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Sample Curriculum Undergraduate Signal Processing

This example curriculum covers sampling and reconstruction of signals, the discrete Fourier transform, system analysis using the z-transform, and frequency selective filter design.

Foundations

  • Signals Everywhere
  • Ever-Present Noise
  • Models, Math, and Real-World Signals
  • Four Signal-Processing Themes
  • Building Signals with Blocks: Basis Expansions
  • Signals: The Basics
  • Sinusoidal Signals
  • Sinusoidal Signals Examples
  • Complex Sinusoids
  • Exponential, Step, and Impulse Signals
  • Introduction to Linear, Time-Invariant Systems
  • Introduction to Difference Equation System Descriptions
  • Impulse Response Descriptions for LTI Systems
  • Frequency Response Descriptions for LTI Systems
  • Introduction to the System Function and System Poles and Zeros
  • The Four Fourier Representations

LTI Systems and Fourier Transforms

  • Impulse Response and LTI Systems - Part II
  • The Fourier Transform:Linking Time and Frequency Domains
  • Properties of the Fourier Transform
  • The Discrete-Time Fourier Transform
  • Discrete-Time Fourier Transform Properties

Sampling and Reconstruction

  • Introduction to Sampling and Reconstruction
  • Aliasing and the Sampling Theorem Simplified
  • Fourier Transform Interpretation of Sampling
  • Reconstruction and the Sampling Theorem
  • Reconstruction and the Sampling Theorem Examples
  • Equivalent Analog Filtering
  • Practical Sampling: Anti-Aliasing Filters
  • Practical Reconstruction: The Zero-Order Hold
  • Practical Digital Filtering and Oversampling
  • Oversampling Example
  • Downsampling: Reducing the Sampling Rate
  • Upsampling: Increasing the Sampling Rate
  • Analog to Digital Conversion: Quantization and Coding
  • Analysis of Quantization Error

The DFT and Applications

  • Discrete Fourier Transform: Sampling the Discrete-Time Fourier Transform
  • Important Discrete Fourier Transform Properties
  • Fast Fourier Transform (FFT) Algorithm
  • Introduction to Circular Convolution and Filtering with the DFT
  • Circular Convolution Property of the Discrete Fourier Transform
  • Filtering with the Discrete Fourier Transform
  • The Discrete Fourier Transform Approximation to the Fourier Transform
  • The Effect of Windowing on the Discrete Fourier Transform Approximation to the Fourier Transform
  • Windows and the Discrete-Time Fourier Transform: Trading Resolution for Dynamic Range
  • An Example of Approximating the Fourier Transform with the Discrete Fourier Transform
  • The Short-Time Fourier Transform and the Spectrogram
  • A Matrix Interpretation of the Discrete Fourier Transform
  • A Matrix Interpretation of the Fast Fourier Transform Algorithm

The z-Transform

  • Introduction to the z-Transform
  • The Region of Convergence for the z-Transform
  • Poles and Zeros of the z-Transform
  • Properties of the Region of Convergence
  • Inversion of the z-Transform via Power Series Expansion
  • Inversion of the z-Transform: Partial Fraction Expansion
  • Properties of the z-Transform
  • z-Transform Analysis of LTI Systems
  • Stability and Causality of LTI Systems Described by Difference Equations
  • Inverse Systems for LTI Systems Described by Difference Equations
  • Minimum-Phase and All-Pass Systems
  • Frequency Response Magnitude and Poles and Zeros
  • Impulse Response and Poles and Zeros

Intro to Filter Design

  • Introduction to Frequency Selective Filtering
  • Characterizing Filter Phase Response
  • Zero-Phase Filtering
  • Overview of FIR and IIR Filters

IIR Filter Design

  • IIR Filter Design Procedure
  • Analog Filters Used for IIR Filter Design
  • Continuous-Time Butterworth Filters
  • Continuous-Time Chebyshev and Elliptic Filters
  • Frequency Transformations for Continuous-Time Systems
  • The Bilinear Transform
  • IIR Filter Examples Designed Using MATLAB
  • Poor IIR Filter Designs: Don't Make These Mistakes

FIR Filter Design

  • Introduction to FIR Filter Design
  • Frequency Sampling FIR Filter Design
  • Linear Phase FIR Filters
  • The Window Method of FIR Filter Design
  • Parks-McClellan FIR Filter Design
  • Examples of Parks-McClellan FIR Filter Design

Primary Sidebar

Courses

  • Foundations

  • Time Domain LTI Systems

  • Fourier Series and Transforms

  • Sampling and Reconstruction

  • The DFT and Applications

  • The Z-Transform

  • Intro to Filter Design

  • IIR Filter Design

  • FIR Filter Design

  • Random Signal Characterization

  • Basis Representations of Signals

  • Estimation of Power Spectra and Coherence

  • Introduction to Signal Estimation and Detection Theory

  • MMSE Filtering and Least-Squares Problems

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