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This method assumes that the inverse transform will produce purely real values in the space domain. Therefore, in the interest of computationalefficiency, the method does not compute the imaginary output values. Therefore, this is not a general purpose 2D complex-to-complex transform. For correct results, the input complex data must match that obtained by performing a forwardtransform on purely real data in the space domain.

Once again it was necessary to sacrifice indentation to force this very long equation to be compatible with this narrow publication format and still bereadable.

Listing 3. The inverseXform2D method.
static void inverseXform2D(double[][]real, double[][] imag,double[][]dataOut){ int height = real.length;int width = real[0].length;System.out.println("height = " + height);System.out.println("width = " + width); //Two outer loops iterate on output data.for(int ySpace = 0;ySpace<height;ySpace++){ for(int xSpace = 0;xSpace<width; xSpace++){//Two inner loops iterate on input data. for(int yWave = 0;yWave<height; yWave++){for(int xWave = 0;xWave<width; xWave++){//Compute real output data. dataOut[ySpace][xSpace] +=(real[yWave][xWave]*cos(2*PI*((1.0 * xSpace* xWave/width) + (1.0*ySpace*yWave/height))) -imag[yWave][xWave]*sin(2*PI*((1.0 * xSpace* xWave/width) + (1.0*ySpace*yWave/height))))/sqrt(width*height); }//end xWave loop}//end yWave loop }//end xSpace loop}//end ySpace loop }//end inverseXform2D method


This method requires three parameters. The first two parameters are references to 2D arrays containing the real and imaginary parts of the complexwavenumber spectrum that is to be transformed into a surface in the space domain.

The third parameter is a reference to a 2D array of the same size that will be populated with the transform results.

The shiftOrigin method

This method deserves some explanation. The reason that this method is needed is illustrated by Figure 1 .

Two views of the same wavenumber spectrum

Both of the images in Figure 1 represent the same wavenumber spectrum, but they are plotted against different coordinate systems.

Figure 1. Two views of the same wavenumber spectrum.
missing image

How the wavenumber spectrum is actually computed

The top image shows how the wavenumber spectrum is actually computed.

The wavenumber spectrum is computed covering an area of wavenumber space with the 0,0 origin in the top-left corner. The computation extends to twice theNyquist folding wave number along each axis.

Computationally sound but not visually pleasing

While this format is computationally sound, it isn't what most of us are accustomed to seeing in plots in wavenumber space. Rather, we are accustomed toseeing wavenumber spectra plotted with the 0,0 origin at the center.

The wavenumber spectrum is periodic

Knowing that the area of wavenumber space shown in the top image of Figure 1 covers one complete period of a periodic surface, the shiftOrigin method rearranges the results (for display purposes only) to that shown in the bottom image in Figure 1 . The origin is at the center in the bottom image of Figure 1 . The edges of the lower image in Figure 1 are the Nyquist folding wave numbers.

Questions & Answers

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
I'm not sure why it wrote it the other way
I got X =-6
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
Idrissa Reply
im all ears I need to learn
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what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
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algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
I'm not good at math so would you help me
what is the problem that i will help you to self with?
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
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what is the function of carbon nanotubes?
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
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
what is system testing
what is the application of nanotechnology?
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
anybody can imagine what will be happen after 100 years from now in nano tech world
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
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
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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