import { useEffect, useMemo, useRef, useState } from 'react' import Controls from './components/Controls' import FilterViz from './components/FilterViz' import ScrollingView from './components/ScrollingView' import CompressionChart from './components/CompressionChart' import MathSection from './components/MathSection' import { DEFAULT_SPEC, designKernel, kernelNorm } from './model/filters' import { theoreticalRateBits } from './model/theory' import type { CodecResult } from './compress/codecs' import type { CompressRequest, CompressResponse } from './worker/compressWorker' const BLOCK_SIZE = 120000 const BLOCK_SEED = 20260729 interface CompressionState { results: CodecResult[] empiricalStd: number computing: boolean error: string | null } /** The nine codec sizes, measured in a worker on a debounced parameter set. */ function useCompression(kernel: Float64Array, sigma: number, dither: boolean): CompressionState { const [state, setState] = useState({ results: [], empiricalStd: 0, computing: true, error: null, }) const workerRef = useRef(null) const idRef = useRef(0) useEffect(() => { const worker = new Worker(new URL('./worker/compressWorker.ts', import.meta.url), { type: 'module', }) worker.onmessage = (e: MessageEvent) => { if (e.data.id !== idRef.current) return setState({ results: e.data.error ? [] : e.data.results, empiricalStd: e.data.empiricalStd, computing: false, error: e.data.error ?? null, }) } workerRef.current = worker return () => { worker.terminate() workerRef.current = null } }, []) useEffect(() => { setState(s => ({ ...s, computing: true })) const id = ++idRef.current const timer = setTimeout(() => { const request: CompressRequest = { id, kernel, sigma, dither, blockSize: BLOCK_SIZE, seed: BLOCK_SEED, } workerRef.current?.postMessage(request) }, 250) return () => clearTimeout(timer) }, [kernel, sigma, dither]) return state } export default function App() { const [sigma, setSigma] = useState(5) const [sampleRateHz, setSampleRateHz] = useState(30000) const [spec, setSpec] = useState(DEFAULT_SPEC) const [dither, setDither] = useState(false) const kernel = useMemo(() => designKernel(spec, sampleRateHz), [spec, sampleRateHz]) const sigmaY = useMemo(() => { const filtered = sigma * kernelNorm(kernel) return dither ? Math.sqrt(filtered * filtered + 1 / 12) : filtered }, [kernel, sigma, dither]) const theoryBits = useMemo(() => theoreticalRateBits(kernel, sigma, dither), [kernel, sigma, dither]) const compression = useCompression(kernel, sigma, dither) return (

Time-series compressibility

Gaussian noise → FIR filter → optional dither → round to integers. How well can the integer stream be losslessly compressed, and does the spectral entropy-rate formula predict the limit?

Model

Filter

Quantized signal z

A window of samples from the model, drawn from a fixed latent noise sequence — changing σ, the filter, or dither transforms the same underlying data, so the trace morphs rather than resampling. Press play to advance through the sequence.

Compression

predicted std of z {sigmaY.toFixed(2)} steps
measured std of z {compression.results.length > 0 ? compression.empiricalStd.toFixed(2) : '…'}{' '} steps
theoretical rate R {theoryBits.toFixed(2)} bits/sample
implied best ratio {theoryBits > 0 ? `${(16 / theoryBits).toFixed(2)}×` : '—'}
{compression.error ? (

Compression failed: {compression.error}

) : ( )}

Measured on a {BLOCK_SIZE.toLocaleString()}-sample block of the same latent data the signal view shows; sizes include everything a decoder needs (ANS symbol table, LPC coefficients). Baseline is raw int16 (16 bits/sample). The dashed line is the theoretical rate R from the spectral formula in the math section — approximate where quantization dominates the spectrum (see the S(f) = 1 threshold on the response plot).

The math

) }