1# timeseries-compressibility
3Interactive exploration of how compressible quantized time series are.
5The generating model is: i.i.d. Gaussian noise (std σ, measured in quantization
6steps) → FIR filter → optional additive uniform dither on [-½, ½) → round to
7integers. The app shows the filter (convolution kernel and frequency response,
8with cutoffs in Hz against a chosen sample rate), a window of the generated
9integer signal (stationary by default, with a play toggle to let it stream
10endlessly), and the measured compression of a block of the generated integers
11under nine methods — zlib, zstd, and an rANS entropy coder, each raw,
12delta-coded, and LPC-residual-coded — as bits per sample and as ratio against
13raw int16 storage. The predictor order and the block size are controls, so the
14measurement can be pushed from 10k to a million samples and LPC from order 1
15to 128. Each prefilter group also carries a hollow bar: the order-0 entropy of
16the stream being coded, the limit a per-sample entropy coder cannot beat, which
17ANS misses by 1–2% (its symbol table plus its own arithmetic loss).
19Alongside the measurements it plots a theoretical bits/sample R: quantization
20is modeled as an additive white noise floor on the spectrum, the one-step
21Wiener prediction error of the resulting process comes from the
22Szegő–Kolmogorov formula, and R is the exact entropy of that innovation
23quantized at unit step:
25```
26S_z(f) = σ²|H(f)|² + σ_q² σ_q² = 1/12 (1/6 with dither)
27σ_e² = exp( 2 ∫₀^½ ln S_z(f) df )
28R = H_Δ(σ_e) (exact quantized-Gaussian entropy)
29```
31Where the spectrum sits well above one step² this reduces to the classical
32Gaussian entropy rate ½log₂(2πe) + ∫log₂S df; the noise floor keeps it finite
33and positive where a deep stopband would send that integral to −∞. LPC + ANS
34should approach R; probing where the approximation holds is the point. The
35math section is a stub for the full derivation.
37## Run it
39```sh
40npm install
41npm run dev
42```
44## Layout
46```
47src/model/ the latent source (fixed seeded randomness indexed by sample
48 position, convolved zero-phase with the kernel on demand),
49 FIR presets, and the theoretical-rate formula
50src/compress/ lossless codecs run in the browser: zlib (fflate), zstd (wasm),
51 ans.ts (a bit-identical port of simple_ans), and FLAC-style
52 integer LPC; borrowed from entropy-quantized-linear-transform
53src/worker/ the codecs run off the main thread on a debounced parameter set
54src/components/ controls, filter plots, signal canvas, compression chart
55```
57Every reported size round-trips through the decoder and includes whatever the
58decoder needs (ANS symbol table, LPC coefficients). The signal view and the
59compression block read the same fixed latent noise sequence — parameter changes
60transform the same underlying data rather than resampling it, and the first
61window shown is the start of the block that gets compressed.