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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

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
Daniel
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
Maciej
characteristics of micro business
Abigail
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
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.
Virgil
is Bucky paper clear?
CYNTHIA
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
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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