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Case 7

Now we are going to make a major change in direction. All of the surfaces from cases 0 through 6 consisted of a few individual points located in specificgeometries in the space domain. All of the remaining points on the surface had a value of zero. This resulted in continuous (but sampled) surfaces in the wavenumber domain.

Now we are going to generate continuous (but sampled) surfaces in the space domain. We will generate these surfaces as sinusoidal surfaces (similar to a sheet of corrugated sheet metal) or the sums of sinusoidal surfaces.

Performing Fourier transforms on these surfaces will produce amplitude spectra consisting of a few non-zero points in wavenumber space with theremaining points in the spectrum having values near zero.

Need to change the surface plotting scale

In order to make these amplitude spectra easier to view, I have modified the program to cause the square representing each point in the amplitude spectrum to be five pixels on each side instead of three pixels on each side. To keep theoverall size of the images under control, I reduced the width and the height of the surfaces from 41 points to 23 points.

Display fewer results

I suspect that you have seen all the real parts, imaginary parts, and unshifted amplitude spectra that you want to see. Therefore, at this point, Iwill begin displaying only the input surface, the amplitude spectrum, and the output surface that results from performing an inverse Fourier transform on thecomplex spectrum.

A zero frequency sine wave

The first example in this category is shown in Figure 12 . The input surface for this example is a sinusoidal wave with a frequency of zero. This results ina perfectly flat surface in the space domain as shown in the leftmost image in Figure 12 . This surface is perfectly flat and featureless.

Figure 12. Graphic output for Case 7.
missing image

The code for this case

The code that was used to generate this surface is shown in Listing 18 . For the case of a sinusoidal wave with zero frequency, every point on the surfacehas a value of 1.0.

Listing 18. Code for Case 7.
case 7: for(int row = 0; row<rows; row++){ for(int col = 0; col<cols; col++){ spatialData[row][col] = 1.0;}//end inner loop }//end outer loopbreak;

A single point at the origin

As shown by the center image in Figure 12 , the Fourier transform of this surface produces a single point at the origin in wavenumber space. This isexactly what we would expect.

The inverse transform output is ugly

The result of performing an inverse Fourier transform on the complex spectrum is shown in the rightmost image in Figure 12 . As was the case earlier in Figure 6 , the ugliness of this plot is an artifact of the 3D plotting schemeimplemented by the class named ImgMod29 . The explanation that I gave there applies here also.

A very small error

Once again, the total error is very small. The numeric output shows that the final output surface matches the input surface to within an error that is lessthan about one part in ten to the thirteenth power. Thus, the program produces the expected results for this test case.

Questions & Answers

find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
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
I'm not sure why it wrote it the other way
I got X =-6
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?
is it a question of log
Commplementary angles
Idrissa Reply
im all ears I need to learn
right! what he said ⤴⤴⤴
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
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
anybody can imagine what will be happen after 100 years from now in nano tech world
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
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
can nanotechnology change the direction of the face of the world
Prasenjit Reply
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.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit 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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