Abstract
In this chapter, we discuss finite wordlengths effects in digital algorithms, i.e., overflow of the number range, quantization and roundoff errors, aliasing, and coefficient errors. We also discuss fixed-point number representations, i.e., two´complement, sign-magnitude, and redundant representations and their quantisation errors. We demonstrate that parasitic oscillations are important issues in recursive algorithms. We show how to scale the signal levels in critical overflow nodes by using Lp-norms. We also show how to determine the quantisation and roundoff noise in several structures and how it can be reduced by using error spectrum shaping. Finally, we derive an important relationship between coefficient sensitivity and roundoff noise. The chapter contains 13 solved examples.
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