Relationship between z-transform and DTFT

• Feb 7, 2006

• #1

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silverstar_28

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Hi bros,

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




thanks,

 

• Feb 7, 2006

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v_c

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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

 

Last edited by a moderator: Aug 27, 2010

• Feb 8, 2006

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neils_arm_strong

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z-transform and DTFT

v_c is exactly right.

 

• Feb 9, 2006

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JoseLeonardo

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z-transform and DTFT

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

 

• Feb 12, 2006

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Shrinaresh

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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.

 

• Feb 14, 2006

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Indian

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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.

 

• Feb 14, 2006

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purnapragna

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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!

 

Last edited by a moderator: Aug 27, 2010

• Jul 10, 2006

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starfish

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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.

 

• Jul 10, 2006

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z-transform and DTFT

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

 

• Jul 15, 2006

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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

 

• Jul 27, 2006

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JoseLeonardo

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z-transform and DTFT

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

 

• Jul 28, 2006

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suvendu

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z-transform and DTFT

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

 

• Jul 28, 2006

• #13

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Frank_usa

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Re: z-transform and DTFT

silverstar_28 said:

Hi bros,

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




thanks,

Click to expand...

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