Contents

Preface

About the Author

Part I DSP Fundamentals

Note 1 Navigating the DSP Landscape

Note 2 Overview of Sampling Techniques

Note 3 Ideal Sampling

Note 4 Practical Application of Ideal Sampling

Note 5 Delta Functions and the Sampling Theorem

Note 6 Natural Sampling

Note 7 Instantaneous Sampling

Note 8 Reconstructing Physical Signals

Part II Fourier Analysis

Note 9 Overview of Fourier Analysis

Note 10 Fourier Series

Note 11 Fourier Transform

Note 12 Discrete-Time Fourier Transform

Note 13 Discrete Fourier Transform

Note 14 Analyzing Signal Truncation

Note 15 Exploring DFT Leakage

Note 16 Exploring DFT Resolution

Part III Fast Fourier Transform Techniques

Note 17 FFT: Decimation-in-Time Algorithms

Note 18 FFT: Decimation-in-Frequency Algorithms

Note 19 FFT: Prime Factor Algorithm

Note 20 Fast Convolution Using the FFT

Part IV Window Techniques

Note 21 Using Window Functions: Some Fundamental Concepts

Note 22 Assessing Window Functions: Sinusoidal Analysis Techniques

Note 23 Window Characteristics

Note 24 Window Choices

Note 25 Kaiser Windows

Part V Classical Spectrum Analysis

Note 26 Unmodified Periodogram

Note 27 Exploring Periodogram Performance: Sinusoids in Additive White Gaussian Noise

Note 28 Exploring Periodogram Performance: Modulated Communications Signals

Note 29 Modified Periodogram

Note 30 Bartlett’s Periodogram

Note 31 Welch’s Periodogram

Part VI FIR Filter Design

Note 32 Designing FIR Filters: Background and Options

Note 33 Linear-Phase FIR Filters

Note 34 Periodicities in Linear-Phase FIR Responses

Note 35 Designing FIR Filters: Basic Window Method

Note 36 Designing FIR Filters: Kaiser Window Method

Note 37 Designing FIR Filters: Parks-McClellan Algorithm

Part V Analog Prototype Filters

Note 38 Laplace Transform

Note 39 Characterizing Analog Filters

Note 40 Butterworth Filters

Note 41 Chebyshev Filters

Note 42 Elliptic Filters

Note 43 Bessel Filters

Part VI z-Transform Analysis

Note 44 The z Transform

Note 45 Computing the Inverse z Transform Using the Partial Fraction Expansion

Note 46 Inverse z Transform via Partial Fraction Expansion Case 1: All Poles Distinct with M < N in System Function

Note 47 Inverse z Transform via Partial Fraction Expansion Case 2: All Poles Distinct with M ≥ N in System Function (Explicit Approach)

Note 48 Inverse z Transform via Partial Fraction Expansion Case 3: All Poles Distinct with M ≥ N in System Function (Implicit Approach)

Part VII IIR Filter Design

Note 49 Designing IIR Filters: Background and Options

Note 50 Designing IIR Filters: Impulse Invariance Method

Note 51 Designing IIR Filters: Bilinear Transformation

Part VIII Multirate Signal Processing

Note 52 Decimation: The Fundamentals

Note 53 Multistage Decimators

Note 54 Polyphase Decimators

Note 55 Interpolation Fundamentals

Note 56 Multistage Interpolation

Note 57 Polyphase Interpolators

Part IX Bandpass and Quadrature Techniques

Note 58 Sampling Bandpass Signals

Note 59 Bandpass Sampling: Wedge Diagrams

Note 60 Complex and Analytic Signals

Note 61 Generating Analytic Signals with FIR Hilbert Transformers

Note 62 Generating Analytic Signals with Frequency-Shifted FIR Lowpass Filters

Note 63 IIR Phase-Splitting Networks for Generating Analytic Signals

Note 64 Generating Analytic Signals with Complex Equiripple FIR Filters

Note 65 Generating I and Q Channels Digitally: Rader’s Approach

Note 66 Generating I and Q Channels Digitally: Generalization of Rader’s Approach

Part X Statistical Signal Processing

Note 67 Parametric Modeling of Discrete-Time Signals

Note 68 Autoregressive Signal Models

Note 69 Fitting AR Models to Stochastic Signals: Yule-Walker Method

Note 70 Fitting All-Pole Models to Deterministic Signals: Autocorrelation Method

Note 71 Fitting All-Pole Models to Deterministic Signals: Covariance Method

Note 72 Autoregressive Processes and Linear Prediction Analysis

Note 73 Estimating Coefficients for Autoregressive Models: Burg Algorithm

Index