Polar Fourier Transform and its similarity to the Z-Transform

1. What is the similarity between Fourier transform and Z transform?
2. What is relation between Z transform and Fourier transform?
3. What is the difference between Fourier transform and Z transform?
4. Why do we use Z transform over Fourier transform?

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.

What is relation between Z transform and 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.

What is the difference between Fourier transform and Z 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. Save this answer.

Why do we use Z transform over 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.