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Practice over 1000+ GATE-level questions from this topic!

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Q#1 Sampling GATE EC 2000 MSQ +2 marks -0 marks

A band-limited signal x(t) with a spectrum X(f) as shown in Figure (a) is processed as shown in Figure (b). p(t) is a periodic train of impulses as in Figure (c). The ideal band-pass filter has a pass band from 26 KHz to 34 KHz.

(a) Calculate the Fourier series coefficients  in the Fourier expansion of p(t) in the form

(b) Find the Fourier Transform of p(t)

(c) Obtain and sketch the spectrum of .

(d) Obtain and sketch the spectrum of y(t).        

(a)

(b)

(c)

41.jpg

(a) \(\scriptstyle {C_n  = 10^4}\)

(b) \(\scriptstyle {\therefore p(f) = \frac{1}{T} \sum_{n=-\infty}^{\infty} \delta(f - nf_0)}\)

\(\scriptstyle {f_0 = \frac{1}{T} = 10^4 = 10 \text{ kHz}}\)

(c)
\(\scriptstyle {X_s(f) = \frac{1}{T} \sum_{n=-\infty}^{\infty} X(f - nf_0)}\)

(d) \(\scriptstyle {Y(f) = \frac{1}{T} [X(f - 3f_0) + X(f + 3f_0)]}\)

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