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


also similar article on official matlab side


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

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    $\begingroup$ 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

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.

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