# 4.6 Java1490-2d fourier transforms using java, part 1  (Page 11/15)

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## The angle of attack is important

We now have a much more complex situation. If the waves continue to impinge on the array from one end or the other, the situation will be exactly the sameas when the sensors were on the wire. However, the apparent wavenumber or wavelength of a wave as seen by the array will depend on the angle of attack.

(There is now a difference between the actual wavelength or wavenumber and the apparent wavelength or wavenumber as seen by the array.)

## Infinite wavelength

For example, if the wave impinges on the array from a broadside direction, all of the sensors will move up and down in unison regardless of theirseparation and regardless of the actual wavelength of the wave. For this case, the wave will appear to the array to have infinite wavelength or zerowavenumber.

(A linear array has no ability to filter on the basis of wavenumber for waves that impinge on the array from the broadside direction. All wavesfrom that direction appear to have zero wavenumber. This will lead us later to consider the use of a two-dimensional array.)

## The 2D wavenumber response of a linear array

Figure 4 shows the two-dimensional wavenumber response for a five element linear array with equal weighting for all of the elements. The array is shown atthe top. The wavenumber response of the array is shown at the bottom.

(In this case, I placed all five elements on adjacent points on the space sampling grid with no spaces in between. This places them so close togetherthat you can't visually separate them in the image and they appear as a white line in a black background.)

Figure 4. The 2D wavenumber response of a linear array.

## The response for a constant wavenumber

If you were to draw a circle centered on the crosshairs (axes) in the center of the wavenumber response, the points on that circle would representa fixed wavenumber for a wave arriving from any direction. The value of the response at any particular point on the circle would indicate the response ofthe array to a wave having that wavenumber from that direction.

## Response versus direction

If the diameter of the circle is larger than the width of the red vertical band, and if you were to plot that response versus direction, you would see thatthe response is maximum for the two directions that are broadside to the array and the response tends to drop off as the direction approaches the end-firedirection of the array.

## Symmetry

You would also notice quite a lot of symmetry. For example, the maximum response occurs in two directions that are 180 degrees apart. In fact, if youpick any direction and a given wavenumber, the response is the same for that direction and for the direction that is 180 degrees around from that direction.

## Not good for the radio transmitter

This wouldn't be a very good design for the radio station that I described earlier. If one of the broadside directions of the array faces northeast and theother faces southwest, then the people who live in the northwest and southeast directions wouldn't receive a very good signal from your transmitter. You need adesign that maximizes the power in the four directions where the people live, and that minimizes the power in the other directions. To accomplish that, wewill need a two-dimensional array in place of our one-dimensional linear array.

find the 15th term of the geometric sequince whose first is 18 and last term of 387
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
hi
salma
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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