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Basis Representations of Signals

February 28, 2019 by 3200 Creative

Representing signals as a weighted sum (or integral) of certain basis signals is a powerful signal-processing tool. It is the very essence of Fourier transforms. In this series of seven lessons you will learn the general form of basis representations. You will also learn about wavelets as an alternative basis expansion to the sinusoids of Fourier methods. You will also learn about principal component analysis, a method for choosing efficient bases for random data.

Course Content

Lessons Status
1

Introduction to Signal Representation Using Bases

2

Introduction to Wavelets

3

Multiresolution Analysis and the Scaling Function

4

Multiresolution Analysis and the Wavelet Decomposition

5

The Discrete Wavelet Transform

6

Wavelet Selection

7

Principal Component Analysis

Filed Under: Uncategorized

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Course Lessons

  • Introduction to Signal Representation Using Bases

  • Introduction to Wavelets

  • Multiresolution Analysis and the Scaling Function

  • Multiresolution Analysis and the Wavelet Decomposition

  • The Discrete Wavelet Transform

  • Wavelet Selection

  • Principal Component Analysis

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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