What are the basic defferences between z-transform and DTFT

z-transform and DTFT

Hi

What is the basic defferences between z-transform and DTFT(Discrete Time Fourier Transform)?

z-transform and DTFT

This may prove helpful:

https://dspcan.homestead.com/files/Ztran/zfour1.htm

also

https://en.wikipedia.org/wiki/Discrete-time_Fourier_transform

You can also try a google.com search for "differences between z-transform and DTFT"

Hope it helps!

Added after 38 seconds:

From wikipedia:

Difference between the DTFT and other Fourier transforms

Essentially, the DTFT is the reverse of the Fourier series, in that the latter has a continuous, periodic input and a discrete spectrum. The applications of the two transforms, however, are quite different.

The DFT and the DTFT can be viewed as the logical result of applying the standard continuous Fourier transform to discrete data. From that perspective, we have the satisfying result that it's not the transform that varies, it's just the form of the input:

* If it is discrete, the Fourier transform becomes a DTFT.
* If it is periodic, the Fourier transform becomes a Fourier series.
* If it is both, the Fourier transform becomes a DFT.

Re: z-transform and DTFT

The principal difference between the Z and the discrete time fourier transform is that, the DTFT is a derived of the Z transform, because, in the Z transform, Z means a complex number (Ae^(Θ)) with any magnitude and any phase angle, but in the DTFT, this complex number is restricted to an only magnitude, A must be only one (1), it's means that the complex number is e^(Θ).

Another difference is that the analysis of the Z transform is valid for all types of signal (periodic, increasing, decreasing, etc), but the DTFT its valid only for signal that has finite energy and the completely periodic signals.

You can find another more complete explication in the SIGNAL AN SYSTEM book.

In discrete time signal, we use ZT or DTFT(discrete time fourier transform). The difference is that ZT is more general version. Z can be any complex. When ZT converges on unit circle(e^jw) then it becomes to fourier transform.