The Bernoulli - Trials Distribution and Wavelet “ . . with my God , I can scale a wall ” - David in Psalm 18
نویسنده
چکیده
ABSTRACT: This paper begins by using the Haar wavelet to analyze the cumulative distribution function of a stream of two-valued Bernoulli trials. We find that this function maps binary numbers in [0,1] into non-uniform binary numbers in [0,1]. More generally, for r-valued Bernoulli trials, the distribution function likewise maps usual base-r numbers into non-uniform base-r numbers. We also find this distribution function obeys a two-scale dilation equation and can be used to construct a family of wavelets. This family contains the Haar wavelet and the piecewise-linear wavelet as special cases.
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