Digital Signal Processing with Field Programmable Gate Arrays

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1 Uwe Meyer-Baese Digital Signal Processing with Field Programmable Gate Arrays Third Edition With 359 Figures and 98 Tables Book with CD-ROM ei Springer

2 Contents Preface Preface to Second Edition Preface to Third Edition VII XI XIII 1. Introduction Overview of Digital Signal Processing (DSP) FPGA Technology Classification by Granularity Classification by Technology Benchmark for FPLs DSP Technology Requirements FPGA and Programmable Signal Processors Design Implementation FPGA Structure The Altera EP2C35F672C Case Study: Frequency Synthesizer Design with Intellectual Property Cores 35 Exercises Computer Arithmetic Introduction Number Representation Fixed-Point Numbers Unconventional Fixed-Point Numbers Floating-Point Numbers Binary Adders Pipelined Adders Modulo Adders Binary Multipliers Multiplier Blocks Binary Dividers Linear Convergence Division Algorithms 93

3 XVI Contents Fast Divider Design Array Divider Floating-Point Arithmetic Implementation Fixed-point to Floating-Point Format Conversion Floating-Point to Fixed-Point Format Conversion Floating-Point Multiplication Floating-Point Addition Floating-Point Division Floating-Point Reciprocal Floating-Point Synthesis Results Multiply-Accumulator (MAC) and Sum of Product (SOP) Distributed Arithmetic Fundamentals Signed DA Systems Modified DA Solutions Computation of Special Functions Using CORDIC CORDIC Architectures Computation of Special Functions using MAC Calls Chebyshev Approximations Trigonometrie Function Approximation Exponential and Logarithmic Function Approximation Square Root Function Approximation 148 Exercises Finite Impulse Response (FIR) Digital Filters Digital Filters FIR Theory FIR Filter with Transposed Structure Symmetry in FIR Filters Linear-phase FIR Filters Designing FIR Filters Direct Window Design Method Equiripple Design Method Constant Coefficient FIR Design Direct FIR Design FIR Filter with Transposed Structure FIR Filters Using Distributed Arithmetic IP Core FIR Filter Design Comparison of DA- and RAG-Based FIR Filters 207 Exercises Infinite Impulse Response (IIR) Digital Filters IIR Theory IIR Coefficient Computation Summary of Important IIR Design Attributes IIR Filter Implementation 224

4 Contents XVII Finite Wordlength Effects Optimization of the Filter Gain Factor Fast IIR Filter Time-domain Interleaving Clustered and Scattered Look-Ahead Pipelining IIR Decimator Design Parallel Processing IIR Design Using RNS 239 Exercises Multirate Signal Processing Decimation and Interpolation Noble Identities Sampling Rate Conversion by Rational Factor Polyphase Decomposition Recursive HR Decimator Fast-running FIR Filter Hogenauer CIC Filters Single-Stage CIC Case Study Multistage CIC Filter Theory Amplitude and Aliasing Distortion Hogenauer Pruning Theory CIC RNS Design Multistage Decimator Multistage Decimator Design Using Goodman Carey Half-band Filters Frequency-Sampling Filters as Bandpass Decimators Design of Arbitrary Sampling Rate Converters Fractional Delay Rate Change Polynomial Fractional Delay Design B-Spline-Based Fractional Rate Changer MOMS Fractional Rate Changer Filter Banks Uniform DFT Filter Bank Two-channel Filter Banks Wavelets The Discrete Wavelet Transformation 332 Exercises Fourier Transforms The Discrete Fourier Transform Algorithms Fourier Transform Approximations Using the DFT Properties of the DFT The Goertzel Algorithm The Bluestein Chirp-z Transform 350

5 XVIII Coatcuts The Rader Algorithm The Winograd DFT Algorithm The Fast Fourier Transform (FFT) Algorithms The Cooley Tukey FFT Algorithm The Good Thomas FFT Algorithm The Winograd FFT Algorithm Comparison of DFT and FFT Algorithms IP Core FFT Design Fourier-Related Transforms Computing the DCT Using the DFT Fast Direct DCT Implementation 388 Exercises Advanced Topics Rectangular and Number Theoretic Transforms (NTTs) Arithmetic Modulo 2 6 ± Eflicient Convolutions Using NTTs Fast Convolution Using NTTs Multidimensional Index Maps Computing the DFT Matrix with NTTs Index Maps for NTTs Using Rectangular Transforms to Compute the DFT Error Control and Cryptography Basic Concepts from Coding Theory Block Codes Convolutional Codes Cryptography Algorithms for FPGAs Modulation and Demodulation Basic Modulation Concepts Incoherent Demodulation Coherent Demodulation 463 Exercises Adaptive Filters Application of Adaptive Filter Interference Cancellation Prediction Inverse Modeling Identification Optimum Estimation Techniques The Optimum Wiener Estimation The Widrow Hoff Least Mean Square Algorithm Learning Curves Normalized LMS (NLMS) Transform Domain LMS Algorithms 498

6 Contents XIX Fast-Convolution Techniques Using Orthogonal Transforms Implementation of the LMS Algorithm Quantization Effects FPGA Design of the LMS Algorithm Pipelined LMS Filters Transposed Form LMS Filter Design of DLMS Algorithms LMS Designs using SIGNUM Function Recursive Least Square Algorithms RLS with Finite Memory Fast RLS Kaiman Implementation The Fast a Posteriori Kaiman ELS Algorithm Comparison of LMS and RLS Parameters 530 Exercises Microprocessor Design History of Microprocessors Brief History of General-Purpose Microprocessors Brief History of RISC Microprocessors Brief History of PDSPs Instruction Set Design Addressing Modes Data Flow: Zero-,One-, Two- or Three-Address Design Register File and Memory Architecture Operation Support Next Operation Location Software Tools Lexical Analysis Parser Development FPGA Microprocessor Cores Hardcore Microprocessors Softcore Microprocessors Case Studies T-RISC Stack Microprocessors LISA Wavelet Processor Design Nios FFT Design 625 Exercises 634 References 645 A. Verilog Source Code

7 XX Contents B. VHDL and Verilog Coding 729 B.1 List of Examples 731 B.2 Library of Parameterized Modules (LPM) 733 B.2.1 The Parameterized Flip-Flop Megafunction (lpmff) 733 B.2.2 The Adder/Subtractor Megafunction 737 B.2.3 The Parameterized Multiplier Megafunction (1pm_mult) 741 B.2.4 The Parameterized ROM Megafunction (1pm_rom) 746 B.2.5 The Parameterized Divider Megafunction (lpm_divide) 749 B.2.6 The Parameterized RAM Megafunction (1pm_ram_dq) 751 C. Glossary 755 D. CD-ROM File: "lreadme.ps" 761 Index 769

All MSEE students are required to take the following two core courses: Linear systems Probability and Random Processes

MSEE Curriculum All MSEE students are required to take the following two core courses: 3531-571 Linear systems 3531-507 Probability and Random Processes The course requirements for students majoring in