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A two-dimensional array

We will achieve the desired array response by using an array having thirteen elements in the form of a cross with very specific weighting applied to eachelement prior to summation. The weighted array and the wavenumber response of the array are shown in Figure 5 .

Figure 5. Wavenumber response of a two-dimensional array.
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Computing the wavenumber response

The wavenumber response of the array (shown at the bottom in Figure 5 ) was produced by performing a 2D Fourier transform on the weighted array (shown at the top in Figure 5 ) .

The center element in the array was weighted by -4.5 before summation. (The signal from this element was amplified by a factor of 4.5 and the sign of the signal was inverted prior to summation.)

The twelve remaining elements were weighted by a factor of 1.0 before summation.

A constant wave number

Regardless of direction, the wavelength or wavenumber of the RF energy transmitted by a commercial radio station is the same and it doesn't change overtime, (unless the frequency on which the station broadcasts changes) .

Once again, we can determine the wavenumber response of the array for a given wavenumber from any direction by drawing a circle on the response plot, centeredat the origin, with the radius of the circle equal to the specific wavenumber of interest.

Assume a wavenumber

Assume that the wavenumber of interest in our case is exactly equal to the distance from the origin to the white spot in the upper right quadrant of thewavenumber response plot. This white spot represents the maximum response of the array.

(If our computation had perfect accuracy, there would be a white spot at the same location in all four quadrants.)

Draw a circle centered on the origin having a radius that causes the circle to go through the white spot.

Determine the response versus direction

The color corresponding to the response at any point on the circle represents the response of the array to that wavenumber for waves arriving from thatdirection (or in the case of a transmitter, for waves being transmitted in that direction) .

The circle passes through yellow, red, and white (indicating a high response) in the general directions of northeast, southeast, southwest, and northwest. This means that a strong RF signal will be transmitted to the peopleliving along the highways in those four directions.

The circle passes through green, cyan, and blue (indicating a lower response) in the general directions of north, south, east, and west. This means that very little of the precious RF energy will be transmitted to thecotton plants and the cows that live in those directions.

A possible solution to the problem

Thus, an array of active transmitter elements arranged and weighted as shown at the top of Figure 5 might be a reasonable design solution for your radio station. (However, I suspect that an experienced RF engineer would have a much more sophisticated solution.)

In any event, you have now seen one possible practical example of the use of a 2D Fourier transform.

Questions & Answers

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
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Akash Reply
it is a goid question and i want to know the answer as well
Maciej
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Abigail
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Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
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
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
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
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Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
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what is system testing?
AMJAD
preparation of nanomaterial
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how did you get the value of 2000N.What calculations are needed to arrive at it
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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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