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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?
