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  This collection is included in Lens: richb's DSP resources
  By: Richard Baraniuk

  Comments:

  "My introduction to signal processing course at Rice University."

  Click the "richb's DSP" link to see all content selected in this lens.

  richb's DSP

Signals

• Signal Classifications and Properties
• Size of A Signal: Norms
• Signal Operations
• Useful Signals
• The Impulse Function
• The Complex Exponential
• Discrete-Time Signals

Systems

• System Classifications and Properties
• Properties of Systems

Time Domain Analysis of Continuous Time Systems

• CT Linear Systems and Differential Equations
• Continuous-Time Convolution
• Properties of Convolution
• BIBO Stability

Time Domain Analysis of Discrete Time Systems

• Discrete-Time Systems in the Time-Domain
• Discrete-Time Convolution
• Circular Convolution and the DFT
• Linear Constant-Coefficient Difference Equations
• Solving Linear Constant-Coefficient Difference Equations

Linear Algebra Overview

• Linear Algebra: The Basics
• Eigenvectors and Eigenvalues
• Matrix Diagonalization
• Eigen-stuff in a Nutshell
• Eigenfunctions of LTI Systems
• Fourier Transform Properties

Continuous Time Fourier Series

• Periodic Signals
• Fourier Series: Eigenfunction Approach
• Derivation of Fourier Coefficients Equation
• Fourier Series in a Nutshell
• Fourier Series Properties
• Symmetry Properties of the Fourier Series
• Circular Convolution Property of Fourier Series
• Fourier Series and LTI Systems
• Convergence of Fourier Series
• Dirichlet Conditions
• Gibbs's Phenomena
• Fourier Series Wrap-Up

Discrete Fourier Transform

• Fourier Analysis
• Fourier Analysis in Complex Spaces
• Matrix Equation for the DTFS
• Periodic Extension to DTFS
• Circular Shifts
• Circular Convolution and the DFT

Fast Fourier Transform (FFT)

• DFT: Fast Fourier Transform
• The Fast Fourier Transform (FFT)
• Deriving the Fast Fourier Transform

Convergence

• Convergence of Sequences
• Convergence of Vectors
• Uniform Convergence of Function Sequences

Discrete Time Fourier Transform (DTFT)

• Discrete Fourier Transformation
• Discrete Fourier Transform (DFT)
• Table of Common Fourier Transforms
• Discrete-Time Fourier Transform (DTFT)
• Discrete-Time Fourier Transform Properties
• Discrete-Time Fourier Transform Pair
• DTFT Examples

Continuous Time Fourier Transform (CTFT)

• Continuous-Time Fourier Transform (CTFT)
• Properties of the Continuous-Time Fourier Transform

Sampling Theorem

• Sampling
• Reconstruction
• More on Reconstruction
• Nyquist Theorem
• Aliasing
• Anti-Aliasing Filters
• Discrete Time Processing of Continuous Time Signals

Laplace Transform and System Design

• The Laplace Transforms
• Properties of the Laplace Transform
• Table of Common Laplace Transforms
• Region of Convergence for the Laplace Transform
• The Inverse Laplace Transform
• Poles and Zeros

Z-Transform and Digital Filtering

• The Z Transform: Definition
• Table of Common z-Transforms
• Region of Convergence for the Z-transform
• Inverse Z-Transform
• Rational Functions
• Difference Equation
• Understanding Pole/Zero Plots on the Z-Plane
• Filter Design using the Pole/Zero Plot of a Z-Transform

Appendix: Hilbert Spaces and Orthogonal Expansions

• Vector Spaces
• Norms
• Inner Products
• Hilbert Spaces
• Cauchy-Schwarz Inequality
• Common Hilbert Spaces
• Types of Basis
• Orthonormal Basis Expansions
• Function Space
• Haar Wavelet Basis
• Orthonormal Bases in Real and Complex Spaces
• Plancharel and Parseval's Theorems
• Approximation and Projections in Hilbert Space

Homework Sets

• Homework #1
• Homework #1 Solutions
• Viewing Embedded LabVIEW Content