Individual Homework
Problem 1 –A wave is sampled at frequency of 4096 Hz. A total of 2048 points aretaken.
a)What is the Nyquist frequency?
b)What is the frequency resolution?
c)The student making the measurement suspects that the sampled waveformcontains several harmonics of 500 Hz. Which of these can be accuratelymeasured? What happens to the others?
Problem 2 –A 150-Hz cosine wave is sampled at a rate of 200 Hz.
a)Draw the wave by hand (for ~ 6 cycles) and show the temporal locations at whichit is measured.
b)What apparent frequency is measured?
c)Justify your answer with calculations.
Problem 3 –An engineer is studying the vibrational spectrum of a large diesel engine.Her modeling estimates suggest that a strong resonance is likely at 250 Hz, and that weaker frequencies (i.e., vibrations with weak magnitude) of up to 2000Hz may beexcited also.
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