A signal x(t) is sampled above its Nyquist rate to form a signal x[n] and is also impulse sampled at the same rate to form an impulse signal x?(t) . The DTFT of x[n] is X(F) = 10 rect(5F) ? ?1(F) or X ( ej? ) = 10 rect (5?/2?) ? ?2? (?) .
(a) If the sampling rate is 100 samples/second, what is the highest frequency at which the CTFT of x(t) is nonzero?
(b) What is the lowest positive frequency greater than the highest frequency in x(t) at which the CTFT of x?(t) is nonzero?
(c) If the original signal x(t) is to be recovered from the impulse sampled signal x?(t) , by using an ideal lowpass filter with impulse response h(t) = A sinc (wt) , what is the maximum possible value of w?
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