fourier transform

Making Our Own Spectrogram

2 months ago

Fourier transforms convert signals between time and frequency domains, enabling spectrogram generation.
A square wave can be approximated by summing cosine waves with harmonics, illustrating how Fourier series work.
Real-world audio (e.g., a mouth pop) can be reconstructed using a limited number of cosine components via FFT.
Windowing functions like Hann windows prevent spectral leakage by tapering signal edges during chunked analysis.
Overlap-add reconstruction with Hann windows yields correct audio, except at boundaries where padding is needed.
The Gabor limit forces a trade-off between time and frequency resolution; choosing FFT size and overlap affects spectrogram sharpness.
Interpolation between frequency bins improves visual smoothness, while disabling it reveals bin boundaries.
Perceptually uniform color maps (e.g., colorcet) enhance readability of spectrograms over simple black-white gradients.
A logarithmic frequency scale with custom interpolation provides better representation of human pitch perception.
Audio input is captured from system devices (e.g., via Loopback) using the cpal crate with a callback for live processing.
UI and audio threads communicate via channels; a bounded VecDeque prevents memory overflow during rendering stalls.
Texture updates in egui involve allocating a handle, drawing to a ColorImage, and uploading to GPU each frame.
Profiling reveals CPU hotspots: 25% of cycles on cloning ColorImage, 40% on texture uploads, and 27% on FFT computations.
The spectrogram visualizes various music genres and sounds (e.g., vibrato, frequency sweeps, bird calls) for educational fun.

Hasty Briefsbeta

fourier transform

Notes on the Fourier Transform

Making Our Own Spectrogram