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How can we compute the array response?

This is where Fourier transforms come into play. We could compute the response of our one-dimensional array for waves propagating along the length ofthe wire by treating the elements of the array as samples in space and performing a one-dimensional Fourier transform on the elements of the array.

A sampled space series

In this case, we would consider the array elements to constitute samples taken in space in the same way that we consider a sampled time series toconstitute samples taken in time. In other words, the array elements constitute a sampled space series. The Fourier transform of a sampled time series is thefrequency spectrum of the time series. The Fourier transform of a sampled space series is the wavenumber spectrum of the space series.

Three example wavenumber spectra

To set the stage for what we will be seeing later, Figure 2 depicts three different two-element arrays with different spacing in the three (black and white) images across the top of the figure. The wavenumber response for each of the three arrays is shown inthe three images in the bottom row of images in Figure 2 .

(In Figure 2 , the array elements are represented by the white dots on the black background.)
Figure 2. Three example wavenumber spectra.
missing image

Plots of 3D surfaces

The images shown in Figure 2 were produced using the class named ImgMod29 , which I explained earlier in the module titled Plotting 3D Surfaces using Java . You can refer back to that module for a detailed explanation of the display format. Briefly, each of the sixindividual images in Figure 2 is a plot of a 3D surface, with the elevation of the surface at any particular point being indicated by the color at that pointbased on the colors on the calibration scale below each plot.

(The calibration scale is the strip that changes color in a smooth gradient from black through blue, cyan, green, yellow, red, and white with black at the leftend and white at the right end.

The three images in the top row of Figure 2 with the white dots on the black background represent the arrayelements for each of the three arrays. The three images in the bottom row of Figure 2 represent the wavenumber response of the corresponding arrays in the top row.)

Black, white, and the colors in between

The lowest (algebraic) elevation in the plot is colored black. Hence the backgrounds are black in the top three plots. The highest elevation is colored white. Thearray elements are white in the top three plots.

Between black and white, the elevation is given by the color scale below the plot with the lowest elevation on the left of the scale and the highestelevation on the right. Thus, a green elevation is about half way between the lowest and highest elevations. Blue elevations are near the low end. Redelevations are near the high end. Cyan and yellow elevations fall in between as shown by the calibration scale.

The maximum array output

All three wavenumber plots have a maximum response at the center, which is the zero wavenumber origin. In effect, this corresponds to infinite wavelength.If the wavelength is infinite, it doesn't matter what the separation between the elements is, they will all move up and down in unison and their electricaloutputs will add constructively to produce a maximum output.

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
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?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
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?
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
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
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
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
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?
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
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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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