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Sample Curriculum Spectral Analysis

This example curriculum is focussed on the methods and techniques for estimating spectra from data.

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

These lessons may be omitted if you have a background in signals and systems.

  • 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
  • Practical Sampling: Anti-Aliasing Filters

The DFT and Applications

  • Discrete Fourier Transform: Sampling the Discrete-Time Fourier Transform
  • Important Discrete Fourier Transform Properties
  • Fast Fourier Transform (FFT) Algorithm
  • 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

Random Signal Characterization

  • Introduction to Random Signal Representations
  • Multivariable Random Signal Characterization
  • Random Processes and Stationarity
  • The Power Spectral Density
  • Cross Spectra and Coherence
  • LTI System Models for Random Signals
  • Autoregressive Models: The Yule-Walker Equations

Estimation of Signal Characteristics

  • Introduction to Estimation Theory
  • Parametric vs. Nonparametric Spectrum Estimation
  • The Periodogram
  • The Averaged Periodogram: Welch's Method
  • Power Spectrum Estimation Examples: Welch's Method
  • Estimation of Coherence and Cross Spectra

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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