Information content in Gaussian noise: optimal compression rates

Details Information content in Gaussian noise: optimal compression rates Information content in Gaussian noise: optimal compression rates

1998-09-03

arxiv.org/abs/physics/9809004v2

International Jounal of Modern Physics C, Vol.10, 687-716 (1999)

Physics

Data Analysis, Statistics and Probability

28 LateX pages and 6 Fig, replaced with minor changes to match published version

Scientific paper

10.1142/S0129183199000528

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.

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