Мне трудно написать код, который отбирает сигнал (на выводе A0) и выполняет мгновенную перекрестную корреляцию в реальном времени с другим известным сигналом (который сохраняется во флэш-памяти Arduino Uno).
Моя проблема в том, что мой код (мое уравнение) включает в себя множество циклов, из-за чего Arduino сложно делать это в реальном времени и сразу после выборки сигнала (используя ISR (TIMER1_COMPA_vect)).
Есть ли идея, как реализовать взаимную корреляцию, чтобы на каждую выборку не уходило много времени?
Уравнение взаимной корреляции: 
для протокола, вот что я уже сделал:
#define NUM_OF_SAMPLES 64
#define NUM_OF_ETALONS 6
const double* const Etalon_Signals[NUM_OF_ETALONS] PROGMEM = {sinWave1, sinWave2, sinWave3, rectWave4, rectWave5, triWave6};
const double Etalon_Signals_Mean[NUM_OF_ETALONS] PROGMEM = {sinWaveMean1, sinWaveMean2, sinWaveMean3, rectWaveMean4, rectWaveMean5, triWaveMean6};
const double Etalon_Signals_Variance[NUM_OF_ETALONS] PROGMEM = {sinWaveVariance1, sinWaveVariance2, sinWaveVariance3, rectWaveVariance4, rectWaveVariance5, triWaveVariance6};
//-------------- SAMPLED SIGNAL ---------------------
volatile double SignalSamples[NUM_OF_SAMPLES];
volatile int idx = 0;
//-------------- CORRELATION VARS -------------------
// Correlations[NUM_OF_ETALONS] - array of 6 values which calculate the correlation for particular 'd' (delay) value.
// MaxCorrelationValues[NUM_OF_ETALONS] - array which holds the maximum value of a praticular Etalon signal,
// which I use later to decide which wave is most simmilar to the sampled wave.
// MaxCorrelationValues[k] = the maximum correlation value out of all the 'd' iterations,
// of Etalon wave number k (look at the formula for better understanding).
// MostSimillarCorrVal - Holds the Maximum value of correlation out of 6 Etalons (every Etalon has a maximum correlation point out of d correlations)
// MostSimillarCorrVal will hold the Absulote Maximum out of the 6 Etalons.
// SignalSamplesVar - Variance of the Sampled Signal -> Eq: (sum(y[i] - my))
// SignalSamplesMean - Mean of the Sampled Signal -> Eq: (my)
// counter - used for smart Circular scanning over the ring buffer "SignalSamples".
// maxCorrWave - Holds the 2^index of the most simmilar wave out of the etalons.
// SignalSamplesVarTemp - a particular substraction of the signal with its mean value -> Eq: (numerator) -> (y(i-d)-my).
volatile double Correlations[NUM_OF_ETALONS] = {0}, MaxCorrelationValues[NUM_OF_ETALONS] = {0}, MostSimillarCorrVal = 0;
volatile double SignalSamplesVar = 0, SignalSamplesMean = 0;
volatile int counter = 0, maxCorrWave = 0;
double EtalonVarianceVal[NUM_OF_ETALONS], SignalSamplesVarTemp;
void setup()
{
SetTimer1CTCforFreq(SAMPLING_FREQUENCY);
DDRB |= WAVE_1 | WAVE_2 | WAVE_3 | WAVE_4 | WAVE_5 | WAVE_6;
pinMode(A0, INPUT);
for(int i = 0; i<NUM_OF_ETALONS;i++)
EtalonVarianceVal[i] = pgm_read_float(&Etalon_Signals_Variance[i]);
}
ISR(TIMER1_COMPA_vect)
{
SignalSamplesVar -= (SignalSamples[idx] - SignalSamplesMean)*(SignalSamples[idx] - SignalSamplesMean);
SignalSamplesMean = SignalSamplesMean * NUM_OF_SAMPLES - SignalSamples[idx];
SignalSamples[idx] = analogRead(ANALOG_INPUT_PIN); // sampling
SignalSamplesMean = (SignalSamplesMean + SignalSamples[idx])/NUM_OF_SAMPLES;
SignalSamplesVar += (SignalSamples[idx] - SignalSamplesMean)*(SignalSamples[idx] - SignalSamplesMean);
// SignalSamplesMean = Mean(SignalSamples, NUM_OF_SAMPLES); // Mean of current state calculations.
// SignalSamplesVar = VarianceSquared(SignalSamples, NUM_OF_SAMPLES); // Variance of current state calculations.
for(int delay = -NUM_OF_SAMPLES; delay < NUM_OF_SAMPLES; delay++) // "shifting" array loop.
{
counter = 0; // counter - an index which runs on SignalSamples array.
while(counter < NUM_OF_SAMPLES) // loop running on the SignalSamples in circle.
{
// SignalSamplesVarTemp = Signal's "Variance" semi-calculation.
SignalSamplesVarTemp = SignalSamples[(idx + counter - delay)%NUM_OF_SAMPLES] - SignalSamplesMean;
// Calculating all Cross Correlations with all the six Etalons.
for(int k = 0; k < NUM_OF_ETALONS; k++)
Correlations[k] += pgm_read_float(&Etalon_Signals[k][counter]) * SignalSamplesVarTemp; // eMean = 0 always.
counter++;
}
for(int k = 0; k < NUM_OF_ETALONS; k++) // updating all the Etalons.
{
Correlations[k] *= Correlations[k];
Correlations[k] /= SignalSamplesVar * pgm_read_float(&EtalonVarianceVal[k]); // The Correlation for particular delay.
// MaxCorrelationValues[k] - Max value of the correlation with Etalon[k].
// At the end we compare which etalon got the biggest correlation value (which is positive).
MaxCorrelationValues[k] = MaxCorrelationValues[k] < Correlations[k] ? Correlations[k] : MaxCorrelationValues[k];
}
}
for(int k = 0; k < NUM_OF_ETALONS; k++)
{
if(MaxCorrelationValues[k] > MostSimillarCorrVal)
{
MostSimillarCorrVal = Correlations[k];
maxCorrWave = k;
}
}
PORTB = 1 << maxCorrWave;
idx = (idx+1)%NUM_OF_SAMPLES;
}
Спасибо тем, кто помогает
