timeseries-compressibility#

Interactive exploration of how compressible quantized time series are.

The generating model is: i.i.d. Gaussian noise (std σ, measured in quantization steps) → FIR filter → optional additive uniform dither on [-½, ½) → round to integers. The app shows the filter (convolution kernel and frequency response, with cutoffs in Hz against a chosen sample rate), a window of the generated integer signal (stationary by default, with a play toggle to let it stream endlessly), and the measured compression of a 120,000-sample block under nine methods — zlib, zstd, and an rANS entropy coder, each raw, delta-coded, and LPC-residual-coded — as bits per sample and as ratio against raw int16 storage.

Alongside the measurements it plots the theoretical bits/sample: the entropy rate of the stationary filtered Gaussian process quantized at unit step, in the high-resolution limit,

R = ½ log₂(2πe) + ∫₀^½ log₂ S(f) df,    S(f) = σ² |H(f)|²

LPC + ANS should approach R — and does, where the formula is valid. Where the filter's stopband pushes S(f) below one step² (see the dashed threshold on the response plot), the formula under-predicts and can go negative; making that breakdown visible is part of the point. The math section is a stub for the full derivation.

Run it#

npm install
npm run dev

Layout#

src/model/       the pipeline (seeded Gaussian stream, FIR presets, dither,
                 rounding) and the entropy-rate integral
src/compress/    lossless codecs run in the browser: zlib (fflate), zstd (wasm),
                 ans.ts (a bit-identical port of simple_ans), and FLAC-style
                 integer LPC; borrowed from entropy-quantized-linear-transform
src/worker/      the codecs run off the main thread on a debounced parameter set
src/components/  controls, filter plots, scrolling canvas, compression chart

Every reported size round-trips through the decoder and includes whatever the decoder needs (ANS symbol table, LPC coefficients). The compression block and the scrolling display are fed by the same Pipeline, so what is compressed is what is shown.