• Skip to primary navigation
  • Skip to main content
  • Skip to primary sidebar

ALLSIGNALPROCESSING.COM

Learn signal processing online

  • Home
  • Courses
  • Courses
  • About
  • FAQ
  • My Account
  • Blog
  • News
  • Contact
  • Login
  • Logout
  • Get All Access

The DFT and Applications

March 19, 2019 by 3200 Creative

The discrete Fourier transform or DFT is the frequency domain workhorse of signal processing. It is the only Fourier representation that can be evaluated with a computer. In this series of 13 lessons you will learn how the DFT is related to the discrete-time Fourier transform, and how the DFT can be used to approximate the Fourier transform. You will learn the principles behind the fast Fourier transform algorithm for efficiently computing the DFT. You will also learn the principles of circular convolution and how to implement filtering using the DFT. This series is essential for everyone interested in spectral analysis of data or any computational Fourier analysis application.

Course Content

Lessons Status
1

Discrete Fourier Transform: Sampling the Discrete-Time Fourier Transform

2

Important Discrete Fourier Transform Properties

3

Fast Fourier Transform (FFT) Algorithm

4

Introduction to Circular Convolution and Filtering with the Discrete Fourier Transform

5

Circular Convolution Property of the Discrete Fourier Transform

6

Filtering with the Discrete Fourier Transform

7

The Discrete Fourier Transform Approximation to the Fourier Transform

8

The Effect of Windowing on the Discrete Fourier Transform Approximation to the Fourier Transform

9

Windows and the Discrete-Time Fourier Transform: Trading Resolution for Dynamic Range

10

An Example of Approximating the Fourier Transform with the Discrete Fourier Transform

11

Jupyter Notebook: Explore the Windowed DFT

12

The Short-Time Fourier Transform and the Spectrogram

13

Jupyter Notebook: Explore the Spectrogram

14

A Matrix Interpretation of the Discrete Fourier Transform

15

A Matrix Interpretation of the Fast Fourier Transform Algorithm

Filed Under: Uncategorized

Primary Sidebar

Course Lessons

  • Discrete Fourier Transform: Sampling the Discrete-Time Fourier Transform

  • Important Discrete Fourier Transform Properties

  • Fast Fourier Transform (FFT) Algorithm

  • Introduction to Circular Convolution and Filtering with the Discrete Fourier Transform

  • Circular Convolution Property of the Discrete Fourier Transform

  • Filtering with the Discrete Fourier Transform

  • The Discrete Fourier Transform Approximation to the Fourier Transform

  • The Effect of Windowing on the Discrete Fourier Transform Approximation to the Fourier Transform

  • Windows and the Discrete-Time Fourier Transform: Trading Resolution for Dynamic Range

  • An Example of Approximating the Fourier Transform with the Discrete Fourier Transform

  • Jupyter Notebook: Explore the Windowed DFT

  • The Short-Time Fourier Transform and the Spectrogram

  • Jupyter Notebook: Explore the Spectrogram

  • A Matrix Interpretation of the Discrete Fourier Transform

  • A Matrix Interpretation of the Fast Fourier Transform Algorithm

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

Copyright © 2023 ALLSIGNALPROCESSING.COM | Site Design by 3200 Creative

  • Terms of Service
  • Privacy Policy
  • Contact