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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

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
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John Reply
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Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
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emma Reply
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Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
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Adjanou
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Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
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Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
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Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
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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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