# 4.7 Java1491-2d fourier transforms using java, part 2  (Page 7/21)

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## End of the ImgMod30 class

Listing 4 also signals the end of the class definition for the class named ImgMod30.

## The program named ImgMod31

The purpose of this program is to exercise and to test the 2D Fourier transform methods and the axis shifting method provided by the class namedImgMod30.

## Command line parameters

The main method in this class reads two command line parameters and uses them to select:

• A specific case involving a particular 3D input surface in the space domain.
• A specific display format.

## Forward and inverse Fourier transforms

The program performs a 2D Fourier transform on that surface followed by an inverse 2D Fourier transform. Six different plots are produced in this processshowing different aspects of the transform and the inverse transform.

## Fourteen cases

There are 14 different cases built into the program with case numbers ranging from 0 to 13 inclusive. Each of the cases is designed such that the results ofthe analysis should be known in advance by a person familiar with 2D Fourier analysis and the wavenumber domain. Thus, these cases can be used to confirmthat the transform code was properly written.

The cases are also designed to illustrate the impact of various space domain characteristics on the wavenumber spectrum. This information will be usefullater when analyzing the results of performing 2D transforms on photographic images for example.

## A stack of output images

Each time the program is run, it produces a stack of six output images in the top-left corner of the screen. A brief description of each of the outputimages is provided in the following list. The top-to-bottom order of the stack is:

1. Space domain output of inverse Fourier transform. Compare with original input in 6 below.
2. Amplitude spectrum in wavenumber domain with shifted origin. Compare with 5 below.
3. Imaginary wavenumber spectrum with shifted origin.
4. Real wavenumber spectrum with shifted origin.
5. Amplitude spectrum in wavenumber domain without shifted origin. Compare with 2 above.
6. Space domain input data. Compare with 1 above.

To view the images near the bottom of the stack, you must physically move those on top to get them out of the way.

## Numeric output

In addition, the program produces some numeric output on the command line screen that may be useful in confirming the validity of the forward and inversetransform processes. Figure 2 shows an example of the numeric output.

Figure 2. Numeric output.
```height = 41 width = 41height = 41 width = 412.0 1.9999999999999916 0.5000000000000002 0.499999999999998450.49999999999999956 0.4999999999999923 1.7071067811865475 1.70710678118655260.2071067811865478 0.20710678118654233 0.20710678118654713 0.207106781186554351.0 1.0000000000000064 -0.4999999999999997 -0.49999999999999484-0.5000000000000003 -0.4999999999999965```

(Note that I manually inserted some and spaces line breaks in Figure 2 to cause the numeric values to line up in columns so as to be morereadable.)

## The size of the surfaces

The first two lines of numeric output in Figure 2 show the size of the spatial surface for the forward transform. The second two lines show the size ofthe wavenumber surface for the inverse transform.

how do they get the third part x = (32)5/4
can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
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
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
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
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
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Uday
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
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algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
is it 3×y ?
J, combine like terms 7x-4y
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
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.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
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
can nanotechnology change the direction of the face of the world
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.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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