::value, V>::type x)
{
union // get bits for float value
{
float x;
int32_t i;
} u;
u.x = x;
u.i = 0x5f375a86 - (u.i >> 1); // gives initial guess y0.
float xu = x * u.x;
float xu2 = xu * u.x;
u.x = (0.125 * 3.0) * xu * (5.0 - xu2 * ((10.0 / 3.0) - xu2)); // Halley's method, repeating increases accuracy
return u.x;
}
template <typename V = T>
static inline V sqrt_internal(typename std::enable_if<std::is_same<V, double>::value, V>::type x)
{
// According to HosrtBaerbel, on the ESP32 the approximation is not faster, so we use the standard function
#ifdef ESP32
return sqrt(x);
#else
union // get bits for float value
{
double x;
int64_t i;
} u;
u.x = x;
u.i = 0x5fe6ec85e7de30da - (u.i >> 1); // gives initial guess y0.
double xu = x * u.x;
double xu2 = xu * u.x;
u.x = (0.125 * 3.0) * xu * (5.0 - xu2 * ((10.0 / 3.0) - xu2)); // Halley's method, repeating increases accuracy
return u.x;
#endif
}
#endif
/* Variables */
T *_vReal = nullptr;
T *_vImag = nullptr;
uint_fast16_t _samples = 0;
#ifdef FFT_SPEED_OVER_PRECISION
T _oneOverSamples = 0.0;
#endif
T _samplingFrequency = 0;
T *_windowWeighingFactors = nullptr;
FFTWindow _weighingFactorsFFTWindow;
bool _weighingFactorsWithCompensation = false;
bool _weighingFactorsComputed = false;
uint_fast8_t _power = 0;
};
#ifdef __AVR__
template <typename T>
const float ArduinoFFT<T>::_c1[] PROGMEM = {
0.0000000000, 0.7071067812, 0.9238795325, 0.9807852804,
0.9951847267, 0.9987954562, 0.9996988187, 0.9999247018,
0.9999811753, 0.9999952938, 0.9999988235, 0.9999997059,
0.9999999265, 0.9999999816, 0.9999999954, 0.9999999989,
0.9999999997};
template <typename T>
const float ArduinoFFT<T>::_c2[] PROGMEM = {
1.0000000000, 0.7071067812, 0.3826834324, 0.1950903220,
0.0980171403, 0.0490676743, 0.0245412285, 0.0122715383,
0.0061358846, 0.0030679568, 0.0015339802, 0.0007669903,
0.0003834952, 0.0001917476, 0.0000958738, 0.0000479369,
0.0000239684};
#endif
template <typename T>
const T ArduinoFFT<T>::_WindowCompensationFactors[10] = {
1.0000000000 * 2.0, // rectangle (Box car)
1.8549343278 * 2.0, // hamming
1.8554726898 * 2.0, // hann
2.0039186079 * 2.0, // triangle (Bartlett)
2.8163172034 * 2.0, // nuttall
2.3673474360 * 2.0, // blackman
2.7557840395 * 2.0, // blackman nuttall
2.7929062517 * 2.0, // blackman harris
3.5659039231 * 2.0, // flat top
1.5029392863 * 2.0 // welch
};
#endif

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/*! \file avrlibdefs.h \brief AVRlib global defines and macros. */
//*****************************************************************************
//
// File Name : 'avrlibdefs.h'
// Title : AVRlib global defines and macros include file
// Author : Pascal Stang
// Created : 7/12/2001
// Revised : 9/30/2002
// Version : 1.1
// Target MCU : Atmel AVR series
// Editor Tabs : 4
//
// Description : This include file is designed to contain items useful to all
// code files and projects, regardless of specific implementation.
//
// This code is distributed under the GNU Public License
// which can be found at http://www.gnu.org/licenses/gpl.txt
//
//*****************************************************************************
#ifndef AVRLIBDEFS_H
#define AVRLIBDEFS_H
//#define F_CPU 4000000
#define MEM_TYPE 1
// Code compatibility to new AVR-libc
// outb(), inb(), inw(), outw(), BV(), sbi(), cbi(), sei(), cli()
#ifndef outb
#define outb(addr, data) addr = (data)
#endif
#ifndef inb
#define inb(addr) (addr)
#endif
#ifndef outw
#define outw(addr, data) addr = (data)
#endif
#ifndef inw
#define inw(addr) (addr)
#endif
#ifndef BV
#define BV(bit) (1<<(bit))
#endif
//#ifndef cbi
// #define cbi(reg,bit) reg &= ~(BV(bit))
//#endif
//#ifndef sbi
// #define sbi(reg,bit) reg |= (BV(bit))
//#endif
#ifndef cli
#define cli() __asm__ __volatile__ ("cli" ::)
#endif
#ifndef sei
#define sei() __asm__ __volatile__ ("sei" ::)
#endif
// support for individual port pin naming in the mega128
// see port128.h for details
#ifdef __AVR_ATmega128__
// not currently necessary due to inclusion
// of these defines in newest AVR-GCC
// do a quick test to see if include is needed
#ifndef PD0
//#include "port128.h"
#endif
#endif
// use this for packed structures
// (this is seldom necessary on an 8-bit architecture like AVR,
// but can assist in code portability to AVR)
#define GNUC_PACKED __attribute__((packed))
// port address helpers
#define DDR(x) ((x)-1) // address of data direction register of port x
#define PIN(x) ((x)-2) // address of input register of port x
// MIN/MAX/ABS macros
#define MIN(a,b) ((a<b)?(a):(b))
#define MAX(a,b) ((a>b)?(a):(b))
#define ABS(x) ((x>0)?(x):(-x))
// constants
#define PI 3.14159265359
//Math
#define sq(x) ((x)*(x))
#define constrain(amt,low,high) ((amt)<(low)?(low):((amt)>(high)?(high):(amt)))
#endif

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//useful things to include in code
#ifndef TYPES_H
#define TYPES_H
#ifndef WIN32
// true/false defines
#define FALSE 0
#define TRUE -1
#endif
// datatype definitions macros
typedef unsigned char u08;
typedef signed char s08;
typedef unsigned short u16;
typedef signed short s16;
typedef unsigned long u32;
typedef signed long s32;
typedef unsigned long long u64;
typedef signed long long s64;
// #ifndef __AVR__
#ifdef __MBED__
// use inttypes.h instead
// C99 standard integer type definitions
typedef unsigned char uint8_t;
typedef signed char int8_t;
typedef unsigned short uint16_t;
typedef signed short int16_t;
/*typedef unsigned long uint32_t;
typedef signed long int32_t;
typedef unsigned long uint64_t;
typedef signed long int64_t;
*/
#endif
// maximum value that can be held
// by unsigned data types (8,16,32bits)
#define MAX_U08 255
#define MAX_U16 65535
#define MAX_U32 4294967295
// maximum values that can be held
// by signed data types (8,16,32bits)
#define MIN_S08 -128
#define MAX_S08 127
#define MIN_S16 -32768
#define MAX_S16 32767
#define MIN_S32 -2147483648
#define MAX_S32 2147483647
#ifndef WIN32
// more type redefinitions
typedef unsigned char BOOL;
typedef unsigned char BYTE;
typedef unsigned int WORD;
typedef unsigned long DWORD;
typedef unsigned char UCHAR;
typedef unsigned int UINT;
typedef unsigned short USHORT;
typedef unsigned long ULONG;
typedef char CHAR;
typedef int INT;
typedef long LONG;
#endif
#endif