Hi,
> From: Ariel Rokem
> However - two elements are off by a factor of approximately 2 - the
> very first element and the very last. ... Does anyone have any idea
> why this would be the case?
>From a quick look at the mlab code, it looks like a bug in
mlab._spectral_helper.
The default spectrum is 'onesided' (same as for Matlab's cpsd). A
single-sided spectrum of a real signal has double the magnitude of a
double-sided spectrum, *except* at the origin (frequency index n = 0)
and Nyquist frequency (n = NFFT / 2), where it is the *same* as the
double-sided one [1]_.
In the mlab code, all the spectral values are simply scaled by a
factor of 2 (among other factors) in this line:
# Scale the spectrum by the norm of the window to compensate for
# windowing loss; see Bendat & Piersol Sec 11.5.2. Also include
# scaling factors for one-sided densities and dividing by the sampling
# frequency, if desired.
Pxy *= scaling_factor / (np.abs(windowVals)**2).sum()
This should be easy to fix (although the function probably needs a
little rework).
Regards,
Ludwig
Quick reference from my bookshelf:
---
.. [1] W. L. Briggs, V. E. Henson, "The DFT: An Owner's Manual for the
Discrete Fourier Transform," Section 1.3, Problem 6 (a), p. 13.
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