ECET345 Week 4 Homework

ECET345 Week 4 Homework

Author: Harvey Maxwell

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1. A shiny metal disk with a dark spot on it, as shown in figure below, is rotating clockwise at 100 revolutions/second in a dark room. A human observer uses a strobe that flashes 99 times/second to observe the spot on the metal disk (a strobe is a flashing light whose rate of flashing can be varied). The spot appears to the human observer as if it is rotating slowly
2. (a) A system samples a sinusoid of frequency 480 Hz at a rate of 100 Hz and writes the sampled signal to its output without further modification. Determine the frequency that the sampling system will generate in its output
(b) Find the output frequency when the input frequency is 425 Hz. Assume fs is unchanged at 100 Hz. Show the value of k chosen.
3. The spectrum of an analog signal is shown below, containing . Such a signal is sampled by an ideal impulse sampler at a 100 Hz rate. List the first 10 positive frequencies that will be produced by the replication. (Hint: Follow the method outlined in the lecture for spectrum replication of sampled signals.)
4. The spectrum of an analog signal is shown below. It is sampled, with an ideal impulse sampler, at a rate of 200 Hz
a) Draw the spectrum of the sampled signal and show the baseband and first two positive frequency replications with their end frequency values marked. (Hint: Follow the method outlined in the lecture.)
b) State below the frequency range of the signal, in baseband, that will become corrupted and thus unrecoverable because the signal was undersampled. (Hint: The area of corruption is the area in which baseband and first positive frequency image overlaps.)
5) Determine the Z transform of the signal,, shown below using the basic definition of Z transform . All values not shown can be assumed to be zero
7) An analog signal is given by f(t) = t (i.e., it increases linearly with time and is thus is a unit ramp.) It is convolved with a second signal, g(t), which is of the form g(t) = 1 (i.e., it has a constant value of 1 or is a unit step function). The two signals are shown below

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