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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 is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
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 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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