tailieunhanh - 06 Quantization of Discrete Time Signals

Signals are usually classified into four categories. A continuous time signal has the field of real numbers R as its domain in that t can assume any real value. | Ramachandran . Quantization of Discrete Time Signals Digital Signal Processing Handbook Ed. Vijay K. Madisetti and Douglas B. Williams Boca Raton CRC Press LLC 1999 1999 by CRC Press LLC Quantization of Discrete Time Signals Ravi P. Ramachandran Rowan University Introduction Basic Definitions and Concepts Quantizer and Encoder Definitions Distortion Measure Optimality Criteria Design Algorithms Lloyd-Max Quantizers Linde-Buzo-Gray Algorithm Practical Issues Specific Manifestations Multistage VQ Split VQ Applications Predictive Speech Coding Speaker Identification Summary References Introduction Signals are usually classified into four categories. A continuous time signal x t has the field of real numbers R as its domain in that t can assume any real value. If the range of x t values that x t can assume is also R then x t is said to be a continuous time continuous amplitude signal. If the range of x t is the set of integers Z then x t is said to be a continuous time discrete amplitude signal. In contrast a discrete time signal x n has Z as its domain. A discrete time continuous amplitude signal has R as its range. A discrete time discrete amplitude signal has Z as its range. Here the focus is on discrete time signals. Quantization is the process of approximating any discrete time continuous amplitude signal into one of a finite set of discrete time continuous amplitude signals based on a particular distortion or distance measure. This approximation is merely signal compression in that an infinite set of possible signals is converted into a finite set. The next step of encoding maps the finite set of discrete time continuous amplitude signals into a finite set of discrete time discrete amplitude signals. A signal x n is quantized one block at a time in that p almost always consecutive samples are taken as a vector x and approximated by a vector y. The signal or data vectors x of dimension p derived from x n are in the vector space .