ABSTRACT
This chapter provides a brief overview of the finite word lengths (FWL) effects in digital filter implementations. It presents the fixed-point and floating-point number representations, the two representations used in most digital signal processing (DSP) chips and discusses finite word-lengths effects in fixed-point implementations. The chapter also presents some of the approaches in the analysis of quantization errors in fixed-point arithmetic implementations. There is the possibility that the output of the filter exhibits limit cycles due to overflow and becomes independent of the input signal. The coefficients of a digital filter implementation are the rounded or truncated filter coefficients obtained during design. Overflow may occur when two fixed-point numbers are added. If the magnitude of the result exceeds the dynamic range available, then an overflow has occurred which causes errors in the computations. The introduction of floating-point DSP chips has made the implementation of digital filters using floating-point arithmetic feasible even for many real-time applications.
