Applied Digital Signal Processing Theory and Practice

In theory, all signal samples, filter coefficients, twiddle factors, other quantities, and the results of any computations, can assume any value, that is, they can be represented with infinite accuracy. However, in practice, any number must be represented in a digital computer or other digital hardware using a finite number of binary digits (bits), that is, with finite accuracy. In most applications, where we use personal computers or workstations with floating point arithmetic processing units, numerical precision is not an issue. However, in analog-to-digital converters, digital-to-analog converters, and digital signal processors that use fixed-point number representations, use of finite wordlength may introduce unacceptable errors. Finite wordlength effects are caused by nonlinear operations and are very complicated, if not impossible, to understand and analyze. Thus, the most effective approach to analyze finite wordlength effects is to simulate a specific filter and evaluate its performance. Another approach is to use statistical techniques to derive approximate results which can be used to make educated decisions in the design of A/D converters, D/A converters, and digital filters. In this chapter we discuss several topics related to the effects of finite wordlength in digital signal processing systems.

Study objectives

After studying this chapter you should be able to:

• Understand the implications of binary fixed-point and floating-point representation of numbers for signal representation and DSP arithmetic operations.

• Understand how to use a statistical quantization model to analyze the operation of A/D and D/A converters incorporating oversampling and noise shaping.

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