Transactions Papers 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 associ- ated 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 pre- sented for the uniform, Gaussian and Laplacian density functions. The moment preserving quantizer is shown to be related to block truncation coding.

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