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Learn how the space domain and the wavenumber domain in two-dimensional analysis are analogous to the time domain and the frequency domain in one-dimensional analysis. Learn about some practical examples showing how 2D Fourier transforms and wavenumber spectra can be useful in solving engineering problems involving antenna arrays.

Revised: Tue Oct 20 11:48:13 CDT 2015

This page is included in the following book: Digital Signal Processing - DSP

Table of contents


This is the first module of a two-part series. In this module, I will:

  • Explain the conceptual and computational aspects of 2D Fourier transforms
  • Explain the relationship between the space domain and the wavenumber domain
  • Provide sufficient background information that you will be able to appreciate the importance of the 2D Fourier transform

Two separate programs

In Part 2 of this series, I will present and explain two separate programs. One program consists of asingle class named ImgMod30 . The purpose of this class is to satisfy the computational requirements for forward and inverse 2D Fouriertransforms. This class also provides a method for rearranging the spectral data into a more useful format for plotting. The second program named ImgMod31 will be used to test the 2D Fourier transform class, and also to illustrate the use of 2D Fourier transforms for some well known samplesurfaces.

A third class named ImgMod29 will be used to display various 3D surfaces resulting from the application of the 2D Fourier transform. Iexplained this class in an earlier module titled Plotting 3D Surfaces using Java ..

Digital signal processing (DSP)

This and the following module will cover some technically difficult material in the general area of Digital Signal Processing, or DSP for short. As usual, the betterprepared you are, the more likely you are to understand the material. For example, it would be well for you to already understand the one-dimensionalFourier transform before tackling the 2D Fourier transform. If you don't already have that knowledge, you can learn about one-dimensional Fourier transforms bystudying the following modules :

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
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