[raxxorrax]

I like practical examples for learning about math-heavy stuff and I came to greater understanding while looking into imaging, specifically how DCT (discrete cosine transformation) works.

You learn how an image is dissected into two matrices (or one complex matrix) containing amplitudes and phases of respective frequencies. A good start for me was playing around with openCV and reading about JPEG (uses DCT).

Why transform an image in the first place? Because you can just set the highest frequencies to zero without influencing the image in real space too much. This effect is leveraged by classical JPEG compression, you just delete data not that important for the image. Being able to analyze, filter, change frequencies in a signal has a lot of other applications.

There are better links but maybe this is a start: https://www.mathworks.com/help/images/discrete-cosine-transf...

There is a ton of literature about DCT because its widespread application. A few google searches lead to good learning material. Fourier and in general LaPlace transformations are a little different, but far easier to understand after seeing an example of their application in my opinion.

This also touches the topic of the article. The problem is that transforming between real space and spectral space results in rounding errors. The article describes a new approach to minimize these.