how to using FFT to study the power spectrum?

get a power from fft

Hello:

I have struggled for days on this problem:
I have a sequency of time points. Assume they are correponding to the zero-cross time points of a sine-like
waveform. From this wave, I can approximately re-construct some sample points by assuming a sine wave connecting two adjacent time points.

Then I use FFT to study its power spectrum. Assume the center frequency is F_c, and my data actually should has small fructuation around F_c. Therefore, I am very interested in the close-in range of F_c on the power spectrum.

Does this mean I have to use a very long window to get high resolution?

I use my method to deal with an ideal sample sequency from an ideal sine wave of F, I found that the generated power spectrum is far from ideal: there are quite some energy on other frequencies than F, and the attenuation from F is not fast. The ideal case is an impulse, but the plot is far from an impulse.

Any idea on how to improve the way of using FFT? Thank you very very much My goal is to see an near-impulse response for an ideal sine wave sample points sequence and does not suffer long computation time.

BTW, I use Matlab. Sometimes I donot pay attention to let fft to generate 2^m points, I just use an arbitrarily large number L and assume Matlab will automatically generated 2^n points, where n is the smallest number for 2^n > L. Is this true that Matlab will do that?

fft power spectrum

greenfrog said:

Hello:

Does this mean I have to use a very long window to get high resolution?

Click to expand...

No. You do not have to have a very long window if you are doing coherent sampling.

I understand your experiment as haveing a lot of time points as zero-crossing points of a signal such as clock. You interpolate the signal sequence by inserting sin wave between two adjacent zero-crossing points.

If that is correct, it is quite natural to have spur in Power spectrum. Because the zero-crossing distance between each other is not exactly the same, then the sin wave you inserted will have different frequency.

sine fft power

If you are sampling a sine wave you should increase number of samples per period. After sampling the sine wave, its shape is a little stairs-like. This introduces harmonics in its spectrum.

regards

I do not understand why it can be important to obtain the power spectrum of a pure sine wave using FFT.
So, I guess that you have a sine wave pluse some other harmonics with it, ( a signal which is mainly consists of a sine wave and the main info. the main info is hidden in the signal )
So you are trying to obtain the main info and to omit the sine wave, it that true?
Then the solution will be to increase the total number of samples, by using either a larger window or ( much more better ) higher sampling frequency.
is this what you are looking for?

coros said:

If you are sampling a sine wave you should increase number of samples per period. After sampling the sine wave, its shape is a little stairs-like. This introduces harmonics in its spectrum.

regards

Click to expand...

Wrong idea. It is not first order sampling,i.e. it is not sample and hold algo. So, only aliasing is there, no stair-case effect.

Since your data doesn't have any amplitude information, only zero-crossings, how about analyzing the histogram of point-to-point spacings, instead of using an FFT? Like an HP/Agilen.t modulation domain analyzer.

Hi,

I could not understand your problem exactly but just something to mention: there are several PSD estimation methods of noisy analog signals from a finite number of its samples. These different approaches have different resolution characteristics for peak locations. You may consider this side of the problem.

Regards

Hi, Guys:

Thank you for all your helpful replies...

I use a 2^22 points of FFT to get the power spectrum I needed. I believe my approach makes sense. Because due to the winder effect, the resultion is decided by the window length. This is explained in Sanjit's book "digital signal processing".

In my case, I am not interested in those spurs or harmonics, I am interested the corruption of an impulse(pure sinusoid) due to fast modulation. I am expecting to see a non-impulse power spectrum plot which is a slightly degradation of an impulse.

Fortunately, the computing time of that many point in Matlab is pretty short.

Thanks

neoflash said:

coros said:

If you are sampling a sine wave you should increase number of samples per period. After sampling the sine wave, its shape is a little stairs-like. This introduces harmonics in its spectrum.

regards

Click to expand...

Wrong idea. It is not first order sampling,i.e. it is not sample and hold algo. So, only aliasing is there, no stair-case effect.

Click to expand...

I apologize for the wrong inputs.

Yes, coros is correct, sampling generate staircase effect. It should be taken care of.