Finite Wordlength Effects

Practical digital filters must be implemented with finite precision numbers and arithmetic. As a result, both the filter coefficients and the filter input and output signals are in discrete form. This leads to four types of finite wordlength effects. Discretization (quantization) of the filter coefficients has the effect of perturbing the location of the

filter poles and zeros. As a result, the actual filter response differs slightly from the ideal response. This deterministic frequency response error is referred to as coefficient quantization error. The use of finite precision arithmetic makes it necessary to quantize filter calculations by rounding or

truncation. Roundoff noise is that error in the filter output that results from rounding or truncation calculations within the filter. As the name implies, this error looks like low-level noise at the filter output. Quantization of the filter calculations also renders the filter slightly nonlinear. For large signals this

nonlinearity is negligible and roundoff noise is the major concern. However, for recursive filters with a zero or constant input, this nonlinearity can cause spurious oscillations called limit cycles. With fixed-point arithmetic it is possible for filter calculations to overflow. The term overflow oscilla-

tion, sometimes also called adder overflow limit cycle, refers to a high-level oscillation that can exist in an otherwise stable filter due to the nonlinearity associated with the overflow of internal filter calculations. In this chapter, we examine each of these finite wordlength effects. Both fixed-point and floating-point

number representations are considered.