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General discussion

The space domain

In Part 1 of this series, I extended the concept of the Fourier transform from the time domain into the space domain. I pointed out that while the time domainis one-dimensional, the space domain is thee-dimensional. However, in order to keep the complexity of this module in check, we will assume that space is onlytwo-dimensional. This will serve us well later for such tasks as image processing.

(Three-dimensional Fourier transforms are beyond the scope of this module. I will write a module on using Fourier transforms inthree-dimensional space later if I have the time.)

A purely real space domain

Although the space domain can be (and often is) complex, many interesting problems, (such as photographic image processing) can be dealt with under the assumption that the space domain is purely real. We willmake that assumption in this module. This assumption will allow us to simplify our computations when performing the 2D Fourier transform to transform our datafrom the space domain into the wavenumber domain.

Preview

I will present and explain two complete Java programs in this module. The first program is a single class named ImgMod30 , which provides the capability to perform forward and inverse Fourier transforms onthree-dimensional surfaces. In addition, the class provides a method that can be used to reformat the wavenumber spectrum to make it more suitable for display.

The second program is named ImgMod31 . This is an executable program whose purpose is to exercise and to test the ImgMod30 class using several examples for which the results should already be known.

Sample programs

The class named ImgMod30

This class provides 2D Fourier transform capability that can be used for image processing and other purposes. The class provides three static methods:

  • xform2D : Performs a forward 2D Fourier transform on a purely real surface described by a 2D array of double values in the space domain to produce a complex spectrum in the wavenumberdomain. The method returns the real part, the imaginary part, and the amplitude spectrum, each in its own 2D array of double values.
  • inverseXform2D : Performs an inverse 2D Fourier transform from the complex wavenumber domain into the real space domainusing the real and imaginary parts of the wavenumber spectrum as input. Returns the surface in the space domain as a 2D array of double values. Assumes that the real and imaginary parts in the wavenumber domainare consistent with a purely real surface in the space domain, and does not return an imaginary surface for the space domain
  • shiftOrigin : The wavenumber spectrum produced by xform2D has its origin in the top-left corner with the Nyquist folding wave numbers near the center. This is not a very suitableformat for visual analysis. This method rearranges the data to place the origin at the center with the Nyquist folding wave numbers along the edges.

The class was tested using JDK 1.8 and Windows 7. The class uses the static import capability that was introduced in J2SE 5.0. Therefore, it should notcompile using earlier versions of the compiler.

Questions & Answers

how can chip be made from sand
Eke Reply
is this allso about nanoscale material
Almas
are nano particles real
Missy Reply
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
Lohitha
where is the latest information on a no technology how can I find it
William
currently
William
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Digital signal processing - dsp. OpenStax CNX. Jan 06, 2016 Download for free at https://legacy.cnx.org/content/col11642/1.38
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