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For example, assume that a photographic image includes a picture of a vase. Assume that the original image is cropped twice along two different bordersproducing two new images. Assume that both of the new images contain the picture of the vase, but in different locations. That vase will contribute the samevalues to the amplitude spectra of the two images regardless of the location of the vase in each of the images. This knowledge will be useful to us in futuremodules when we begin using 2D Fourier transforms to process photographic images.

Amplitude spectrum is the same

If you compare Figure 8 with Figure 7 , you will see that the amplitude spectrum is the same for both surfaces despite the fact that the box is in adifferent location in each of the two surfaces. However, the real and imaginary parts of the spectrum in Figure 8 are considerably different from the real and imaginary parts of the spectrum in Figure 7 .

The code that was used to create the surface for this case is straightforward. You can view that code in Listing 22 near the end of the module.

Case 4

This case draws a short line containing eight points along the diagonal from top-left to lower right in the space domain. You can view this surface in thetop-left image in Figure 9 . You can view the code that generated this surface in Listing 22 near the end of the module.

Figure 9. Graphic output for Case 4.
missing image

Another example of sin(x)/x

On the basis of prior experience, we would expect the wavenumber amplitude spectrum, (when viewed along any line in wavenumber space parallel to the line in space) , to have a rectified sin(x)/x shape. We would expect the peak of that shape to be centered on the origin in wavenumber space. We wouldexpect the width of the peak in wavenumber space to be inversely proportional to the length of the line in space.

We would expect the amplitude spectrum when viewed along any line in wavenumber space perpendicular to the line in space to have a constant value.

Our expectations are borne out

The shape of the amplitude spectrum shown in the lower right image in Figure 9 agrees with our expectations. Although not shown here, if we were to make theline of points longer, the width of the peak in the rectified sin(x)/x would become narrower. If we were to make the line of points shorter, the peak wouldbecome wider, as we will demonstrate in Case 5.

Our expectations regarding symmetry and asymmetry for the real and imaginary parts shown in the center images of Figure 9 are borne out. The real part is at the top center and the imaginary part is at the bottom center.

The output from the inverse Fourier transform shown in the bottom left of Figure 9 matches the original space domain surface in the top left of Figure 9 .

Case 5

This case draws a short line consisting of only four points perpendicular to the diagonal from top-left to lower right. This line of points is perpendicularto the direction of the line of points in Case 4.

You can view the surface for this case in the top-left image of Figure 10 . You can view the code that generated this surface in Listing 22 near the end of the module.

Questions & Answers

Discuss the differences between taste and flavor, including how other sensory inputs contribute to our  perception of flavor.
John Reply
taste refers to your understanding of the flavor . while flavor one The other hand is refers to sort of just a blend things.
Faith
While taste primarily relies on our taste buds, flavor involves a complex interplay between taste and aroma
Kamara
which drugs can we use for ulcers
Ummi Reply
omeprazole
Kamara
what
Renee
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Renee
is a drug
Kamara
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Kamara
Omeprazole Cimetidine / Tagament For the complicated once ulcer - kit
Patrick
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Nency Reply
Not really sure
Eli
to drain extracellular fluid all over the body.
asegid
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include: 1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Adama
what is anatomy
Oyindarmola Reply
Anatomy is the identification and description of the structures of living things
Kamara
what's the difference between anatomy and physiology
Oyerinde Reply
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
AI-Robot
what is enzymes all about?
Mohammed Reply
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
yes
Prince
how does the stomach protect itself from the damaging effects of HCl
Wulku Reply
little girl okay how does the stomach protect itself from the damaging effect of HCL
Wulku
it is because of the enzyme that the stomach produce that help the stomach from the damaging effect of HCL
Kamara
function of digestive system
Ali Reply
function of digestive
Ali
the diagram of the lungs
Adaeze Reply
what is the normal body temperature
Diya Reply
37 degrees selcius
Xolo
37°c
Stephanie
please why 37 degree selcius normal temperature
Mark
36.5
Simon
37°c
Iyogho
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature
Stephanie
37A c
Wulku
what is anaemia
Diya Reply
anaemia is the decrease in RBC count hemoglobin count and PVC count
Eniola
what is the pH of the vagina
Diya Reply
how does Lysin attack pathogens
Diya
acid
Mary
I information on anatomy position and digestive system and there enzyme
Elisha Reply
anatomy of the female external genitalia
Muhammad Reply
Organ Systems Of The Human Body (Continued) Organ Systems Of The Human Body (Continued)
Theophilus Reply
what's lochia albra
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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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