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(Solved): (Impulse Sampling): Consider the continuous-time signal x(t)=(2cos(10\pi t)+4cos(30\pi t))*cos(200\p ...

(Impulse Sampling): Consider the continuous-time signal

x(t)=(2cos(10\pi t)+4cos(30\pi t))*cos(200\pi t).

(a) Find and sketch

x(\omega )

, the Fourier Transform of

x(t)

.

cos(x)cos(y)=(1)/(2)[cos(x-y)+cos(x+y)]

(b) The signal is now impulse sampled at 3 X the Nyquist sampling rate. What sampling rate

f_(s)

was used? (c) For the sampling rate found above, sketch the spectrum of the impulse-sampled signal. Denote the spectrum of the sampled signal as

x_(\delta )(\omega )

. (d) You'd like to recover the original spectrum

x(\omega )

from the impulse sampled spectrum

x_(\delta )(\omega )

using an ideal low-pass filter with cutoff frequency

\omega _(c)

. What range of cutoff frequencies could be used?

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