# Relationship between z-transform and DTFT

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#### silverstar_28

##### Junior Member level 3
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.

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#### neils_arm_strong

##### Full Member level 5
z-transform and DTFT

v_c is exactly right.

#### JoseLeonardo

##### Full Member level 1
z-transform and DTFT

#### Shrinaresh

##### Newbie level 3
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

##### Junior Member level 3
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!

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#### starfish

##### Member level 2
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

##### Banned
z-transform and DTFT

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

#### nag_0075

##### Newbie level 1
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

##### Full Member level 1
z-transform and DTFT

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

#### suvendu

##### Full Member level 3
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

##### Newbie level 5
Re: z-transform and DTFT

silverstar_28 said:
Hi bros,

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

thanks,

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

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