Dtft

Link between DFS, DFT, DTFT

Link between DFS, DFT, DTFT
  1. What is the relation between DTFT and DFT?
  2. What is difference between DFS and DFT?
  3. How is DFT related to DTFT and Z transform?
  4. Is DFS and DTFT same?

What is the relation between DTFT and DFT?

DFT (Discrete Fourier Transform) is a practical version of the DTFT, that is computed for a finite-length discrete signal. The DFT becomes equal to the DTFT as the length of the sample becomes infinite and the DTFT converges to the continuous Fourier transform in the limit of the sampling frequency going to infinity.

What is difference between DFS and DFT?

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

How is DFT related to DTFT 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.

Is DFS and DTFT same?

now coming to DTFS and DFS the difference is that you apply DTFS to a periodic signal and DFS to a finite discrete signal which is not periodic but made periodic by adding some values.

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