Notes on Digital Signal Processing

Preface xi About the Author xiii







Part I: DSP Fundamentals

Note 1: Navigating the DSP Landscape 1-1

Note 2: Overview of Sampling Techniques 2-1

Note 3: Ideal Sampling 3-1

Note 4: Practical Application of Ideal Sampling 4-1

Note 5: Delta Functions and the Sampling Theorem 5-1

Note 6: Natural Sampling 6-1

Note 7: Instantaneous Sampling 7-1

Note 8: Reconstructing Physical Signals 8-1



Part II: Fourier Analysis

Note 9: Overview of Fourier Analysis 9-1

Note 10: Fourier Series 10-1

Note 11: Fourier Transform 11-1

Note 12: Discrete-Time Fourier Transform 12-1

Note 13: Discrete Fourier Transform 13-1

Note 14: Analyzing Signal Truncation 14-1

Note 15: Exploring DFT Leakage 15-1

Note 16: Exploring DFT Resolution 16-1



Part III: Fast Fourier Transform Techniques

Note 17: FFT: Decimation-in-Time Algorithms 17-1

Note 18 FFT: Decimation-in-Frequency Algorithms 18-1

Note 19: FFT: Prime Factor Algorithm 19-1

Note 20: Fast Convolution Using the FFT 20-1



Part IV: Window Techniques

Note 21: Using Window Functions: Some Fundamental Concepts 21-1

Note 22: Assessing Window Functions: Sinusoidal Analysis Techniques 22-1

Note 23: Window Characteristics 23-1

Note 24: Window Choices 24-1

Note 25: Kaiser Windows 25-1



Part V: Classical Spectrum Analysis

Note 26: Unmodified Periodogram 26-1

Note 27: Exploring Periodogram Performance: Sinusoids in Additive White Gaussian Noise 27-1

Note 28: Exploring Periodogram Performance: Modulated Communications Signals 28-1

Note 29: Modified Periodogram 29-1

Note 30: Bartlett's Periodogram 30-1

Note 31: Welch's Periodogram 31-1



Part VI: FIR Filter Design

Note 32: Designing FIR Filters: Background and Options 32-1

Note 33: Linear-Phase FIR Filters 33-1

Note 34: Periodicities in Linear-Phase FIR Responses 34-1

Note 35: Designing FIR Filters: Basic Window Method 35-1

Note 36: Designing FIR Filters: Kaiser Window Method 36-1

Note 37: Designing FIR Filters: Parks-McClellan Algorithm 37-1



Part V: Analog Prototype Filters

Note 38: Laplace Transform 38-1

Note 39: Characterizing Analog Filters 39-1

Note 40: Butterworth 40-1

Note 41: Chebyshev Filters 41-1

Note 42: Elliptic Filters 42-1

Note 43: Bessel Filters 43-1



Part VI: z-Transform Analysis

Note 44: The z Transform 44-1

Note 45: Computing the Inverse z Transform Using the Partial Fraction Expansion 45-1

Note 46: Inverse z Transform via Partial Fraction Expansion

Case 1: All Poles Distinct with M < N in System Function 46-1

Note 47: Inverse z Transform via Partial Fraction Expansion

Case 2: All Poles Distinct with M = N in System Function (Explicit Approach) 47-1

Note 48: Inverse z Transform via Partial Fraction Expansion

Case 3: All Poles Distinct with M = N in System Function (Implicit Approach) 48-1



Part VII: IIR Filter Design

Note 49: Designing IIR Filters: Background and Options 49-1

Note 50: Designing IIR Filters: Impulse Invariance Method 50-1

Note 51: Designing IIR Filters: Bilinear Transformation 51-1



Part VIII: Multirate Signal Processing

Note 52: Decimation: The Fundamentals 52-1

Note 53: Multistage Decimators 53-1

Note 54: Polyphase Decimators 54-1

Note 55: Interpolation Fundamentals 55-1

Note 56: Multistage Interpolation 56-1

Note 57: Polyphase Interpolators 57-1



Part IX: Bandpass and Quadrature Techniques

Note 58: Sampling Bandpass Signals 58-1

Note 59: Bandpass Sampling: Wedge Diagrams 59-1

Note 60: Complex and Analytic Signals 60-1

Note 61: Generating Analytic Signals with FIR Hilbert Transformers 61-1

Note 62: Generating Analytic Signals with Frequency-Shifted FIR Lowpass Filters 62-1

Note 63: IIR Phase-Splitting Networks for Generating Analytic Signals 63-1

Note 64: Generating Analytic Signals with Complex Equiripple FIR Filters 64-1

Note 65: Generating I and Q Channels Digitally: Rader's Approach 65-1

Note 66: Generating I and Q Channels Digitally: Generalization of Rader's Approach 66-1



Part X: Statistical Signal Processing

Note 67: Parametric Modeling of Discrete-Time Signals 67-1

Note 68: Autoregressive Signal Models 68-1

Note 69: Fitting AR Models to Stochastic Signals: Yule-Walker Method 69-1

Note 70: Fitting All-Pole Models to Deterministic Signals: Autocorrelation Method 70-1

Note 71: Fitting All-Pole Models to Deterministic Signals: Covariance Method 71-1

Note 72: Autoregressive Processes and Linear Prediction Analysis 72-1

Note 73: Estimating Coefficients for Autoregressive Models: Burg Algorithm 73-1

Index I-1