Fixed-point signal processing [electronic resource] / Wayne T. Padgett, David V. Anderson.

Padgett, Wayne Thomas, 1965-
[San Rafael, Calif.] : Morgan & Claypool, c2009.
Synthesis Lectures on Signal Processing ; #9.
Synthesis Lectures on Signal Processing, 1932-1236 ; #9
1 online resource (ix, 121 p.) : col. ill
Signal processing -- Digital techniques -- Mathematics.
System Details:
Mode of access: World Wide Web.
This book is intended to fill the gap between the "ideal precision" digital signal processing (DSP) that is widely taught, and the limited precision implementation skills that are commonly required in fixed-point processors and field programmable gate arrays (FPGAs). These skills are often neglected at the university level, particularly for undergraduates. We have attempted to create a resource both for a DSP elective course, and for the practicing engineer with a need to understand fixed-point implementation. Although we assume a background in DSP, Chapter 2 contains a review of basic theory, and Chapter 3 reviews random processes to support the noise model of quantization error. Chapter 4 details the binary arithmetic that underlies fixed-point processors, and then introduces fractional format for binary numbers. Chapter 5 covers the noise model for quantization error and the effects of coefficient quantization in filters. Because of the numerical sensitivity of IIR filters, they are used extensively as an example system in both Chapters 5 and 6. Fortunately, the principles of dealing with limited precision can be applied to a wide variety of numerically sensitive systems, not just IIR filters. Chapter 6 discusses the problems of product roundoff error, and various methods of scaling to avoid overflow. Chapter 7 discusses limit cycle effects and a few common methods for minimizing them. There are a number of simple exercises integrated into the text to allow you to test your understanding. Answers to the exercises are included in the footnotes. A number of Matlab examples are provided in the text. They generally assume access to the Fixed- Point Toolbox. If you lack access to this software, consider either purchasing or requesting an evaluation license from The Mathworks. The code listed in the text and other helpful Matlab code is also available at and You will also find Matlab exercises designed to demonstrate each of the four types of error discussed in Chapters 5 and 6. Simulink examples are also provided on the web site.
1. Getting started
Design flow
2. DSP concepts
Basic systems theory
Linear, time-invariant systems
Difference equations
Poles and zeros
Block diagrams and filter implementation
Transpose filters
Cascaded second-order sections
Frequency response
Frequency response from the z-transform
Frequency response examples
3. Random processes and noise
Random variables
Expectations and moments
Stationary and ergodic processes
Definitions and properties
Random processes and Fourier analysis
Fourier transform of correlation and covariance
Power spectral density
Filtering a random sequence
Filtering a white random sequence
4. Fixed point numbers
Binary arithmetic
Unsigned binary representation
Signed binary representation
Fixed-point arithmetic
An FIR filter example
Quantization example, computing y[0]
Quantization example, computing y[1]
Quantization example, results
Matlab example
Block floating-point.
Title from PDF title page (Morgan & Claypool, viewed Sept. 30, 2009).
Includes bibliographical references (p. 119-121).
Anderson, David Verl, 1968-
Other format:
Print version:
9781598292596 (ebook)
1598292595 (ebook)
1598292587 (pbk.)
9781598292589 (pbk.)
Publisher Number:
10.2200/S00220ED1V01Y200909SPR009 doi
Access Restriction:
Restricted for use by site license.
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