# 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 → 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
block of the generated integers 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. The predictor order and the
block size are controls, so the measurement can be pushed from 10k to a million
samples and LPC from order 1 to 128. Each prefilter group also carries a hollow
bar: the order-0 entropy of the stream being coded, the limit a per-sample
entropy coder cannot beat, which ANS misses by 1–2% (its symbol table plus its
own arithmetic loss).

The entropy rate R of the process — the bits/sample limit no lossless method
can beat — is estimated in the browser by the method of the companion
[timeseries-entropy](https://github.com/concept-collection/timeseries-entropy)
package: an unbiased Monte-Carlo estimator of H(z_next | a long past), by Gibbs
sampling the latent Gaussian under the rounding constraints and applying
Rhee–Glynn randomized telescoping to the sampled chain. A button starts a web
worker that averages one independent past at a time (live mean ± se, dashed
line on the chart) until stopped; the app also shows the exact command to run
the Python original at the same settings as an independent check. The
in-browser code in `src/entropy/` is a hand-synced TypeScript port of that
package — change one, change the other. A WebGPU Gibbs sweep may replace the
scalar one someday; the sweep is isolated so it can be swapped.

## Run it

```sh
npm install
npm run dev
```

## Layout

```
src/model/       the latent source (fixed seeded randomness indexed by sample
                 position, convolved zero-phase with the kernel on demand)
                 and the FIR presets
src/entropy/     the unbiased entropy-rate estimator: hand-synced TypeScript
                 port of the timeseries-entropy package (Gibbs conditional
                 sampler, Rhee–Glynn telescoping, Cody erfc / Acklam ndtri,
                 xoshiro128** RNG)
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 and the estimator run off the main thread; the
                 estimator worker refines one past at a time until terminated
src/components/  controls, filter plots, signal canvas, compression chart,
                 and the entropy-rate method note
```

Every reported size round-trips through the decoder and includes whatever the
decoder needs (ANS symbol table, LPC coefficients). The signal view and the
compression block read the same fixed latent noise sequence — parameter changes
transform the same underlying data rather than resampling it, and the first
window shown is the start of the block that gets compressed.