Fourier Transform and Convolution

Fourier Transform and Convolution

For access to this article, please select a purchase option:

Buy chapter PDF
(plus tax if applicable)
Buy Knowledge Pack
10 chapters for £75.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Your details
Why are you recommending this title?
Select reason:
Digital Techniques for Wideband Receivers — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

In this chapter, both the Fourier transform and Fourier series will be discussed. The properties of the Fourier transform will be presented and the concept of impulse function will be introduced. The definition of convolution and its relation with Fourier transform will be presented. Examples of some commonly used Fourier transforms are given and the results are presented in a table for quick reference. There are many good books on this subject. A few of the books are listed at the end of this chapter. Readers with a background in this area can skip this chapter. However, Examples 3.10 and 3.11 may be of interest, because the former one is related to the radar pulse train and the latter will be used in the Hilbert transform.

Chapter Contents:

  • 3.1 Introduction
  • 3.2 Fourier Transform
  • 3.3 Impulse Function
  • 3.4 Properties of Fourier Transform
  • 3.4.1 Linearity
  • 3.4.2 Even and Odd Functions
  • 3.4.3 Duality
  • 3.4.4 Scaling
  • 3.4.5 Time Shift
  • 3.4.6 Frequency Shift
  • 3.4.7 Derivative
  • 3.4.8 Integral
  • 3.5 Fourier Series
  • 3.6 Comb Function
  • 3.7 Convolution
  • 3.8 Parseval's Theorem
  • 3.9 Examples
  • 3.10 Summary
  • References

Inspec keywords: convolution; Fourier series; Fourier transforms

Other keywords: Hilbert transform; convolution; radar pulse train; Fourier series; Fourier transform; impulse function

Subjects: Signal processing and detection; Signal processing theory; Integral transforms; Integral transforms

Preview this chapter:
Zoom in

Fourier Transform and Convolution, Page 1 of 2

| /docserver/preview/fulltext/books/ra/sbra005e/SBRA005E_ch3-1.gif /docserver/preview/fulltext/books/ra/sbra005e/SBRA005E_ch3-2.gif

Related content

This is a required field
Please enter a valid email address