Moment preserving quantization [signal processing]

Author

Delp, Edward J. ; Mitchell, Owen Robert

Author_Institution

Sch. of Electr. Eng., Purdue Univ., West Lafayette, IN, USA

Volume

39

Issue

11

fYear

1991

fDate

11/1/1991 12:00:00 AM

Firstpage

1549

Lastpage

1558

Abstract

The general solution to the moment-preserving (MP) quantizer problem is presented. It is shown that the moment preserving quantizer is related to the Gauss-Jacobi mechanical quadrature, the output levels of the N-level MP quantizer are the N zeros of an Nth degree orthogonal polynomial associated with the input probability distribution function, and the N-1 thresholds of the MP quantizer are related to the Christoffel numbers through the Chebyshev-Markov-Stieltjes separation theorem. The statistical convergence of the MP quantizer is investigated. MP quantizer tables are presented for the uniform, Gaussian, and Laplacian density functions. The moment-preserving quantizer is shown to be related to block truncation coding

Keywords

data compression; encoding; signal processing; statistical analysis; Chebyshev-Markov-Stieltjes separation theorem; Christoffel numbers; Gauss-Jacobi mechanical quadrature; Gaussian density functions; Laplacian density functions; MP quantizer tables; block truncation coding; data compression; encoding; input probability distribution; moment preserving quantizer; orthogonal polynomial; signal processing; statistical convergence; Gaussian processes; Image coding; Image processing; Mean square error methods; Polynomials; Probability distribution; Pulse modulation; Quantization; Random variables; Signal processing;

fLanguage

English

Journal_Title

Communications, IEEE Transactions on

Publisher

ieee

ISSN

0090-6778

Type

jour

DOI

10.1109/26.111432

Filename

111432