Refactored Ppg for frequency based algorithm. (#1486)

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).

6 files changed, 721 insertions, 0 deletions

diff --git a/src/libs/arduinoFFT-develop/Examples/FFT_01/FFT_01.ino b/src/libs/arduinoFFT-develop/Examples/FFT_01/FFT_01.ino
new file mode 100644
index 00000000..22b5024a
--- /dev/null
+++ b/src/libs/arduinoFFT-develop/Examples/FFT_01/FFT_01.ino
@@ -0,0 +1,119 @@
+/*
+
+	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();
+}
diff --git a/src/libs/arduinoFFT-develop/Examples/FFT_02/FFT_02.ino b/src/libs/arduinoFFT-develop/Examples/FFT_02/FFT_02.ino
new file mode 100644
index 00000000..7164dab1
--- /dev/null
+++ b/src/libs/arduinoFFT-develop/Examples/FFT_02/FFT_02.ino
@@ -0,0 +1,125 @@
+/*
+
+	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();
+}
diff --git a/src/libs/arduinoFFT-develop/Examples/FFT_03/FFT_03.ino b/src/libs/arduinoFFT-develop/Examples/FFT_03/FFT_03.ino
new file mode 100644
index 00000000..ee2b2946
--- /dev/null
+++ b/src/libs/arduinoFFT-develop/Examples/FFT_03/FFT_03.ino
@@ -0,0 +1,114 @@
+/*
+
+	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();
+}
diff --git a/src/libs/arduinoFFT-develop/Examples/FFT_04/FFT_04.ino b/src/libs/arduinoFFT-develop/Examples/FFT_04/FFT_04.ino
new file mode 100644
index 00000000..b125991d
--- /dev/null
+++ b/src/libs/arduinoFFT-develop/Examples/FFT_04/FFT_04.ino
@@ -0,0 +1,110 @@
+/*
+
+	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();
+}
diff --git a/src/libs/arduinoFFT-develop/Examples/FFT_05/FFT_05.ino b/src/libs/arduinoFFT-develop/Examples/FFT_05/FFT_05.ino
new file mode 100644
index 00000000..a6f4df7a
--- /dev/null
+++ b/src/libs/arduinoFFT-develop/Examples/FFT_05/FFT_05.ino
@@ -0,0 +1,124 @@
+/*
+
+	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();
+}
diff --git a/src/libs/arduinoFFT-develop/Examples/FFT_speedup/FFT_speedup.ino b/src/libs/arduinoFFT-develop/Examples/FFT_speedup/FFT_speedup.ino
new file mode 100644
index 00000000..a059a170
--- /dev/null
+++ b/src/libs/arduinoFFT-develop/Examples/FFT_speedup/FFT_speedup.ino
@@ -0,0 +1,129 @@
+/*
+
+	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();
+}