Information content in uniformly discretized Gaussian noise: Optimal compression rates

We approach the theoretical problem of compressing a signal dominated by Ga ussian noise. We present expressions for the compression ratio which can he reached, under the light of Shannon's noiseless coding theorem, for a line arly quantized stochastic Gaussian signal (noise). The compression ratio de creases logarithmically with the amplitude of the frequency spectrum P(f) o f the noise. Entropy values and compression rates are shown to depend on th e shape of this power spectrum, given different normalizations. The cases o f white noise (w.n.), f(np) 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 behaviors and useful approximations are provided.