From the Fourier Series to the Spectrogram, Part 1: From Sound to the DFT
Part 1 of 3: from air pressure and a guitar string, through sampling and the Fourier series — to the DFT, derived honestly, delta functions and all.
Fourier
From the Fourier Series to the Spectrogram, Part 2: Reading the DFT
Part 2 of 3: learning to read the DFT’s output — which bin is which frequency, why resolution is one over duration, the mirror symmetry, and the Nyquist frequency.
From the Fourier Series to the Spectrogram, Part 3: From the DFT to the Spectrogram
Part 3 of 3: cut the signal into frames, pay for the cut with leakage, patch it with windows, stack the columns — the spectrogram, and its mel-compressed cousin that speech models actually consume.