Question

1. An analog signal \(\mathrm{x}(\mathrm{t})\) contains frequencies from 0 up to \(10 \mathrm{kHz}\). You can assume any arbitrary spectrum for this signal. (Note that this signals also has frequencies from 0 to \(-10 \mathrm{KHz} .)\)

a) Draw the frequency spectrum of the signal after it has been sampled with a sampling frequency \(\mathrm{F}_{\mathrm{s}}=25 \mathrm{kHz}\)

b) What range of sampling frequencies allows exact reconstruction of this signal from its samples?

c) How is the original signal reconstructed from the sampled signal?

d) Draw the frequency spectrum of the signal after it has been sampled with a sampling frequency \(\mathrm{F}_{\mathrm{s}}=8 \mathrm{kHz}\)

e) What are the specs for the anti-aliasing filter that could be used to limit the distortion in the case where the sampling frequency is \(\mathrm{F}_{\mathrm{s}}=8 \mathrm{kHz}\) ? Draw the block diagram for all the steps of anti-aliasing, sampling and recovering the signal. Draw the frequency spectrum of the recovered signal.

Answer 1

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