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There are more efficient ways to write this method taking known symmetry and asymmetry conditions into account. However, I wrote the method the way that Idid because I wanted it to mimic the behavior of an FFT algorithm. Therefore, the complex input must extend from zero to the sampling frequency.

The method does not implement an FFT algorithm. Rather, the inverseTransform method implements a straight-forward sampled-data version of the continuous inverse Fourier transform that is defined usingintegral calculus.

Parameters for the inverseTransform method

The parameters to the inverseTransform method are:

  • double[] realIn - incoming real data
  • double[] imagIn - incoming image data
  • double[] realOut - outgoing real data

The method considers the data length to be realIn.length , and considers the computational time increment to be 1.0/realIn.length .

Assumptions

The method returns a number of points equal to the data length. It assumes that the real input consists of positive frequency points for a symmetric realfrequency function. That is, the real input is assumed to be symmetric about the folding frequency. The method does not test this assumption.

The method assumes that the imaginary input consists of positive frequency points for an asymmetric imaginary frequency function. That is, the imaginaryinput is assumed to be asymmetric about the folding frequency. Once again, the method does not test this assumption.

A real output

A symmetric real part and an asymmetric imaginary part guarantee that theimaginary output will be all zero values. Having made that assumption, the program makes no attempt to compute an imaginary output. If the assumptionsdescribed above are not valid, the results won't be valid.

The program was tested using JDK 1.8 under Windows 7.

Beginning of the inverseTransform method

The beginning of the class and the beginning of the static inverseTransform method is shown in Listing 5 .

Listing 5. Beginning of the class named InverseComplexToReal01.
public class InverseComplexToReal01{ public static void inverseTransform(double[] realIn,double[] imagIn,double[] realOut){int dataLen = realIn.length; double delT = 1.0/realIn.length;double startTime = 0.0;

Listing 5 declares and initializes some variables that will be used later.

The inverse transform computation

Listing 6 contains a pair of nested for loops that perform the actual inverse transform computation.

Listing 6. The inverse transform computation.
//Outer loop interates on time domain // values.for(int i=0; i<dataLen;i++){ double time = startTime + i*delT;double real = 0; //Inner loop iterates on frequency// domain values. for(int j=0; j<dataLen; j++){ real += realIn[j]* Math.cos(2*Math.PI*time*j)+ imagIn[j]*Math.sin(2*Math.PI*time*j); }//end inner looprealOut[i] = real;}//end outer loop }//end inverseTransform}//end class InverseComplexToReal01

If you have been studying the earlier modules in this series, you should be able to understand the code in Listing 6 without further explanation. Pay particular attention to the comments that describe the two for loops.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
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
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
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
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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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