Cosine and Wavelet Transform

Uses just $\cos$ functions.

We modify the input signal to make it even so that the $\sin$ coefficients turn into zeroes.

We don’t use complex numbers anymore, but we also lose some of the nice properties of the transform.

Good tool for compression, not so much for signal analysis.

Fast DCT (F-DCT) — uses FDFT under the hood.

Coefficients are divided into "DC" (zero frequency) and "AC" (other frequencies).

Uses wavelets — functions with a peak at zero and brief, diminishing oscillations.

Compared to FT, which captures global frequency information, WT provides temporal information as well.

First DWT invented by Alfréd Haar. Haar wavelets are the most educational. TODO