A function and its transform are shown in Figure P1233 It is

A function and its transform are shown in Figure P12.33. It is sampled (made into a digital signal) by multiplication with an infinite impulse train of 1ms spacing and amplitude 1. Sketch the sampled signal. Sketch also the spectrum of the sampled signal by making use of operational transform pair 9 in Table 12.2, which states that multiplication in the time domain corresponds to convolution in frequency. The spectrum of the impulse train was found in Problem 12.32.

Solution

The resultant spectrum is the frequencies lying within the

Band |Fhz|<=500(less than or equal to 500hz ) the other frequencies are ignored.