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

- Publication:
- [San Rafael, Calif.] : Morgan & Claypool, c2009.
- Series:
- Synthesis Lectures on Signal Processing ; #9.

Synthesis Lectures on Signal Processing, 1932-1236 ; #9 - Format/Description:
- Book

1 online resource (ix, 121 p.) : col. ill - Subjects:
- Signal processing -- Digital techniques -- Mathematics.
- System Details:
- Mode of access: World Wide Web.
- Summary:
- 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 http://www.morganclaypool.com/page/padgett and http://www.rose-hulman.edu/padgett/fpsp. 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.
- Contents:
- 1. Getting started

Design flow

Tools

2. DSP concepts

Basic systems theory

Linear, time-invariant systems

Difference equations

Convolution

Z-transform

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

Periodograms

4. Fixed point numbers

Binary arithmetic

Unsigned binary representation

Addition

Subtraction

Multiplication

Division

Signed binary representation

Q-format

Fixed-point arithmetic

Multiplication

Addition

Rounding

An FIR filter example

Quantization example, computing y[0]

Quantization example, computing y[1]

Quantization example, results

Matlab example

Floating-point

Block floating-point. - Notes:
- Title from PDF title page (Morgan & Claypool, viewed Sept. 30, 2009).

Includes bibliographical references (p. 119-121). - Contributor:
- Anderson, David Verl, 1968-
- Other format:
- Print version:
- ISBN:
- 9781598292596 (ebook)

1598292595 (ebook)

1598292587 (pbk.)

9781598292589 (pbk.) - OCLC:
- 441946587
- Publisher Number:
- 10.2200/S00220ED1V01Y200909SPR009 doi
- Access Restriction:
- Restricted for use by site license.
- Online:
- Connect to full text.

http://hdl.library.upenn.edu/1017.12/498431Connect to full text (PDF format).

http://hdl.library.upenn.edu/1017.12/498432 -
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