The author explores the realm of frequency domains, challenging the dominance of the Fourier transform with the Walsh-Hadamard transform. Contrary to the traditional approach of deconstructing signals into sine harmonics, the Walsh-Hadamard transform dissects data into square waves through a matrix of +1s and -1s. The detailed explanation covers the construction of the Walsh matrix from the Hadamard matrix, including a bitwise arithmetic trick for efficient computation. The article concludes with a demonstration of the inverse function transforming the frequency domain back to the original signal, showcasing the potential of the Walsh-Hadamard transform in signal processing.
https://lcamtuf.substack.com/p/is-the-frequency-domain-a-real-place