# 4.6 Java1490-2d fourier transforms using java, part 1  (Page 7/15)

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## Response of the leftmost array

Now consider the leftmost pair of images where the two array elements are relatively close together. The wavenumber response of this array has a pair ofnull points about midway between the center and either end, as indicated by the blue and black colors. This is the wavenumber for which the element spacing isan exact multiple of one-half of the wavelength, causing the elements to move in equal but opposite directions in response to the wave motion. Thus, the outputfrom one element cancels the output from the other element producing zero voltage in the sum.

This same pair of images shows high responses at either end as indicated by the red areas. This is the wavenumber for which the element spacing is an exactmultiple of one wavelength.

## The Nyquist folding wavenumber

If this were a frequency spectrum analysis, we would say that the end points are at the Nyquist folding frequency, which is one-half of the samplingfrequency. Thus, we can say that in the wavenumber domain, the end points on the two leftmostplots are at the Nyquist folding wavenumber, which is one-half the sampling wavenumber.

As in the frequency domain, the wavenumber spectrum is periodic. The section of the wavenumber spectrum that we are viewing represents one complete period of a periodic wavenumber spectrum ranging from minus the folding wavenumber on the left, through zero wavenumberat the center, to plus the folding wavenumber on the right.

(If you are already familiar with this sort of thing, you may have figured out that the separation between our elements in this example istwice the sampling distance that determines the location of the folding wavenumber.)

## Estimating the array response from the colors

The leftmost array response shows a white area at the center.

(The white area is split by the vertical component of red axes drawn on the plot. The color of the axes has nothing to do with elevations on thesurface. I simply decided to draw them in red to make them stand out.)

This array response also shows the two black areas mentioned earlier. You can use the orange, yellow, green, and cyan locations on the calibration scale toestimate the response of the array to different wavenumber values between maximum and minimum.

## Additional separation between array elements

Now consider the two images in the center of Figure 2 where the wavenumber range is the same as the wavenumber plot on the left. The elements for thisarray are separated more than the elements in the leftmost pair of images. Again, the wavenumber response for this array has a maximum value at the origin,which is at the center of the wavenumber response in the lower image. In addition, this array response has a high (red) response at four other wavenumber zones (for a total of five) , whereas the array on the left had only three red zones. Similarly, this array has a low response (black and blue) at four differentwavenumber zones whereas the array on the left has a low response at only two wavenumber zones.

how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
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
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?
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 ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
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
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
how did you get the value of 2000N.What calculations are needed to arrive at it
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