Concepts

Frequency range

Frequency range for the PSD estimate can one of ‘onesided’, ‘twosided’, ‘centered’. The default is ‘onesided’ for real-valued signals and ‘twosided’ for complex signals.

More details follows this convention:

  • ‘onesided’: returns the one-sided PSD estimate of a real-valued input signal, x. If NFFT is even, PSD has length NFFT/2 + 1 over the interval [0,pi]. If NFFT is odd, the length of PSD is (NFFT+1)/2 and the interval is [0, pi)

  • ‘twosided’ returns the two-sided PSD estimate for either real or complex values. PSD has the length NFFT and is computed over the interval [0,2pi).

  • ‘centered’ returns the centered two-sided PSD estimate for either real or complex values. PSD has length NFFT and is computed over (-pi,pi] for even length NFFT and (-pi,pi] for odd length NFFT.

Padding

NFFT is used to compute the fft with NFFT points. If the data is shorter, the data is padded with zeros so that the frequency signal has a length equal to NFFT. The PSD’s length is not equal to NFFT (see above).

PSD length for real data case

N = 8; FFT gives X0, X1,X2,X3, XN/2, X3,X2,X1 –> PSD length=2+6=5=NFFT/2+1 N = 9; FFT gives X0, X1,X2,X3, X4,X4, X3,X2,X1 –> PSD length=1+3+1=5=(NFFT+1)/2

if one sets the psd, the NFFT is set manually to 2+ (N - 2) * 2 if one sets the psd, we assume that the original data is even.