MOMENT PRESERVING QUANTIZATION

In this paper, we present a new criteria for quantizer design whereby moments of the input and output of the quantizer are preserved. The moment preserving (MP) quantizer is shown to be related to the Gauss-Jacobi mechanical quadrature. The output levels of the N-level MP quantizer are shown to be the N zeros of an Nth degree orthogonal polynomial associated with the input probability distribution function. The N-1 thresholds of the MP quantizer are shown to be related to the Christoffel numbers through the Separation Theorem of Chebyshev-Markov-Stieltjes. The statistical convergence of the MP quantizer is also 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.