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(Recall that for the plotting format used in Figure 14 , the color white is reserved for the single point with the highest elevation. Thedifference in an elevation colored white and an elevation colored red for this plotting format might be as small as one part in ten to the fourteenthor fifteenth power. As a practical matter, red and white indicate the same elevation for this plotting format.)

For a sinusoidal surface with eight samples per cycle, we would expect the peaks to occur in the wavenumber spectrum about one-fourth of the distance fromthe origin to the folding wavenumber. Figure 14 meets that expectation.

The peaks are surrounded on both sides by blue and cyan colors, indicating very low values.

The inverse Fourier transform output

The output from the inverse Fourier transformed performed on the complex spectrum is shown in the rightmost image in Figure 14 . This output compares very favorably with the input surface shown in the leftmost image. The differencebetween the two is that the input has white vertical bands whereas the output has red vertical bands (with a single white spot) . The above explanation of white versus red applies here also.

You can view the code that created this surface in Listing 22 near the end of the module.

Case 12

This case draws a sinusoidal surface on the horizontal axis with three samples per cycle plus a sinusoidal surface on the vertical axis with eightsamples per cycle as shown by the leftmost image in Figure 15 .

Figure 15. Graphic output for Case 12.
missing image

The wavenumber spectrum

Performing a forward Fourier transform produces symmetrical peaks on the horizontal and vertical axes on all four sides of the wave number origin. Thesepeaks are indicated by the red and white squares in the center image in Figure 15 .

(See the earlier discussion regarding the difference in elevation indicated by red and white for this plotting format.)

The peaks on the vertical axis should be about one-fourth of the way between the origin and the folding wavenumber. This appears to be the case. The peaks onthe horizontal axis should be about two-thirds of the way between the origin and the folding wavenumber, which they also appear to be.

Inverse Fourier transform output

The output produced by performing an inverse Fourier transform on the complex spectrum is shown in the rightmost image in Figure 15 . Taking the red versus white issue into account, this output compares favorably with the input surface shown in theleftmost image in Figure 15 .

You can view the code that created this surface in Listing 22 near the end of the module.

Case 13

This case draws a sinusoidal surface at an angle of approximately 45 degrees relative to the horizontal as shown in the leftmost image in Figure 16 . This sinusoid has approximately eight samples per cycle.

Figure 16. Graphic output for Case 13.
missing image

The wavenumber spectrum

Performing a forward Fourier transform on this surface produces a pair of peaks in the wavenumber spectrum that are symmetrical about the origin atapproximately 45 degrees relative to the horizontal axis. These peaks are indicated by the red and white squares in the center image in Figure 16 .

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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David Reply
what is viscosity?
David
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emma Reply
what is chemistry
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
Adjei
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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
Magreth
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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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