Z-transform vs fourier transform

Fourier transforms are for converting/representing a time-varying function in the frequency domain. Z-transforms are very similar to laplace but are discrete time-interval conversions, closer for digital implementations. They all appear the same because the methods used to convert are very similar.

1. Is Z-transform same as Fourier transform?
2. Why we use Z-transform instead of Fourier transform?
3. What is the difference between Z-transform and Laplace transform?
4. What is the similarity between Fourier transform and Z-transform?

Is Z-transform same as Fourier transform?

Also, if r = 1, then the discrete time Fourier transform (DTFT) is same as the Z-transform. In other words, the DTFT is nothing but the Z-transform evaluated along the unit circle centred at the origin of the z-plane.

Why we use Z-transform instead of Fourier transform?

A significant advantage of the z-transform over the discrete-time Fourier transform is that the z-transform exists for many signals that do not have a discrete-time Fourier transform. Thus, it is a more general analysis tool.

What is the difference between Z-transform and Laplace transform?

The Z-transform is used to analyse the discrete-time LTI (also called LSI - Linear Shift Invariant) systems. The Laplace transform is used to analyse the continuous-time LTI systems. The ZT converts the time-domain difference equations into the algebraic equations in z-domain.

What is the similarity between Fourier transform and Z-transform?

Detailed Solution. The Fourier transform and the z-transform converts the discrete-time domain to the frequency spectrum domain.