GATE EC 2015 Set 3 — Question 55
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Question
Consider a continuous-time signal defined aswhere '' denotes the convolution operation and is in seconds. The Nyquist sampling rate (in samples/sec) for is ________.
Correct answer
0.39 to 0.41
Solution
Let (normalized sinc, ).Spectrum of the pulse. Since , time scaling giveswhich is nonzero only for Hz. So is band-limited to Hz.Effect of the impulse train. Convolving with repeats every s, so is periodic with fundamental frequency Hz. Its spectrum is a set of lines at with Fourier-series coefficientsThe nonzero lines are those with , i.e. (frequencies Hz); gives Hz, which lies outside the band, so and so on.Nyquist rate. The highest frequency present is Hz, so(Note that the answer is not : the periodic repetition keeps only the harmonics of Hz that fall inside the pulse's band.)Answer: samples/sec (accepted range to )
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