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CHAPTER 10
Round-off Effects
in Digital Filters
In the latter part of Chapter 6 we discussed the finite-precision number
representations for the purpose of implementing filtering operations
on digital hardware. In particular, we focused on the process of number
quantization, the resulting error characterizations, and the effects of filter
coefficient quantization on filter specifications and responses. In this
chapter, we further extend the effects of finite-precision numerical effects
to the filtering aspects in signal processing.
We begin by discussing analog-to-digital (A/D) conversion noise using
the number representations and quantization error characteristics developed
in Chapter 6. We then analyze the multiplication and addition
quantization (collectively known as arithmetic round-off error) models.
The effects of these errors on filter output are discussed as two topics:
correlated errors called limit cycles and uncorrelated round-off noise.
10.1 ANALYSIS OF A/D QUANTIZATION NOISE
From the quantizer characteristics obtained in Chapter 6, it is obvious
that the quantized value Q[x] isanonlinear operation on the value x.
Hence the exact analysis of the finite word-length effects in digital filters
is generally difficult and one has to consider less ideal analysis techniques
that work well in practice.
One such technique is the statistical modeling technique. It converts
the nonlinear analysis problem into a linear one and allows us to examine
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