5 ms·
Another cool thing is that orthonormal bases are not unique - there are many other basis functions that you can choose beyond just sine and cosine to decompose
by thearn4 13y ago
Another cool thing is that orthonormal bases are not unique - there are many other basis functions that you can choose beyond just sine and cosine to decompose a function (or digital signal). Though they are a natural choice if you are specifically looking to analyze periodicities.
One direction to go in for further study:
https://en.wikipedia.org/wiki/Wavelet https://en.wikipedia.org/wiki/Wavelet
- GrantS 13y agoYes! Same goes for pulling eigenvectors out of a data set e.g. for PCA (Principal Components Analysis) -- those form an orthonormal basis. You can even pick a set of random orthogonal vectors of the same number and dimension as your original data and re-represent the data with no loss of information. I had a lot of fun demonstrating this concept for reconstructing images via a Processing sketch a few years ago and still use it for teaching from time to time. All source code for quick and dirty Haar, Eigen, Random, and Fourier-like methods included here: http://www.cc.gatech.edu/~phlosoft/transforms/ http://www.cc.gatech.edu/~phlosoft/transforms/