https://jen1995.github.io/tags/fourier/Recent content in Fourier on Cohomology ZeroHugoen-USSun, 26 Jul 2026 00:00:00 +0000https://jen1995.github.io/posts/fourier-series-to-spectrogram-part-1/Sun, 26 Jul 2026 00:00:00 +0000https://jen1995.github.io/posts/fourier-series-to-spectrogram-part-1/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.https://jen1995.github.io/posts/fourier-series-to-spectrogram-part-2/Sun, 26 Jul 2026 00:00:00 +0000https://jen1995.github.io/posts/fourier-series-to-spectrogram-part-2/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.https://jen1995.github.io/posts/fourier-series-to-spectrogram-part-3/Sun, 26 Jul 2026 00:00:00 +0000https://jen1995.github.io/posts/fourier-series-to-spectrogram-part-3/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.