3 - Quantization in digital filters

Abstract

This chapter discusses the quantization and the method used for the reduction of quantization noise. Quantization is widely employed in many signal processing applications, such as data compression and analog-to-digital conversion. Quantization noise is usually assumed to be a wide-sense stationary white process with each input sample being uniformly distributed over the range of the quantization error. In order to approximate quantization as a polynomial function, a polynomial fitting technique is employed. Since the quantization function is an odd function, all coefficients associated to the even power terms are zero, and the polynomial with only odd power terms is enough for the approximation. It is found that if the quantizer can be modeled by a polynomial, then the quantizer performs a weighted sum of multiplications of the input signal in the time domain. In the frequency domain, the quantizer performs a weighted sum of convolutions of the input signal. It is observed that in order to design an optimal code such that the signal-to-noise ratio is maximized, a modified gradient descent method is employed.