What's the difference between Discrete Fourier Series and Discrete Fourier Transform? [duplicate]

1. What is the difference between discrete Fourier series and discrete Fourier transform?
2. What is the main difference between DCT and DFT?
3. Which is better DCT or DFT?
4. What is the main difference between discrete Fourier transform DFT and fast Fourier transform 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.

Which is better DCT or DFT?

This is why DCTs...generally perform better for signal compression than DFTs and DSTs. In practice, a type-II DCT is usually preferred for such applications, in part for reasons of computational convenience. Additionally, you may find that this answer is useful too (from math.stackexchange.com).

What is the main difference between discrete Fourier transform DFT and fast Fourier transform 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.