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Building Signals with Blocks: Basis Expansions

February 8, 2019 by 3200 Creative

The notion of building complex signals using elementary signals – metaphorical “blocks” – is central to many signal processing tools, such as Fourier transforms, wavelet transforms, and principle component analysis. The details of these different tools vary and can appear complex. This lesson presents a unified, big picture view of this topic that will help you maintain the proper perspective when you later study the details of specific methods.

Key Concepts and Transcript

Concepts and Transcript for Building Signals with Blocks

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Building Signals With Blocks


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Course Lessons

  • Signals Everywhere

  • Ever-Present Noise

  • Models, Math, and Real-World Signals

  • Four Signal-Processing Themes

  • Building Signals with Blocks: Basis Expansions

  • Jupyter Notebook: Explore FIR Filtering

  • Jupyter Notebook: Explore Image Filtering

  • 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

  • Summary Problems for Foundations

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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