Matlab - fourier transform of random signal

Author

fourier transform of random signal

Ramsey

2006-10-31, 7:10 pm

I would like to take the Fourier transform of a random signal with
each data point taken every 9.5 milliseconds for a total of 256 data
points. I think I should use the fft function. But how do I figure
out the x-axis units with this function?

Thanks

NZTideMan

2006-10-31, 7:11 pm

Ramsey wrote:
> I would like to take the Fourier transform of a random signal with
> each data point taken every 9.5 milliseconds for a total of 256 data
> points. I think I should use the fft function. But how do I figure
> out the x-axis units with this function?
>
> Thanks

It's irrelevant because for a truly random signal (white noise), the
spectrum is flat, i.e., a straight horizontal line.

Randy Poe

2006-10-31, 7:11 pm

NZTideMan wrote:
> Ramsey wrote:
>
> It's irrelevant because for a truly random signal (white noise), the
> spectrum is flat, i.e., a straight horizontal line.

But for a finite-length signal, it can't be truly white.

To the OP: Take a look at the calculation of the frequency axis
in the example under "doc fft".

The frequency spacing is 1/T where T is the total length of
your data sample (256*0.0095 sec in your case). The first
frequency is 0. The final frequency, the 256-th point is
at (255/256)*(1/dT) where dT = 0.0095 sec.

If you plot the magnitude of your FFT, you will see a point of
symmetry at point number 129. This is the Nyquist frequency,
the highest frequency measurable at this sampling rate.

Check out FFTSHIFT. That might be a more convenient way
to view your data.

- Randy

NZTideMan

2006-10-31, 7:11 pm

Randy Poe wrote:
> NZTideMan wrote:
>
> But for a finite-length signal, it can't be truly white.

Yes, but what is the significance of its variability with frequency?
It means nothing, IMHO.

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