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The Fourier Transform: Linking Time and Frequency Domains

February 8, 2019 by 3200 Creative

Fourier Transform

The Fourier transform is the primary tool for analyzing signals and signal-processing systems in the frequency domain, especially when signals are sampled or converted from discrete time to continuous time. In this lesson you will learn the definition of the Fourier transform and how to evaluate the corresponding integrals for several common signals.  You will also build your intuition for the relationships between time- and frequency-domain descriptions of signals.  Developing time- and frequency-domain intuition is an essential skill for the signal-processing practitioner.

Prerequisites

  • The Four Fourier Representations

Key Concepts and Screenshots

Concepts and Screenshots for the Fourier Transform

 Supplementary Materials

Table of Fourier Transform Pairs

QuizzesStatus
1

The Fourier Transform


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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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