#signal-processing

2 articles

01 ·Numerical Computing·FREE·PAPER·16 min read The Fourier Transform from Scratch — Reading a Signal as a Stack of Pure Tones A signal drawn against time hides the thing you usually want to know: which frequencies are in it, and how much of each. This article builds the Fourier transform from one idea — measure a signal against a pure tone with an inner product — then takes the continuous integral apart symbol by symbol, does the same for the DFT, separates two tones by hand, and ends on the three traps that bite in practice: aliasing, finite resolution, and spectral leakage. 02 ·Numerical Computing·★ MEMBER·PAPER·9 min read The FFT from Scratch — Why Convolution Turns into Multiplication A from-zero walk through the Fourier transform: a smoothie metaphor, the spinning-needle intuition, the DFT formula, and the divide-and-conquer trick behind the FFT — ending with the polynomial-multiplication view that makes the convolution theorem feel obvious.