HW5 - To circumvent this first remove the dc component from...

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1 HOMEWORK #5 1. Write a MATLAB program to demonstrate aliasing and A/D resolution for a sine wave. The program should do the following: Prompt the user for input waveform and A/D characteristics (e.g., amplitude, dc offset, and frequency of sine wave, full-scale A/D range, # bits) Plot the true waveform Prompt the user for the sampling frequency Plot the "sampled points" superimposed on the true waveform and the reconstructed waveform (using the cardinal series). I suggest you try and reproduce the sample case in the class notes using the cardinal series. Run the following cases and explain your results. a. For the sine wave 0.01sin(2 10 ) dc t π + , and a 16-bit A/D with a full-scale range of +/- 5 V and a sampling frequency of 50 Hz, note what happens when the dc component is increased from 0 to a higher value of 3 V. In particular, note the high-frequency wiggles in the reconstructed signal.
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Unformatted text preview: To circumvent this, first remove the dc component from the signal, then use the cardinal series to reconstruct the ac signal, then add back in the dc component. Try this. b. Next, for 3 0.001sin(2 10 ) t + and a N-bit A/D with a full-scale range of +/- 5 V and a sampling frequency of 50 Hz, let’s investigate the effect of the # of bits. Show and explain your results for N=8, 12, 14, and 16 bits. If you have a low-resolution A/D and are interested in measuring both the dc and ac components, how can you accomplish this? (Hint: recall our discussion of AC coupling.) c. For a sine wave 3sin(2 10 ) t and a 12-bit A/D with a full-scale range of +/- 5 V, what happens when the sampling frequency is 6, 8, 20, 21, 40, 50, 100 Hz? Is the signal aliased or folded? What is the digitized or apparent frequency? When does the cardinal series provide an accurate reconstruction of the signal?...
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