## Description

Designed for the undergraduate discrete-time signal processing course

*Discrete-Time Signal Processing* covers the information that the undergraduate electrical computing and engineering student needs to know about DSP. Core material, with necessary theory and applications, is presented in Chapters 1-7. Four unique chapters that focus on advanced applications follow the core material. MATLAB^{®} is heavily emphasized throughout the book. Most applications have an accompanying lab or sequence of homework problems that have a lab component.

## Table of Contents

The analog circuit analysis

A digital filter replacement

1.2 Overview of Analysis and Design

The Analysis Process

The Design Process

**CHAPTER 2 Discrete-Time Signals**

2.0 Introduction

2.1 Discrete-Time Signals and Systems

Unit Impulse and Unit Step Functions

Related operations

2.2 Transformations of Discrete-Time Signals

Time Transformations

Amplitude Transformations

2.3 Characteristics of Discrete-Time Signals

Even and Odd Signals

Signals Periodic in n

Signals Periodic in &

2.4 Common Discrete-Time Signals

2.5 Discrete-Time Systems

2.6 Convolution for Discrete-Time Systems

Impulse representation of discrete-time signals

Convolution

Properties of convolution

Power gain

Chapter Summary

**CHAPTER 3 Frequency Domain Concepts**

3.0 Introduction

3.1 Orthogonal Functions and Fourier Series

The Exponential Fourier Series

Discrete Fourier Series

3.2 The Fourier Transform

Definition of the Fourier Transform

Properties of the Fourier Transform

Fourier Transforms of Periodic Functions

3.3 The Discrete-Time Fourier Transform

The Discrete-Time Fourier Transform (DTFT)

Properties of the Discrete-Time Fourier Transform

Discrete-Time Fourier Transforms of Periodic Sequences

3.4 Discrete Fourier Transform

Shorthand Notation for the DFT

Frequency resolution of the DFT

3.5 Fast Fourier Transform

Decomposition-in-Time Fast Fourier Transform Algorithm

Applications of the Discrete / Fast Fourier Transform

Calculation of Fourier Transforms

Convolution Calculations with the DFT/FFT

Linear Convolution with the DFT

Computational Efficiency

3.6 The Laplace Transform

Properties of the Laplace transform

Transfer functions

Frequency response of continuous-time LTI systems

3.7 The z-Transform

Definitions of z-Transforms

z-Transforms

Regions of Convergence

Inverse z-Transforms

z-Transform Properties

LTI System Applications

Transfer Functions

Causality

Stability

Invertibility

Discrete-Time Fourier Transform–z-transform Relationship

Frequency Response Calculation

Chapter Summary

**Chapter 4 Sampling and Reconstruction **

4.1 Sampling Continuous-Time Signals

Impulse Sampling

Shannon’s sampling theorem

Practical sampling

4.2 Anti-aliasing Filters

Low pass analog Butterworth filters

A low pass Butterworth analog filter has a transfer function given by Switched-capacitor filters

