# use chirp z transform for spectral resolution

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

• 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. – David Mar 26 '14 at 13:09
• 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. – hotpaw2 Mar 26 '14 at 15:36