Spectral analysis and processing: FFT, STFT, and the phase vocoder

Every live coder eventually hits the wall where sample manipulation stops being enough: the vocal chop needs to stretch across two bars without turning into a chipmunk, the found-sound texture needs to sit in the mix at a different tempo, the ambient set needs a pad that breathes with the formants of a field recording. This module builds toward that whole task — fluent spectral-domain transformation of real material, live, with parameter choices you can defend.

The arc starts supported. You first compute a DFT by hand (the double-loop pseudocode makes the phasor accumulation concrete), then immediately confront why real sounds need windowing to tame spectral leakage. From there you slide the window along a drum loop to build a spectrogram, drilling the habit that anchors everything downstream: reading time-frequency plots and choosing window length against the resolution tradeoff. A real-time spectroscope on your rig makes this a performance skill, not just a plotting exercise. Mid-module the scaffolding loosens — overlap-add reconstruction shows how block-based effects avoid boundary artifacts, and the phase vocoder atoms hand you the machinery to decouple time from pitch, exactly what naive rate-change playback cannot do. The capstone then removes the rails: stretch, shift, and cross-synthesize a recording of your choosing, justifying FFT size, window, and hop.

The required atoms gate this directly — you cannot pick sane STFT parameters without the tradeoff principle, nor explain vocoder artifacts without phase-frame reasoning, nor complete the final capstone step without cross-synthesis, the bin-by-bin spectral multiplication that imposes one sound’s envelope on another; the two L4 procedures (spectral mapping, scale design for inharmonic sources) extend the same toolkit into experimental tuning territory. Supporting atoms enrich the why: Gabor’s uncertainty relation grounds the tradeoff, convolution duality explains cross-synthesis as spectral multiplication, and critical-band psychoacoustics tells you which spectral details the audience will actually hear.

Runnable examples

Generated from the context/ instrument corpus by concept (redistributable idioms only). Do not edit — regenerate with gen-module-examples.mjs.

reverse-playback

d1 $ sound "bd sn" # speed "-1"

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