Discrete Cosine Transform

Discrete Cosine Transform is the way to take finite list of real numbers and rewrite it as a sum of cosine waves at different frequencies

DCT is commonly used transformation for compression algorithms (eg. JPEG image compression)

Intuition §

If you have a 1D signal

$$x[0],x[1],\dots ,x[N-1]$$

DCT finds weights $X[k]$ so that the original signal can be approximated by adding cosine patterns