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An analog signal contains frequencies up to 10 kHz.

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

(b) Suppose that we sample this signal with a sampling frequency Fs = 8 kHz. Examine what happens to the frequency F1 = 5 kHz.

(c) Repeat part.(b) for a frequency F2 = 9 kHz.

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(a)

The maximum frequency of the analog or message signal is  .

The sampling theorem states that,

Here,

 is the sampling frequency,

 is the maximum frequency of the analog or message signal.

Calculate the range of frequencies that allows exact reconstruction of the message signal.

Therefore, the range of frequencies for reconstruction of message signal is 

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(b)

Sample the message signal with sampling frequency, Fs = 8kHz

Calculate the folding frequency.

(broken image)

Folding frequency is the maximum frequency that can be represented uniquely by the sampled signals.

For the frequency, F1 = 5kHz, observe that the frequency F1 is greater than the folding frequency. Aliasing will occur as it is higher than folding frequency and frequencies up to folding frequency can only be recovered. Particular frequency will be changed as,

(broken image)

Now,  5kHz signal frequency will be changed by aliasing effect.

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(c)

For the frequency, F2 = 9kHz, observe that the frequency F2  is greater than the folding frequency. Aliasing will occur as it is higher than folding frequency and frequencies up to folding frequency can only be recovered. Particular frequency will be changed as,

(broken image)

Now,  9kHz signal frequency will be changed by aliasing effect.

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