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(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?