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Information Content In Uniformly Discretized Gaussian Noise: Optimal Compression Rates

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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)

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.

Suggested Citation

  • August Romeo & Enrique Gaztañaga & Jose Barriga & Emilio Elizalde, 1999. "Information Content In Uniformly Discretized Gaussian Noise: Optimal Compression Rates," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 687-716.
    • Handle: RePEc:wsi:ijmpcx:v:10:y:1999:i:04:n:s0129183199000528
    DOI: 10.1142/S0129183199000528
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