DSPA
Collection edited by: Janko Calic
Content authors: Douglas Jones, Don Johnson, Ricardo Radaelli-Sanchez, Richard Baraniuk,
Stephen Kruzick, Catherine Elder, Melissa Selik, Robert Nowak, Anders Gjendemsjø, Michael
Haag, Benjamin Fite, Ivan Selesnick, and Phil Schniter
Online: < http://cnx.org/content/col10599/1.5>
This selection and arrangement of content as a collection is copyrighted by Janko Calic.
It is licensed under the Creative Commons Attribution License: http://creativecommons.org/licenses/by/2.0/
Collection structure revised: 2010/05/18
For copyright and attribution information for the modules contained in this collection, see the " Attributions" section at the end of the collection.
DSPA
Table of Contents
Preface for Digital Signal Processing: A User's Guide
Chapter 1. Background, Review, and Reference
1.1. Discrete-Time Signals and Systems
Real- and Complex-valued Signals
1.2. Systems in the Time-Domain
1.3. Discrete Time Convolution
Convolution and Circular Convolution
1.4. Introduction to Fourier Analysis
1.5. Continuous Time Fourier Transform (CTFT)
1.6. Discrete-Time Fourier Transform (DTFT)
1.7. DFT as a Matrix Operation
Representing DFT as Matrix Operation
Proof part 1 - Spectral considerations
Proof part II - Signal reconstruction
Systems view of sampling and reconstruction
Ideal system including anti-aliasing
Reconstruction with hold operation
Sampling CT Signals: A Frequency Domain Perspective
Understanding Sampling in the Frequency Domain
The DFT: Frequency Domain with a Computer Analysis
Discrete Fourier Transform (DFT)
Discrete-Time Processing of CT Signals
Application: 60Hz Noise Removal
General Formulas for the Difference Equation
Conversion to Frequency Response
Basic Definition of the Z-Transform
Understanding Pole/Zero Plots on the Z-Plane
Introduction to Poles and Zeros of the Z-Transform
Interactive Demonstration of Poles and Zeros
Applications for pole-zero plots
Pole/Zero Plots and the Region of Convergence
Frequency Response and Pole/Zero Plots
Chapter 2. Digital Filter Design
2.1. Overview of Digital Filter Design
Restrictions on h(n) to get linear phase
Frequency Sampling Design Method for FIR filters
Comments on frequency-sampled design
Extended frequency sample design
Parks-McClellan FIR Filter Design
Formal Statement of the L-∞ (Minimax) Design Problem
Conditions for L-∞ Optimality of a Linear-phase FIR Filter
Optimality Conditions for Even-length Symmetric Linear-phase Filters
L-∞ Optimal Lowpass Filter Design Lemma
Outline of IIR Filter Design Material
Comments on IIR Filter Design Methods
Prototype Analog Filter Design
Elliptic Function Filter (Cauer Filter)
IIR Digital Filter Design via the Bilinear Transform
Digital-to-Digital Frequency Transformations
Chapter 3. The DFT, FFT, and Practical Spectral Analysis
3.1. The Discrete Fourier Transform
Spectrum Analysis Using the Discrete Fourier Transform
Discrete-Time Fourier Transform
Relationships Between DFT and DTFT
DFT and Discrete Fourier Series
DFT and DTFT of finite-length data
Relationship between continuous-time FT and DFT
Classical Statistical Spectral Estimation
Auto-correlation-based approach
3.3. Fast Fourier Transform Algorithms
Overview of Fast Fourier Transform (FFT) Algorithms
Decimation-in-time (DIT) Radix-2 FFT
Radix-2 decimation-in-time FFT
Decimation-in-Frequency (DIF) Radix-2 FFT
Radix-2 decimation-in-frequency algorithm
Efficient FFT Algorithm and Programming Tricks
Trade additions for multiplications
3.6. FFTs of prime length and Rader's conversion
Another fact from number theory
Winograd minimum-multiply convolution and DFT algorithms
Winograd Fourier Transform Algorithm (WFTA)
3.7. Choosing the Best FFT Algorithm
Selecting a power-of-two-length algorithm
4.1. Time Frequency Analysis and Continuous Wavelet Transform
Limitations of Fourier Analysis
Time-Frequency Uncertainty Principle
4.3. Discrete Wavelet Transform
Discrete Wavelet Transform: Main Concepts
The Haar System as an Example of DWT
A Hierarchy of Detail in the Haar System
Haar Approximation at the kth Coarseness Level
Values of g[n] and h[n] for the Haar System
Wavelets: A Countable Orthonormal Basis for the Space of Square-Integrable
Filterbanks Interpretation of the Discrete Wavelet Transform
Initialization of the Wavelet Transform
Regularity Conditions, Compact Support, and Daubechies' Wavelets
Computing the Scaling Function: The Cascade Algorithm
Finite-Length Sequences and the DWT Matrix
DWT Applications - Choice of phi(t)
Chapter 5. Multirate Signal Processing
5.1. Overview of Multirate Signal Processing
Outline of Multirate DSP material
General Rate-Changing Procedure
5.2. Interpolation, Decimation, and Rate Changing by Integer Fractions
Interpolation: by an integer factor L
Decimation: sampling rate reduction (by an integer factor M)
Rate-Changing by a Rational Fraction L/M
5.3. Efficient Multirate Filter Structures
Efficient Decimation Structures
5.4. Filter Design for Multirate Systems
Direct polyphase filter design
5.5. Multistage Multirate Systems
Filter design for Multi-stage Structures
L-infinity Tolerances on the Pass and Stopbands
Efficient Narrowband Lowpass Filtering
5.7. Quadrature Mirror Filterbanks (QMF)
Chapter 6. Digital Filter Structures and Quantization Error Analysis
Transpose-form FIR filter structures
Direct-form I IIR Filter Structure
Direct-Form II IIR Filter Structure
Transpose-Form IIR Filter Structure
State-Variable Representation of Discrete-Time Systems
State and the State-Variable Representation
Transfer Function and the State-Variable Description
Fixed-Point Number Representation
Two's-Complement Integer Representation
Fractional Fixed-Point Number Representation
6.3. Quantization Error Analysis
Finite-Precision Error Analysis
Fundamental Assumptions in finite-precision error analysis
Summary of Useful Statistical Facts
Input Quantization Noise Analysis
Quantization Error in FIR Filters
Data Quantization in IIR Filters
Roundoff noise analysis in IIR filters
IIR Coefficient Quantization Analysis