FFT truncation

[v***@gmail.com]

Supposed that I'm only interested in the lowest 100 frequencies of a
very large time series. How would I do it in Matlab? I couldn't find
such algorithm on the internet.

Thanks

[Srikanth]

The length of the time sequence dictates the resolution of the
frequencies in the fft - if I choose a 100 sample window, the
resolution would be F/100. What I think you want is to limit the
frequencies for which the fft is calculated. Maybe fft(x,size) would
work for this...

[Dong Ta]

As I understand the Cooley-Tukey algorithm. It computes the spectrum for
each frequency independently with the computational cost log(n), doesn't
it? If so, given a set of m frequencies, can we exact the information of
those m frequencies (from the whole time series) in m*log(n)?

Thanks.

Post by Srikanth
The length of the time sequence dictates the resolution of the
frequencies in the fft - if I choose a 100 sample window, the
resolution would be F/100. What I think you want is to limit the
frequencies for which the fft is calculated. Maybe fft(x,size) would
work for this...

[Bruno Luong]

Post by Dong Ta
As I understand the Cooley-Tukey algorithm. It computes

the spectrum for

Post by Dong Ta
each frequency independently with the computational cost

log(n), doesn't

Post by Dong Ta
it?

I don't think so if you take each frequency separately. When
you do a simple scan of n data points, you already have a
complexity of n.

Bruno

[Bruno Luong]

Post by v***@gmail.com
Supposed that I'm only interested in the lowest 100

frequencies of a

Post by v***@gmail.com
very large time series. How would I do it in Matlab? I

couldn't find

Post by v***@gmail.com
such algorithm on the internet.

Simply undersampling your signal vector. i.e., use fft on
signale(1:n:end), n is apropriate number.

Bruno

[Srikanth]

Post by Bruno Luong
Simply undersampling your signal vector. i.e., use fft on
signale(1:n:end), n is apropriate number.
Bruno

Hi
Could you explain that? I haven't figured out how fft on a downsampled
version would work. If the original data is at 16khz, and you drop
alternate samples, the fft would give you a range 0-8khz (step size
depending on the length of the fft). But if you downsample a lot (say,
to limit 16khz to 1khz), you end up causing aliasing, right? Maybe I'm
missing something here...
Srikanth

[Bruno Luong]

You could do several fft on shifted downsampling vectors,
then combine the results.

Properties of fft on downsampling, shifting, etc... are
pretty wellknown, I'm sure you can find somewhere a good
book that explains it well.

Bruno

[Tom Bryan]

Post by v***@gmail.com
Supposed that I'm only interested in the lowest 100 frequencies of a
very large time series. How would I do it in Matlab? I couldn't find
such algorithm on the internet.
Thanks

If you have Signal Processing Toolbox, you can use goertzel:

help goertzel
GOERTZEL Second-order Goertzel algorithm.
GOERTZEL(X,INDVEC) computes the discrete Fourier transform (DFT)
of X at indices contained in the vector INDVEC, using the
second-order Goertzel algorithm. The indices must be integer values
from 1 to N where N is the length of the first non-singleton dimension.
If empty or omitted, INDVEC is assumed to be 1:N.

GOERTZEL(X,[],DIM) or GOERTZEL(X,INDVEC,DIM) computes the DFT along
the dimension DIM.

In general, GOERTZEL is slower than FFT when computing all the possible
DFT indices, but is most useful when X is a long vector and the DFT
computation is required for only a subset of indices less than
log2(length(X)). Indices 1:length(X) correspond to the frequency span
[0, 2*pi) radians.

EXAMPLE:
% Resolve the 1.24 kHz and 1.26 kHz components in the following
% noisy cosine which also has a 10 kHz component.
Fs = 32e3; t = 0:1/Fs:2.96;
x = cos(2*pi*t*10e3)+cos(2*pi*t*1.24e3)+cos(2*pi*t*1.26e3)...
+ randn(size(t));

N = (length(x)+1)/2;
f = (Fs/2)/N*(0:N-1); % Generate frequency vector
indxs = find(f>1.2e3 & f<1.3e3); % Find frequencies of interest
X = goertzel(x,indxs);

hms = dspdata.msspectrum((abs(X)/length(X)).^2,f(indxs),'Fs',Fs);
plot(hms); % Plot the mean-square spectrum.