Discrete Fourier transform of an exponential decay

1. What is the Fourier transform of a discrete signal?
2. Why DFT is used instead of DTFT?
3. What is the difference between DFT and DTFS?
4. What are the the disadvantage of DTFT?

What is the Fourier transform of a discrete signal?

The DTFT is a transform-pair relationship between a DT signal and its continuous-frequency transform that is used extensively in the analysis and design of DT systems.

Why DFT is used instead of DTFT?

original sequence spans all the non-zero values of a function, its DTFT is continuous (and periodic), and the DFT provides discrete samples of one cycle. If the original sequence is one cycle of a periodic Page 2 function, the DFT provides all the non-zero values of one DTFT cycle.

What is the difference between DFT and DTFS?

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 are the the disadvantage of DTFT?

Two computational disadvantages of the DTFT are: the direct DTFT is a function of a continuously varying frequency and the inverse DTFT requires integration. The Fourier series coefficients constitute a periodic sequence of the same period as the signal; thus both are periodic.