Is my transform the essence of DFT?

1. Why is DFT essential?
2. How DFT is related to Z transform?
3. What is Fourier transform explain with DFT?
4. What is difference between continuous Fourier transform and discrete Fourier transform?
5. Why we need DFT when we have DTFT?

Why is DFT essential?

The Discrete Fourier Transform (DFT) is of paramount importance in all areas of digital signal processing. It is used to derive a frequency-domain (spectral) representation of the signal.

How DFT is related to 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.

What is Fourier transform explain with DFT?

In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency.

What is difference between continuous Fourier transform and discrete Fourier transform?

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.

Why we need DFT when we have 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.