About Discrete Fourier Transform vs. Discrete Fourier Series

1. What is the difference between discrete Fourier series and discrete Fourier transform?
2. What is the main difference between DCT and DFT?
3. What is the difference between DTFS and DTFT?
4. What is difference between DIT and DIF FFT?

What is the difference between discrete Fourier series and discrete Fourier transform?

There is no operational difference between what is commonly called the Discrete Fourier Series (DFS) and the Discrete Fourier Transform (DFT).

What is the main difference between DCT and DFT?

DCTs are equivalent to DFTs of roughly twice the length, operating on real data with even symmetry (since the Fourier transform of a real and even function is real and even), whereas in some variants the input or output data are shifted by half a sample. There are eight standard DCT variants, of which four are common.

What is the difference between DTFS and DTFT?

The DTFS is used to represent periodic discrete-time signals in the frequency domain. It's continuous-time counterpart studied previously is the Fourier Series (FS). The DTFT is used to represent non-periodic discrete-time signals in the frequency domain.

What is difference between DIT and DIF FFT?

In DIT algorithm firstly computed multiplier then adder but in DIF firstly computed adder then multiplier. In this paper we study of different types of multiplier i.e. array multiplier; sing multiplier (Baugh Wooley) and complex multiplier. In proposed complex multiplier is consuming three multipliers.