Projection of a spherical distribution and its inversion

Author

Blachman, Nelson M.

Author_Institution

GFT Gov. Syst. Corp., Mountain View, CA, USA

Volume

39

Issue

11

fYear

1991

fDate

11/1/1991 12:00:00 AM

Firstpage

2544

Lastpage

2547

Abstract

A single integral expresses the projection of a spherically (or circularly) symmetric distribution on a space of n dimensions onto a subspace (or plane or line) of m<n dimensions. This transformation is inverted by a derivative of order ( n-m)/2, which, for odd (n-m), is given by a single integral. These relationships are applied to several examples that illuminate the interrelations among a number of classical probability distributions and reveal the probability density function of the angle between a unit n-dimensional vector with uniformly distributed direction and any m-dimensional subspace

Keywords

information theory; probability; signal processing; circularly symmetric distribution; information theory; inversion; m-dimensional subspace; n-dimensional vector; probability density function; probability distributions; signal processing; single integral; spherical distribution projection; Fourier transforms; Gaussian channels; Gaussian distribution; Gaussian noise; Government; Interference; Maxwell-Boltzmann distribution; Narrowband; Probability density function;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.98010

Filename

98010