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Foundations

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

Time Domain LTI Systems

  • Impulse Response and LTI Systems - Part II
  • Graphical Evaluation of Discrete-Time Convolution
  • Graphical Evaluation of Continuous-Time Convolution
  • Difference Equations: Solving System Responses with Stored Energy
  • Characteristics of Systems Described by Difference Equations - Free Lesson
  • Differential Equations: Solving System Responses with Stored Energy
  • Characteristics of Systems Described by Differential Equations
  • Two-Dimensional Signal Processing: Discrete Space
  • Problems for Time Domain LTI Systems

Fourier Series and Transforms

  • The Fourier Series: Continuous-Time Periodic Signals
  • Square Wave Fourier Series and the Sinc Function
  • Fourier Series Properties
  • The Fourier Transform: Linking Time and Frequency Domains - Free Lesson
  • Properties of the Fourier Transform
  • The Discrete-Time Fourier Transform - Free Lesson
  • Discrete-Time Fourier Transform Properties
  • Fourier Transforms and Discrete-Time Fourier Transforms for Periodic Signals
  • Frequency-Domain Descriptions for Continuous-Time Linear Time-Invariant Systems
  • Frequency-Domain Descriptions for Discrete-Time Linear Time-Invariant Systems
  • Two-Dimensional Signal Processing: Continuous Space

Sampling and Reconstruction

  • Introduction to Sampling and Reconstruction
  • Aliasing and the Sampling Theorem Simplified - Free Lesson
  • Fourier Transform Interpretation of Sampling - Free Lesson
  • Reconstruction and the Sampling Theorem
  • Reconstruction and the Sampling Theorem Examples
  • Two-Dimensional Sampling Theorem
  • 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 - Free Lesson
  • Important Discrete Fourier Transform Properties
  • Fast Fourier Transform (FFT) Algorithm - Free Lesson
  • Introduction to Circular Convolution and Filtering with the Discrete Fourier Transform
  • 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
  • Jupyter Notebook: Explore the Windowed DFT
  • An Example of Approximating the Fourier Transform with the Discrete Fourier Transform
  • The Short-Time Fourier Transform and the Spectrogram
  • Jupyter Notebook: Explore the Spectrogram
  • A Matrix Interpretation of the Discrete Fourier Transform
  • A Matrix Interpretation of the Fast Fourier Transform Algorithm

The Z-Transform

  • Minimum-Phase and All-Pass Systems
  • Frequency Response Magnitude and Poles and Zeros
  • Impulse Response and Poles and Zeros
  • 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
  • Introduction to the z-Transform
  • The Region of Convergence for the z-Transform
  • Poles and Zeros of the z-Transform - Free Lesson
  • Properties of the Region of Convergence
  • Inversion of the z-Transform via Power Series Expansion

Intro to Filter Design

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

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 - Free Lesson
  • Poor IIR Filter Designs: Don't Make These Mistakes
  • Jupyter Notebook: IIR Filter Design Examples

FIR Filter Design

  • Introduction to FIR Filter Design
  • Frequency Sampling FIR Filter Design
  • Linear Phase FIR Filters - Free Lesson
  • The Window Method of FIR Filter Design
  • Parks-McClellan FIR Filter Design
  • Examples of Parks-McClellan FIR Filter Design
  • Jupyter Notebooks: FIR Filter Design

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 - Free Lesson

Basis Representations of Signals

  • Introduction to Signal Representation Using Bases
  • Introduction to Wavelets - Free Lesson
  • Multiresolution Analysis and the Scaling Function
  • Multiresolution Analysis and the Wavelet Decomposition
  • The Discrete Wavelet Transform
  • Wavelet Selection
  • Principal Component Analysis

Estimation of Power Spectra and Coherence

  • Parametric vs. Nonparametric Spectrum Estimation
  • The Periodogram
  • The Averaged Periodogram: Welch's Method - Free Lesson
  • Power Spectrum Estimation Examples: Welch's Method
  • Estimation of Coherence and Cross Spectra

Introduction to Signal Estimation and Detection Theory

  • Introduction to Estimation Theory
  • Parameter Estimation Criteria
  • Maximum Likelihood Estimation Examples
  • Introduction to Detection Theory
  • The Likelihood Ratio Test
  • The Generalized Likelihood Ratio Test

MMSE Filtering and Least-Squares Problems

  • Introduction to Minimum Mean-Squared Error Filtering - Free Lesson
  • Solving for the Minimum Mean-Squared Error Weights
  • Solving Least-Squares Problems with Gradient Descent: the Least Mean-Square Algorithm
  • Convergence, Tracking, and the LMS Algorithm Step Size

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