# An analog signal xa (t) = sin(480πt) + 3 sin(720 πt) is sampled 600 times per second.

An analog signal xa (t) = sin(480πt) + 3 sin(720 πt) is sampled 600 times per second.

(a) Determine the Nyquist sampling rate for xa(t).

(b) Determine the folding frequency.

(c) What are the frequencies, in radians, in the resulting discrete time signal x(n)?

(d) If x(n) is passed through an ideal D/A converter, what is the reconstructed signal Ya(t)?

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(a) Consider an analog signal.

An analog signal is sampled at F= 600 Hz

Nyquist sampling rate:

The minimum rate at which a signal can be sampled without introducing errors, which is twice the highest or maximum frequency present in the signal.

It is observed that   contains two frequency components. Compare the signal with the standard signal, . That are,

And,

From the concept of sampling theorem, the maximum frequency component is, f2. Now calculate the Nyquist sampling rate.

Thus, the Nyquist sampling rate for   is, .

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(c) Consider an analog signal.

The discrete time signal is,

Therefore, the discrete time signal is,

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Compare the signal with the standard signal, . So, the frequencies of discrete time signal  in radians are,

and

Thus, the frequencies of discrete time signal are,  .

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(d) Consider the discrete time signal.

If the discrete time signal is passed through the ideal D/A converter, then the output of the converter is, . That is,

Thus, the reconstructed signal,  is, .

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(b) Half of the sampled frequency is called the folding frequency. That is,

Thus, the folding frequency is,  .

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