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Origin of the definitions of 16 types of discrete normalized/non-normalized Sine and Cosine transforms

Origin of the definitions of 16 types of discrete normalized/non-normalized Sine and Cosine transforms
  1. What is the difference between DFT and DCT?
  2. Why do we use DFT?

What is the difference between DFT and DCT?

Like the discrete Fourier transform (DFT), a DCT operates on a function at a finite number of discrete data points. The obvious distinction between a DCT and a DFT is that the former uses only cosine functions, while the latter uses both cosines and sines (in the form of complex exponentials).

Why do we use DFT?

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.

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