TITLE:
On Approximating Two Distributions from a Single Complex-Valued Function
AUTHORS:
William Dana Flanders, George Japaridze
KEYWORDS:
Probability Distribution, Sinc Approximation, Cardinal Function, Fourier Transform, Wavelet
JOURNAL NAME:
Applied Mathematics,
Vol.1 No.6,
December
27,
2010
ABSTRACT: We consider the problem of approximating two, possibly unrelated probability distributions from a single complex-valued function and its Fourier transform. We show that this problem always has a solution within a specified degree of accuracy, provided the distributions satisfy the necessary regularity conditions. We describe the algorithm and construction of and provide examples of approximating several pairs of distributions using the algorithm.