VLSI Digital Signal Processing Systems: Design and Implementation

11.1    INTRODUCTION

When a digital filter transfer function is implemented using a digital system, it invariably involves quantization of signals and coefficients in the system. As a result, the overall input-output behavior is not ideal. There are two basic types of quantization effects in any implementation [1],[2]. The first is due to parameter (coefficient) quantization. The result of parameter quantization is that the actual implemented transfer function is different from the ideal transfer function. In fixed-point VLSI implementations or software implementations using fixed-point programmable DSPs, study of finite wordlength behavior in digital filters is extremely important.

The second type of quantization is due to signal rounding. The internal signals in a digital filter are invariably subject to quantization, causing an error in the computed output. Such quantization is clearly a nonlinear phenomenon and can be further subdivided into two types of effects, i.e., limit-cycle oscillations and roundoff noise. Limit-cycle oscillations can be defined as undesirable periodic components at the filter output and are due to the fact that quantization is a nonlinear operation. Notice that oscillations are always possible when there exist nonlinear operations in feedback paths. Conversely, roundoff noise affects the filter output in the form of a random disturbance and can be analyzed by suitable noise modeling and by the use of linear system theory.

In addition to the parameter ...