psd function

PsdResult psd(List<double> data, double fs)

Compute the Power Spectral Density

This method computes the power spectral density and the vector of normalized frequencies of the given real signal like matlab. Uses this simple algorithm:

  N = length(x);
  xdft = fft(detrend(x));
  xdft = xdft(1:N/2+1);
  psdx = (1/(Fs*N)) * abs(xdft).^2;
  psdx(2:end-1) = 2*psdx(2:end-1);
  freq = 0:(Fs)/length(x):Fs/2;

data: List of double with the signal to compute fs: sample rate of the signal

Implementation

PsdResult psd(List<double> data, double fs) {
  assert(data.isNotEmpty, "Input data must not be empty");
  assert(fs > 0, "Fs must be greather than 0");

  final n = data.length;
  // Compute the DFT of the real signal
  var dft = rfft(detrend(data));

  // Compute the power spectral from the DFT
  var psd = signalTimesNum(pow(abs(dft), 2), (1 / (fs * n)));
  // Double the value of each elements except the first and the last
  for (var i = 1; i < psd.length - 1; i++) {
    psd[i] = 2 * psd[i];
  }

  // Compute the normalized frequency vector
  final freq = linspace(0, (fs / 2), num: psd.length, endpoint: false);

  return PsdResult(psd, freq);
}