Relation between DFT to CTFT

1. What is the relationship between DFT and DFS?
2. What is difference between CTFT and DTFT?
3. What is the relation between DFT and Z transform?
4. How is the DTFT related to the continuous Fourier transform?

What is the relationship between DFT and DFS?

The discrete Fourier series (DFS) is used to represent periodic time functions and the DFT is used to repre- sent finite-duration time functions.

What is difference between CTFT and DTFT?

The difference is pretty quickly explained: the CTFT is for continuous-time signals, i.e., for functions x(t) with a continuous variable t∈R, whereas the DTFT is for discrete-time signals, i.e., for sequences x[n] with n∈Z.

What is the relation between DFT and Z 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.

How is the DTFT related to the continuous Fourier transform?

This means that the sampling frequency in the continuous-time Fourier transform, , becomes the frequency in the discrete-time Fourier transform. The discrete-time frequency corresponds to half the sampling frequency, or . The second key piece of the equation is that there are an infinite number of copies of spaced by .