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The Discrete-Time Fourier Transform

February 8, 2019 by 3200 Creative

The discrete-time Fourier transform (DTFT) is the tool of choice for frequency domain analysis of discrete-time signals and signal-processing systems. In this lesson you will learn the definition of the DTFT and how to evaluate the DTFT of several common signals. You will also build your intuition for the relationships between time and frequency domain descriptions of discrete-time signals. A significant portion of discrete-time signal-processing theory and applications are based on the foundation provided in this lesson.

Prerequisites

  • The Four Fourier Representations

Key Concepts and Screenshots

Concepts and Screenshots for The Discrete-Time Fourier Transform

Supplementary Materials

Table of Discrete-Time Fourier Transform Pairs

QuizzesStatus
1

The Discrete Time 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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