Digital Signal Processing: Discrete Fourier Transform (DFT)

Name: Digital Signal Processing: Discrete Fourier Transform (DFT)
Rating: 4.5 (17 reviews)

DFT, Properties of DFT

Created byKoti Reddy

Last updated 1/2021

English

What you'll learn

Discrete Fourier Transform
Properties of DFT
Inverse Discrete Fourier Transform
Circular convolution

Course content

1 section • 14 lectures • 1h 59m total length

Introduction12:40
Procedure to find DFT18:58
Learn the procedure to find the discrete Fourier transform (DFT), demonstrated with omega-based calculations and a three-by-three matrix, to illustrate expanding the DFT step by step.
Periodicity property, DFT of a real valued signal9:29
Example problems7:16
Circular convolution, Parseval's Theorem20:32
Time expansion property5:00
Examine the time expansion property of the discrete Fourier transform, showing how a signal's samples expand in time and how this affects the dft representation.
Performing Linear convolution using Circular convolution8:25
Circular time reversal8:44
Expansion of x(n) , Expansion of X(k)9:41
Example Problem5:37
Example Problem4:34
Example Problem2:22
Example Problem2:30
Example Problem3:38

Requirements

Basics of Signals and Systems

Description

The Discrete Fourier Transform (DFT) is one of the most important tools in Digital Signal Processing. It enables us to find the spectrum of a finite duration sequence.

Discrete Fourier Transform (DFT) is an algorithm to implement Discrete Time Fourier Transform (DTFT) on computers for signal processing by sampling at equally spaced frequency points of one cycle of DTFT. Unlike DTFT (DTFT is continuous), the output of DFT is discrete and hence can be implemented on a computer.

DTFT is a continuous function of frequency, where as DFT is a discrete function of frequency.

Computing the DFT is equivalent to solving a set of linear equations.

In direct DFT method, the computational part is too long.

The Discrete Fourier Transform (DFT) can be computed efficiently using a Fast Fourier Transform (FFT).

Fast Fourier Transform (FFT) is an algorithm to reduce number of complex additions and complex multiplications while calculating DFT.

In this course, I have explained about Discrete Fourier Transform ( DFT) and Inverse DFT (IDFT).

The topics are

Relationship between DFT and DTFT

Finding DFT for a given x(n)

Properties of DFT

Linear convolution

Circular convolution or Periodic convolution

Difference between circular convolution and linear convolution

Performing linear convolution using circular convolution

Many example problems are also explained on all concepts.

After the completion of this course, definitely you are able solve problems on your own.

Who this course is for:

Engineering students