Electronics Engineering

Electronics EngineeringSignals and SystemsMultiple Choice (MCQ)2 Marks
Q1.

Consider a continuous-time finite-energy signal f(t)f(t) whose Fourier transform vanishes outside the frequency interval [ωc,ωc][-\omega_c, \omega_c], where ωc\omega_c is in rad/sec.

The signal f(t)f(t) is uniformly sampled to obtain y(t)=f(t)p(t)y(t) = f(t) p(t). Here, p(t)=n=δ(tτnTs),p(t) = \sum_{n=-\infty}^{\infty} \delta(t - \tau - nT_s), with δ(t)\delta(t) being the Dirac impulse, Ts>0T_s > 0, and τ>0\tau > 0. The sampled signal y(t)y(t) is passed through an ideal lowpass filter h(t)=ωcTssin(ωct)πωcth(t) = \omega_c T_s \frac{\sin(\omega_c t)}{\pi \omega_c t} with cutoff frequency ωc\omega_c and passband gain TsT_s.

The output of the filter is given by __________.

A
f(t)f(t) if Ts<π/ωcT_s < \pi/\omega_c
B
f(tτ)f(t - \tau) if Ts<π/ωcT_s < \pi/\omega_c
C
f(tτ)f(t - \tau) if Ts<2π/ωcT_s < 2\pi/\omega_c
D
Tsf(t)T_s f(t) if Ts<2π/ωcT_s < 2\pi/\omega_c
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