Relationship between z-transform and DTFT

[silverstar_28]

Hi bros,

any one knows the relation between z-transform and dtft?




thanks,

 

[v_c]

Re: z-transform and DTFT

The DTFT is a special case of the z-transform. The z-tranform is given by the sum

\[ X(z) = \sum_{n=-\infty}^{n=\infty} x[n] z^{-n}\]

If we evaluate the z-transform at \[z=e^{-j \omega}\], then we get the DTFT -- this evaluation is equivalent to evaluating the z-transform on the unit circle in the complex plane.

You can read more about this at Discrete-time Fourier transform - Wikipedia, the free encyclopedia

 

[neils_arm_strong]

z-transform and DTFT

v_c is exactly right.

 

[JoseLeonardo]

z-transform and DTFT

you can read more about this topics in Digital Signal Processing by Proakis

 

[Shrinaresh]

Re: z-transform and DTFT

you can find more on this in signals and systems by oppenheim, willsky and in discrete-time signal processing by oppenheim schafer and buck.

 

[Indian]

Re: z-transform and DTFT

In case of DTFT of a system function, it can do the transform only if the h[n] is a stable sequence Σh[n] should be less than infinite. So we can take DTFT only for stable systems. But by using z-transform we can transform even the unstable systems and can analysis the stability criterion.

 

[purnapragna]

Re: z-transform and DTFT

ZT is more general clas of analysis of signals. For example DTFT of \[u[n]\] does not converge absolutely but ZT will converge absolutely.

thnx

purna!

 

[starfish]

Re: z-transform and DTFT

Z transform is a more general case than DTFT. Practically Z Transform is used only to analyze whether a given system , filter etc is stable or not.

 

[papu]

z-transform and DTFT

there is no such differnce between them....
z=exp-(jw)

 

[nag_0075]

Re: z-transform and DTFT

z-transform:dtft :: laplace transform:fourier transform

In casse there are super exponential signals, one cannot find the Fourier Transform. In order to obtain a transform, not necessarily the spectrum, the signal is first "killed" by a super-super exponential and the transform taken.The advantage it offers is that a larger family of signals can be transformed.In the digital domain it is the DTFT and z-tranform, while in the analog domain it is the Fourier transform and the Laplace transform

 

[JoseLeonardo]

z-transform and DTFT

You can read "Digital Signals Processing" by Jhon Proakis.

 

[suvendu]

z-transform and DTFT

DTFT is nothing but the Z transform obtained on unit circle.so it is the special class of z transform.

 

[Frank_usa]

Re: z-transform and DTFT

Hi bros,

any one knows the relation between z-transform and dtft?




thanks,

z-transform is similar to dtft only when ω=1