Asymptotic White noise Hypothesis for PCM quantization
Sergiy V. Borodachov, Yang Wang · 2008
For a signal distributed in Rdwith an arbitrary density we find the limit distribution as the cell size goes to zero of the quantization noise in the case of a redundant system and the pulse-code modulation scheme. The dimension the support of the limiting distribution equals the largest number of non-comeasurable vectors in the frame and the limit distribution is uniform over its support. This gives the necessary and sufficient conditions for the asymptotic form of the white noise hypothesis.