# Convolution of two probability distributions using FFT

by jamie_m
Tags: convolution, convolution theorem, fft
 Sci Advisor P: 3,252 Perhaps it's "circular convolution" $(p*q)_n = \sum_{m=0}^3 { p_m q_{n-m} }$ e.g. $(p*q)_0 = \sum_{m = 0}^3 {p_m} q_{0-m}$ $= p_0 q_0 + p_1 q_{-1} + p_2 q_{-2} + p_3 q_{-3}$ Where we regard $q_{-1} = q_3 , q_{-2}= q_2$ etc $= (0.1)(0.4) + (0.2)(0.1) + (0.3)(0.2) + (0.4)(0.3) = 0.24$
 Quote by Stephen Tashi Perhaps it's "circular convolution" $(p*q)_n = \sum_{m=0}^3 { p_m q_{n-m} }$