Acoustic Pulse Ultrasound Measurements and Calculation Exam hiI have an homework of 4 questions measurements and calculation ultrasonic acoustic pulseplease the answers typed Problem #1:

Figure 1 shows an example of an ultrasonic acoustic pulse that one might measure in

a laboratory. The acoustic signal shown in the figure consists of a constant

wavelength (CW) pulse, with a small amount of random broadband noise in the data.

Let fo be the frequency of the CW pulse. From Fig. 1, what is fo in this case?

Problem #1

1

(a)

0.5

Amplitude

0

-0.5

-1

1.4

1.5

1.8

1.9

1.6

1.7

Time (ms)

0

(b)

-10

-20

Magnitude (dB)

-30

-40

-50

-60

0

50

100 150

350

400

450

200 250 300

Frequency (kHz)

Figure 1: (a) Amplitude v. time (in milliseconds) of an ultrasonic acoustic signal, and (b) the

corresponding Fast Fourier Transform (FFT) magnitude (in decibels) v. frequency (in kilo Hertz).

Problem #2

In class we covered discrete time signals and the effects of sampling an analog signal.

(a) What is the sampling theorem?

(b) Define what the Nyquest frequency is.

(c) The time step, At, for the data shown in Fig. 1(a) is At = 1 microsecond (us).

Calculate the Nyquest frequency for the data in Fig. 1.

Problem #3:

Figure 2 shows a measurement of the exact same ultrasonic acoustic pulse from

Problem #1 (shown in Fig. 1), except that the measurement system in this case used

a sampling frequency of only 1.25fo.

(a) Does the measurement meet the criteria described in the sampling theorem?

Why or why not?

(b) From the results shown in Fig. 2(b), there is now a peak in the FFT magnitude at

25 kHz (denoted by the orange arrow) that was not present in the data shown

in Fig. 1(b). Where did this additional peak come from?

Problem #3

1

(a)

0.5

Amplitude

ho

0

-0.5

-1

1.4

1.5

1.8

1.9

1.6

1.7

Time (ms)

0

(b)

-10

-20

Magnitude (dB)

-30

-40

-50

-60

0

25

100

50

75

Frequency (kHz)

Figure 2: (a) Amplitude v. time in milliseconds) of an ultrasonic acoustic signal, and (b) the

corresponding Fast Fourier Transform (FFT) magnitude (in decibels) v. frequency (in kiloHertz).

Problem #4:

Figure 3 shows the magnitude of a filter you wish to use on your ultrasonic acoustic

pulse data.

(a) For each region A, B, and C labeled in Fig. 3, identify whether the region is a

passband or a stopband.

(b) Based on your answers from part (a), what type of filter is shown in Fig. 3?

(c) Do you think the filter shown in Fig. 3 might be useful for the data shown in

Fig. 1? In a few sentences explain your answer.

Problem #4

1.2

1

0.8

A

B

с

Magnitude

0.6

0.4

0.2

0

0

100

400

500

200

300

Frequency (kHz)

Figure 3: Filter magnitude v. frequency.

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