1
$\begingroup$

let us suppose that we some signal $x(t)$,which consist of sinusoidal components and white noise,i would like to know how to use chirp z transform for improving spectral resolution?i found this article about chirp z transform

http://prod.sandia.gov/techlib/access-control.cgi/2005/057084.pdf

also similar article on official matlab side

http://www.mathworks.com/help/signal/ref/czt.html

but as i know always in spectral estimation methods,some knowledge we should know how process is going,or some other things,let us suppose that we know sampling frequency lat say $Fs=100$,and also we know that it consist as i mentioned by periodic components(sin or cosine),but i dont know number of components,neither frequency or neither phases(+neither amplitudes),how can i apply chirp z transform to this signal?we have just some signal samples with size $N=294$ ,please help me how to choose correct components so that get effectively spectral structure and if let say one frequency is $f_1=13$ and second $f_2=13.5$,this transform be able to separate this frequencies from each other,thanks

$\endgroup$
  • 1
    $\begingroup$ With standard Fourier techniques (even CZT) the resolution is given by $1/T$ where $T$ is the length of the signal. In this case your resolution is going to be $100/294=0.34$ Hz. Due to the filtering effects in the CZT, your resolution is going to degrade. The CZT allows you to zoom in on a particular band of interest, it won't increase your resolution. Since you don't know where the frequencies are, I doubt the CZT will be of use. Similar to CZT is the Zoom - FFT, which is a frequency shift, filter and Decimate, and small size FFT. $\endgroup$ – David Mar 26 '14 at 13:09
  • $\begingroup$ The resolution of all spectral estimation techniques depends on some assumption of sparsity (thus the max number of components). Otherwise any peak or gap or single FFT bin could contain a mix of 100's of unresolvable smaller sinusoids. $\endgroup$ – hotpaw2 Mar 26 '14 at 15:36
5
$\begingroup$

If you have no prior knowledge about the approximate locations of the frequencies, the Chirp Z-transform is of no immediate use to you. The Chirp Z-transform functions like a magnifying glass, so you need to know where you want to look and the Chirp Z-transform will show you the details. I would suggest you use an FFT to get an idea where the frequencies are, and if you need a very high resolution in a certain area of the spectrum, then the Chirp Z-transform can be useful. However, if computational complexity and memory are no issue, you can simply use a long FFT to achieve the same. If you want to know more about the Chirp Z-transform I would recommend this paper to you.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.