Gersho's bounds on the asymptotic performance of vector quantizers are valid for vector distortions which are powers of the Euclidean norm. Yamada, Tazaki and Gray generalized the results to distortion measures that are increasing functions of the norm of their argument. In both cases, the distortion is uniquely determined by the vector quantization error, i.e., the Euclidean difference between the original vector and the codeword into which it is quantized. We generalize these asymptotic bounds to input-weighted quadratic distortion measures, a class of distortion measure often used for perceptually meaningful distortion. The generalization involves a more rigorous derivation of a fixed rate result of Gardner and Rao and a new result for variable rate codes. We also consider the problem of source mismatch, where the quantizer is designed using a probability density different from the true source density. The resulting asymptotic performance in terms of distortion increase in dB is shown...

Packet speech on the Arpanet: A history of early LPC speech and its accidental impact on the

Optimal 1-step prediction ¿ What is the optimal predictor of the form ˜ Xm = p(X0,..., Xm−1)? Optimal 1-step linear prediction ¿ What is the optimal linear predictor of the form ˜ Xm = − � m l=1 alXm−l? Modeling/density estimation ¿ What is the probability density function (pdf) that “best ” models X m? Spectrum Estimation ¿ What is the “best ” estimate of the power spectral density or covariance of the underyling random process? California Coding 3 The Application Speech Coding ¿ How apply linear prediction to produce low bit rate speech of sufficient quality for speech understanding and speaker recognition? Wide literature exists on all of these topics in a speech context and they are intimately related. See, e.g., J. Makhoul’s classic survey [35] and J.D. Markel and A.H. Gray’s classic book [41]. Clearly problems ill-posed unless define terms like “optimal” and assume some structure.