Oversampling

4.3 The Sampling Process

Errors in the sampling process

4.4 Analog to Digital Conversion

Conversion techniques

Successive Approximation Converter

Flash Converter

Sigma-Delta Conversion

Error in A/D conversion process

Dither

4.5 Digital to Analog Conversion

D/A conversion techniques

4.6 Anti-Imaging Filters

**Chapter 5 FIR Filter Design and Analysis **

5.1 Filter Specifications

5.2 Fundamentals of FIR Filter Design

Linear phase and FIR filters

Conditions for linear phase in FIR filters

Restrictions Imposed by Symmetry

Window Functions and FIR Filters

High pass, band pass, and band stop filters

5.3 Advanced Window Functions

Kaiser Window

Dolph-Chebyshev window

5.4 Frequency Sampling FIR filters

5.5 The Parks-McClellan Design Technique for FIR filters

5.6 Minimum Phase FIR filters

5.7 Applications

Moving Average FIR Filter

Comb Filters

Differentiators

Hilbert Transformers

5.8 Summary of FIR Characteristics

**Chapter 6 Analysis and Design of IIR Filters**

6.1 Fundamental IIR design Using the Bilinear Transform

Example 6.1

6.2 Stability of IIR Filters

6.3 Frequency transformations

6.4 Classic IIR filters

The Butterworth Filter

Chebyshev Filters

Inverse Chebyshev filter

Elliptic Filters

Summary of Classic IIR Filters

Invariant Impulse Response

6.5 Poles and Zeros in the z-Plane for IIR Filters

Summary of pole and zero locations for IIR filters

6.6 Direct Design of IIR Filters

Design by pole/zero placement

Design of resonators and notch filters of second order

Numerical Direct Design — Pade method

Numerical Direct Design — Prony's method

Numerical Direct Design — Yule-Walker method

6.7 Applications of IIR Filters

All Pass Filters

IIR Moving Average Filters

IIR Comb Filters

Inverse Filters

Chapter Summary

**Chapter 7 Sample Rate Conversion**

7.1 Integer Decimation

Frequency spectrum of the down sampled signal

Cascaded Decimation

7.2 Integer Interpolation

Cascaded Interpolators

7.3 Conversion by a Rational Factor

7.4 FIR Implementation

Decimation filters

Interpolation filters

7.5 Narrow Band Filters

7.6 Conversion by an Arbitrary Factor

Hold interpolation

Linear Interpolation

7.7 Bandpass Sampling

7.8 Oversampling in Audio Applications

Chapter Summary

**Chapter 8 Realization and Implementation of Digital Filters**

8.1 Implementation Issues

8.2 Number Representation

Two’s Complement

Sign/Magnitude

Floating point representation

8.3 Realization Structures

FIR Structures

IIR Structures

State Space Representation

8.4 Coefficient Quantization Error

8.5 Output Error due to Input Quantization

8.6 Product Quantization

8.7 Quantization and Dithering

8.8 Overflow and Scaling

8.9 Limit Cycles

8.10 DSP on Microcontrollers

Microcontroller Characteristics for DSP

Implementation in C

FIR Implementation in C

IIR Implementation in C

Speed optimization

**Chapter 9 Digital Audio Signals**

9.1 The Nature of Audio Signals

9.2 Audio File Coding

Pulse Code Modulation

Differential Pulse Code Modulation

9.3 Audio File Formats

Lossless file format examples

Lossless compressed format examples

Lossy compressed format examples

9.4 Audio Effects

Oscillators and signal generation

Delay

Flanging

Chorus

Tremolo and Vibrato

Reverberation

The Doppler Effect

Equalizers

Chapter Summary

**Chapter 10 Introduction to Two-Dimensional Digital Signal Processing**

10.1 Representation of Two-Dimensional Signals

Properties of Two-Dimensional Difference Equations

10.2 Two-Dimensional Transforms

The Z-Transform in Two Dimensions

The two-dimensional Discrete Fourier Transform

Properties of the 2D DFT

The Two Dimensional DFT and Convolution

The Two-Dimensional DFT and Optics

The Discrete Cosine Transform in Two Dimensions

10.3 Two-Dimensional FIR Filters

Window method

Frequency Sampling in Two-Dimensions

Transform methods

Applying FIR Filters to Images

Chapter Summary

**Chapter 11 Introduction to Wavelets**

11.1 Overview

11.2 The Short Term Fourier Transform

11.3 Wavelets and the Continuous Wavelet Transform

The HAAR Wavelet

The Daubechies Wavelet

Other Wavelet Families

11.4 Interpretation of the Wavelet Transform Data

11.5 The Undecimated Discrete Wavelet Transform

11.6 The Discrete Wavelet Transform

Chapter Summary

**APPENDIX A Analog Filter Design**

A.1 Analog Butterworth Filters

A.2 Analog Chebyschev Filters

A.3 Analog Inverse Chebyschev Filters

A.4 Analog Elliptic Filters

A.5 Summary of analog filter characteristics

**APPENDIX B Bibliography**

**APPENDIX C Background Mathematics**

C.1. Summation Formulas for Geometric Series

C.2. Euler’s Relation

C.3. Inverse Bilateral Z-Transforms by Partial Fraction Expansion

C.4. Matrix Algebra

C.5 State Variable Equations

**APPENDIX D MATLAB® User Functions and Commands**

D.1. MATLAB User Functions

D.2. MATLAB Commands

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