dorsal/arxiv
View SchemaInformation content in Gaussian noise: optimal compression rates
| Authors | August Romeo, Enrique Gaztanaga, Jose Barriga, Emilio Elizalde |
|---|---|
| Categories | |
| ArXiv ID | physics/9809004 |
| URL | https://arxiv.org/abs/physics/9809004 |
| DOI | 10.1142/S0129183199000528 |
| Journal | International Jounal of Modern Physics C, Vol.10, 687-716 (1999) |
Abstract
We approach the theoretical problem of compressing a signal dominated by Gaussian noise. We present expressions for the compression ratio which can be reached, under the light of Shannon's noiseless coding theorem, for a linearly quantized stochastic Gaussian signal (noise). The compression ratio decreases logarithmically with the amplitude of the frequency spectrum $P(f)$ of the noise. Entropy values and compression rates are shown to depend on the shape of this power spectrum, given different normalizations. The cases of white noise (w.n.), $f^{n_p}$ power-law noise ---including $1/f$ noise---, (w.n.$+1/f$) noise, and piecewise (w.n.+$1/f |$ w.n.$+1/f^2$) noise are discussed, while quantitative behaviours and useful approximations are provided.
{
"annotation_id": "923f5ff4-9a09-42df-b759-d639a1d5922d",
"date_created": "2026-03-02T18:01:21.877000Z",
"date_modified": "2026-03-02T18:01:21.877000Z",
"file_hash": "c0594e8f8d03e7864a70c3059c223b79ff6f042475d295bfe499899686d1d976",
"private": false,
"record": {
"abstract": "We approach the theoretical problem of compressing a signal dominated by\nGaussian noise. We present expressions for the compression ratio which can be\nreached, under the light of Shannon\u0027s noiseless coding theorem, for a linearly\nquantized stochastic Gaussian signal (noise). The compression ratio decreases\nlogarithmically with the amplitude of the frequency spectrum $P(f)$ of the\nnoise. Entropy values and compression rates are shown to depend on the shape of\nthis power spectrum, given different normalizations. The cases of white noise\n(w.n.), $f^{n_p}$ power-law noise ---including $1/f$ noise---, (w.n.$+1/f$)\nnoise, and piecewise (w.n.+$1/f |$ w.n.$+1/f^2$) noise are discussed, while\nquantitative behaviours and useful approximations are provided.",
"arxiv_id": "physics/9809004",
"authors": [
"August Romeo",
"Enrique Gaztanaga",
"Jose Barriga",
"Emilio Elizalde"
],
"categories": [
"physics.data-an",
"astro-ph"
],
"doi": "10.1142/S0129183199000528",
"journal_ref": "International Jounal of Modern Physics C, Vol.10, 687-716 (1999)",
"title": "Information content in Gaussian noise: optimal compression rates",
"url": "https://arxiv.org/abs/physics/9809004"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "65bfcede-e3b3-40f5-a6e5-e4b7d014b177",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}