مرکز منطقه ای اطلاع رساني علوم و فناوري - Moments of the sum of circularly symmetric random variables (Corresp.)

DocumentCode :

917258

Title :

Moments of the sum of circularly symmetric random variables (Corresp.)

Author :

Goldman, Joel

Volume :

Issue :

fYear :

1972

fDate :

3/1/1972 12:00:00 AM

Firstpage :

297

Lastpage :

298

Abstract :

Let $(X_1,Y_1), \\cdots ,(X_N, Y_N)$ be $N$ independent pairs of circularly symmetric random variables, A simple expression is derived for the even moments of the (Euclidean) norm of the vector sum $(X_1, Y_1)$ + $\\cdots + (X_N, Y_N)$ in terms of the moments of $(X_i ^2 + Y_i ^2)^{1/2}, i = 1,\\cdots ,N$ . As an application of our results we find an expression for the moments of the "envelope" of a sum of randomly phased cosinusoids.