# 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.

Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
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
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
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
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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
how did you get the value of 2000N.What calculations are needed to arrive at it
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