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Fourier Series and Transforms

March 24, 2019 by 3200 Creative

This series of lessons reviews the basics of Fourier transforms and series.  You will learn the details of how to represent signals in the frequency domain and the properties of Fourier representations. You will also gain understanding how to use Fourier methods to analyze interactions between signals and systems.  This series is designed to efficiently teach you the knowledge you need to use and understand Fourier methods in signal processing.

Course Content

Lessons Status
1

The Fourier Series: Continuous-Time Periodic Signals

2

Square Wave Fourier Series and the Sinc Function

3

Fourier Series Properties

4

The Fourier Transform: Linking Time and Frequency Domains

5

Properties of the Fourier Transform

6

The Discrete-Time Fourier Transform

7

Discrete-Time Fourier Transform Properties

8

Fourier Transforms and Discrete-Time Fourier Transforms for Periodic Signals

9

Frequency-Domain Descriptions for Continuous-Time Linear Time-Invariant Systems

10

Frequency-Domain Descriptions for Discrete-Time Linear Time-Invariant Systems

11

Two-Dimensional Signal Processing: Continuous Space

Filed Under: Uncategorized

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Course Lessons

  • 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

  • Properties of the Fourier Transform

  • The Discrete-Time Fourier Transform

  • 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

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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