Dft in matlab without using inbuilt functions

1. What are the disadvantages of direct computation of DFT?
2. What is difference between DFT and FFT?
3. Why we need DFT when we have DTFT?

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.

What is difference between DFT and FFT?

Discrete Fourier Transform (DFT) is the discrete version of the Fourier Transform (FT) that transforms a signal (or discrete sequence) from the time domain representation to its representation in the frequency domain. Whereas, Fast Fourier Transform (FFT) is any efficient algorithm for calculating the DFT.

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.