Digital Signal Processing

Transcription

1 Digital Signal Processing Everything you need to know to get started Michael Parker Altera Corporation AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO Newnes is an imprint of Elsevier

2 Newnes is an imprint of Elsevier 30 Corporate Drive, Suite 400, Burlington, MA 01803, USA The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, UK 2010 ELSEVIER Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. Library of Congress Cataloging-in-Publication Data Parker, Michael, Digital signal processing 101: everything you need to know to get started / Michael Parker. p. cm. Includes bibliographical references and index. ISBN (alk. paper) 1. Signal processing Digital techniques. I. Title. TK P dc British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. For information on all Newnes publications visit our Web site at Printed in the United States of America

3 Table of Contents Introduction viii Acknowledgments x Chapter 1: Numerical Representation Integer Fixed-Point Representation Fractional Fixed-Point Representation Floating-Point Representation Chapter 2: Complex Numbers and Exponentials Complex Addition and Subtraction Complex Multiplication Complex Conjugate The Complex Exponential Measuring Angles in Radians Chapter 3: Sampling, Aliasing, and Quantization Nyquist Sampling Rule Quantization Chapter 4: Frequency Response Frequency Response and the Complex Exponential Normalizing Frequency Response Sweeping across the Frequency Response Example Frequency Responses Linear Phase Response Normalized Frequency Response Plots Chapter 5: Finite Impulse Response (FIR) Filters FIR Filter Construction Computing Frequency Response Computing Filter Coefficients Effect of Number of Taps on Filter Response Chapter 6: Windowing Truncation of Coefficients Tapering of Coefficients Example Coefficient Windows iii

4 iv Table of Contents Chapter 7: Decimation and Interpolation Decimation Interpolation Resampling by Non-Integer Value Chapter 8: Infinite Impulse Response (IIR) Filters IIR and FIR Filter Characteristic Comparison Bilinear Transform Frequency Prewarping Chapter 9: Complex Modulation and Demodulation Modulation Constellations Modulated Signal Bandwidth Pulse-Shaping Filter Raised Cosine Filter Chapter 10: Discrete and Fast Fourier Transforms (DFT, FFT) DFT and IDFT Equations Fast Fourier Transform (FFT) Filtering Using the FFT and IFFT Bit Growth in FFTs Bit-Reversal Addressing Chapter 11: Digital Upconversion and Downconversion Digital Upconversion Digital Downconversion IF Subsampling Chapter 12: Error Correction Coding Linear Block Encoding Linear Block Decoding Minimum Coding Distance Convolutional Encoding Viterbi Decoding Soft Decision Decoding Cyclic Redundancy Check Shannon Capacity and Limit Theorems Chapter 13: Analog and TDMA Wireless Communications Early Digital Innovations Frequency Modulation Digital Signal Processor Digital Voice Phone Systems TDMA Modulation and Demodulation

5 Table of Contents v Chapter 14: CDMA Wireless Communications Spread Spectrum Technology Direct Sequence Spread Spectrum Walsh Codes Concept of CDMA Walsh Code Demodulation Network Synchronization RAKE Receiver Pilot PN Codes CDMA Transmit Architecture Variable Rate Vocoder Soft Handoff Uplink Modulation Power Control Higher Data Rates Spectral Efficiency Considerations Other CDMA Technologies Chapter 15: OFDMA Wireless Communications WiMax and LTE OFDMA Advantages Orthogonality of Periodic Signals Frequency Spectrum of Orthogonal Subcarrier OFDM Modulation Intersymbol Interference and the Cyclic Prefix MIMO Equalization OFDMA System Considerations OFDMA Spectral Efficiency OFDMA Doppler Frequency Shift Peak to Average Ratio Crest Factor Reduction Digital Predistortion Remote Radio Head Chapter 16: Radar Basics Radar Frequency Bands Radar Antennas Radar Range Equation Stealth Aircraft Pulsed Radar Operation Pulse Compression Pulse Repetition Frequency Detection Processing

6 vi Table of Contents Chapter 17: Pulse Doppler Radar Doppler Effect Pulsed Frequency Spectrum Doppler Ambiguities Radar Clutter PRF Trade-offs Target Tracking Chapter 18: Synthetic Array Radar SAR Resolution Pulse Compression Azimuth Resolution SAR Processing SAR Doppler Processing SAR Impairments Chapter 19: Introduction to Video Processing Color Spaces Interlacing Deinterlacing Image Resolution and Bandwidth Chroma Scaling Image Scaling and Cropping Alpha Blending and Compositing Video Compression Video Interfaces Chapter 20: Implementation Using Digital Signal Processors DSP Processor Architectural Enhancements Scalability Floating Point Design Methodology Managing Resources Ecosystem Chapter 21: Implementation Using FPGAs FPGA Design Methodology DSP Processor or FPGA Choice Design Methodology Considerations Dedicated DSP Circuit Blocks in FPGAs Floating Point in FPGAs Ecosystem Future Trends

