INFORMATION CONTENT IN UNIFORMLY DISCRETIZED GAUSSIAN NOISE: OPTIMAL COMPRESSION RATES

August Romeo (), Enrique Gaztañaga, Jose Barriga and Emilio Elizalde
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August Romeo: Consejo Superior de Investigaciones Científicas (CSIC), Institut d'Estudis Espacials de Catalunya (IEEC), Edifici Nexus-201, c. Gran Capità 2-4, 08034 Barcelona, Spain
Enrique Gaztañaga: Consejo Superior de Investigaciones Científicas (CSIC), Institut d'Estudis Espacials de Catalunya (IEEC), Edifici Nexus-201, c. Gran Capità 2-4, 08034 Barcelona, Spain
Jose Barriga: Consejo Superior de Investigaciones Científicas (CSIC), Institut d'Estudis Espacials de Catalunya (IEEC), Edifici Nexus-201, c. Gran Capità 2-4, 08034 Barcelona, Spain
Emilio Elizalde: Consejo Superior de Investigaciones Científicas (CSIC), Institut d'Estudis Espacials de Catalunya (IEEC), Edifici Nexus-201, c. Gran Capità 2-4, 08034 Barcelona, Spain

International Journal of Modern Physics C (IJMPC), 1999, vol. 10, issue 04, 687-716

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 spectrumP(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.),fnppower-law noise (including1/fnoise),(w.n.+1/f)noise, and piecewise(w.n.+1/f |w.n.+1/f2) noise are discussed, while quantitative behaviors and useful approximations are provided.

Keywords: Information theory; Signal compression (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1142/S0129183199000528

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