question about normalization in mtfftc.m and mtspectrumc.m

[David Groppe]

Reply
from David Groppe <dgr...@cogsci.ucsd.edu>
to webm...@chronux.org
date Sat, Jan 1, 2011 at 11:24 AM
subject question about normalization in mtfftc.m and mtspectrumc.m
mailed-by gmail.com
hide details 11:24 AM (20 minutes ago)
Hi Chronuxitarians,
I have a question about the normalization performed by Chronux
when estimating the power spectra for continuous data via the function
mtspectrumc.m. mtspectrumc.m calls mtfftc.m to perform an FFT on a
set of continuous data. mtfftc.m normalizes the output of fft.m via
the sampling rate:

J=fft(data_proj,nfft)/Fs; % fft of projected data <-line 23 of
mtfftc.m

Then mtspectrumc.m computes the power spectrum as follows:
S=squeeze(mean(conj(J).*J,2)); <-line 63 of mtspectrumc.m

Normalizing by the sampling rate in mtfftc.m makes no sense to me.
Shouldn't you be normalizing by the number of data points to make the
sum of spectral power equal to the sum of squares of the time series
(i.e., to satisfy Parseval's theorem)? In other words, shouldn't line
23 of mtfftc.m be:
J=fft(data_proj,nfft)/nfft;

Thanks very much for your time.
-David Groppe