Title :
Moment preserving quantization [signal processing]
Author :
Delp, Edward J. ; Mitchell, Owen Robert
Author_Institution :
Sch. of Electr. Eng., Purdue Univ., West Lafayette, IN, USA
fDate :
11/1/1991 12:00:00 AM
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;
Journal_Title :
Communications, IEEE Transactions on
