The Application of Dither to the Quantization of Speech Signals
Nikil S. Jayant, L. R. Rabiner · Bell System Technical Journal · 1972
By adding a pseudo-random “dither” noise to a signal X that is to be quantized, and by subtracting an identical noise sequence from the quantizer output, it is possible to break up undesirable signal-dependent patterns in the quantization error sequence, without increasing the variance of the error E. The idea has been widely discussed in the context of picture coding, and it is the purpose of this paper to demonstrate application of the technique to the quantization of speech signals. Computer simulations have shown how the use of dither whitens the quantization error sequence in PCM encoding, and renders it more acceptable than signal-correlated errors of equal variance. We demonstrate, for conditions of dither and no dither, typical speech recordings, illustrative error waveforms, and data on signal-to-error correlation C, and indicate how the advantage of dithering increases monotonically with crudeness of signal quantization and becomes significant when the number of bits per sample is less than about six. While the parameter C is a simple criterion for demonstrating the effect of dither, it must be emphasized that the truly relevant criterion is the statistical independence of E and X, and not merely the decorrelation of these functions. Thus, for example, we show that for the case of a reciprocal PDF (probability density function) for X, a zero value of C can be achieved without dither. For purposes of implementation, it is desirable to employ dither noise values characterized by a discrete PDF, with a support that is equal to an integral multiple of the step-size Δxin the quantizer. We show that for effective dithering, the step-size ΔNin the noise PDF need be no smaller, typically, than Δx/4. Finally, we indicate an application of dither to the quantization of speech signals by delta modulation.