Marymount University Sampling Theorem & Nyquist Frequency Questions I need someone to do the HW for me in class called experimental technology. please try

Marymount University Sampling Theorem & Nyquist Frequency Questions I need someone to do the HW for me in class called experimental technology. please try your best so I get full mark. ENGR 518 Experimental Techniques for Graduate Students
Spring 2020
Homework Assignment #3
Due: Tuesday, 21 April 2020
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 f0 be the frequency of the CW pulse. From Fig. 1, what is f0 in this case?
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 kiloHertz).
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, Dt, for the data shown in Fig. 1(a) is Dt = 1 microsecond (µs).
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 1.25f0.
(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?
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.
Figure 3: Filter magnitude v. frequency.
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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?
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