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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.

image

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  image contains two frequency components. Compare the signal with the standard signal, image. That are,

image

And,

image

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

image

Thus, the Nyquist sampling rate for  image is, image.

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(c) Consider an analog signal.

image

The discrete time signal is,

image

Therefore, the discrete time signal is,

image

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

image

 and 

image

Thus, the frequencies of discrete time signal are, image .

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(d) Consider the discrete time signal.

image

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

image

Thus, the reconstructed signal, image is, image.

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

image

Thus, the folding frequency is, image .

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