The Application of Dither to the Quantization of Speech Signals

Signal quantizers, in general, produce quantization error sequences that have signal-dependent patterns. The perceptibility of such patterns 1293 1294 T H E BELL SYSTEM TECHNICAL JOURNAL, J U L Y - A U G U S T 1972 tends to be very small for quantizations that are fine enough to provide practically useful signal-to-error ratios; while with relatively cruder quantizations, the perceptibility of signal-dependent errors increases to a point where techniques that can make the errors independent of signal samples become very attractive, even if they do not decrease the error variance itself. Dithering 1 is precisely such a scheme. It is based on the concept of forcing the quantization error E, conditional to a given input X, to be a zero-mean random variable, rather than a deterministic function of X. The randomization of conditional error E{X) is accomplished by the addition of a random dither noise sample N to the input, and quantizing {X + N) instead of X. The use of a pseudo-random dither sample N permits the subtraction of N from the quantizer output (X + N) Q , and this insures an error variance that is essentially no greater than that in the undithered system. Roberts 1 provided an excellent demonstration of the above concept in his pioneering paper on the use of dither for picture coding. Subsequent work on dither 2,3 has also referred to picture signals. Specifically, Limb2 has studied application to differential quantizers, and Lippel, et al.,3 have demonstrated the use of two-dimensional, non-random dither patterns the inherent low visibility of which makes dither subtraction from (X + N)Q irrelevant, perceptually.