An Inverse Self-Convolution Algorithm for Probabilistic Distribution Estimation

Abstract

In this paper, an inverse self-convolution algorithm for probabilistic distribution estimation is proposed. The Fourier transform of the self-convolution is the square of the Fourier transform of the original function. Therefore, the calculation of the square root of the Fourier transform makes it possible to calculate inverse self-convolution. However, it is not straightforward to calculate inverse self-convolution because the square root of the complex number is not determined uniquely. To deal with this difficulty, we preprocess the data sequence to enhance the smoothness of the discrete Fourier transform, and extrapolate the complex number by means of the polynomial approximation.