7 Table of Contents vii Appendix A: Q Format Shift with Fractional Multiplication Appendix B: Evaluation of FIR Design Error Minimization Appendix C: Laplace Transform Appendix D: Z-Transform Appendix E: Binary Field Arithmetic Index

8 Introduction This book is intended for those who work in or provide components for industries that are made possible by digital signal processing, or DSP. Sample industries are wireless mobile phone and infrastructure equipment, broadcast and cable video, DSL modems, satellite communications, medical imaging, audio, radar, sonar, surveillance, electrical motor control this list goes on. While the engineers who implement these systems must be very familiar with DSP, there are many others executive and midlevel management, marketing, technical sales and field engineers, business development, and others who can benefit from a basic knowledge of the fundamental principles of DSP. Others who are a potential audience include those interested in studying or working in any of these areas. High school seniors or undeclared college majors considering a future in the industries made possible by DSP technology may gain sufficient understanding that enables them to decide whether to continue further. That, then, is the purpose of this book: to provide a basic tutorial on DSP. This topic seems to have a dearth of easy-to-read and understand explanations. Unlike most technical resources, this is a treatment in which mathematics is minimized and intuitive understanding maximized. This book attempts to explain many difficult concepts like sampling, aliasing, imaginary numbers, and frequency response using easy-to-understand examples. In addition, there is an overview of the DSP functions and implementation used in several DSP-intensive fields or applications, from error correction to CDMA mobile communication to airborne radar systems. So this book is intended for those of you who, like me, are somewhat dismayed when presented with a blackboard (or whiteboard) full of equations as an explanation on DSP. The intended readers include those who have absolutely no previous experience with DSP, but are comfortable with high-school-level math skills. Many technical details have been deliberately left out, in order to emphasize just the key concepts. While this book is not expected to be used as a university-course-level text, it can initiate readers prior to tackling a proper text on DSP. But it may also be all you need to talk intelligently to other people involved in a DSP-centric industry and understand many of the fundamental concepts. viii

9 Introduction ix To start with, just what is DSP? Well, DSP is performing operations on a digital signal of some sort and using a digital semiconductor device. Most commonly, multipliers and adders are used. If you can multiply and add, you can probably understand DSP. Actually, signal processing was around long before digital electronics. Examples of this are radios and TVs. Early tuners used analog circuits with variable capacitors to dial a station. Resistors, capacitors, and vacuum tubes were used to either attenuate or amplify different frequencies or to provide frequency shifting. These are examples of basic signal processing applications. The signals were analog signals, and the circuits doing the processing were analog, as was the final output. Today, most signal processing is performed digitally. The reason is that digital circuits have progressively become cheaper and faster, as well as due to the inherent advantages of repeatability, tolerance, and consistency that digital circuits enjoy compared to analog circuits. If the signal is not in a digital form, then it must first by converted, or digitized. A device called an analog-to-digital converter (ADC) is used. If the output signal needs to be analog, then it is converted back using a digital-to-analog converter (DAC). Of course, many signals are already digitized and can be processed by digital circuits directly. DSP is at the heart of a wide range of everyday devices in our lives, although many people are unaware of this. A few everyday examples are cellular phones, DSL modems, digital hearing aids, MRI and ultrasound equipment, audio equipment, set top boxes, flat-screen televisions, satellite communications, and DVD players. As promised, the mathematics will be minimized, but it cannot be eliminated altogether. Some basic trigonometry and the use of complex numbers are unavoidable, so an early chapter is included to introduce these concepts, using as simple examples as possible. There is also one appendix section where very basic calculus is used, but this is not essential to the overall understanding.

10 Acknowledgments This book grew out of a need for Altera marketing and technical sales people to have an intuitive-level understanding of DSP fundamentals and applications, in order to better work on issues that our customers face as they implement DSP systems. I am grateful to the Altera management for the support this book has received, in particular from Steve Mensor and Chris Balough. My understanding of the topics in this book is based on many years of engineering implementation work and collaboration and explanations from many of my colleagues at multiple firms over the years. More recently, within Altera, many people have contributed to my knowledge in these areas. I would like to especially acknowledge a few people who have been helpful both in DSP domain and relevant applications and implementations. Within Altera engineering, this includes Volker Mauer, Martin Langhammer, and Mike Fitton. Within the Altera technical sales organization, people who have been especially helpful to my understanding of some of the relevant DSP applications include Colman Cheung, Ben Esposito, Brian Kurtz, and Mark Santoro. Within Altera publications, James Adams has been instrumental in getting this project off the ground and working with the publisher. Finally, the support of my wife, Zaida, and daughter, Ariel, have been most important. This book has been primarily an evenings and weekends project, and their patience has been essential. x