Confusion related to norm of dft

1. What are the disadvantages of direct computation of DFT?
2. How DFT is related to Z transform?
3. What is the result of DFT?

What are the disadvantages of direct computation of DFT?

For the computation of N-point DFT, N2 complex multiplications and N[N-1] Complex additions are required. If the value of N is large than the number of into lakhs. This proves inefficiency of direct DFT computation.

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 the result of 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.