1
GATE ECE 2000
MCQ (Single Correct Answer)
+2
-0.6
The Hilbert transform of $$\left[ {\cos \,{\omega _1}t + \,\sin {\omega _2}t\,} \right]$$ is
A
$$\sin \,{\omega _1}t + \,\cos {\omega _2}t$$
B
$$\sin \,{\omega _1}t + \,\cos {\omega _2}t$$
C
$$\cos \,{\omega _1}t + \,\sin {\omega _2}t$$
D
$$\sin {\omega _1}t + \,\sin {\omega _2}t$$
2
GATE ECE 2000
Subjective
+5
-0
For the linear, time-invariant system whose block diagram is shown in Fig.(a), with input x(t) and output y(t).

(a) Find the transfer function.
(b) For the step response of the system [i.e. find y(t) when x(t) is a unit step function and the initial conditions are zero]
(c) Find y(t), if x(t) is as shown in Fig.(b), and the initial conditions are zero. GATE ECE 2000 Signals and Systems - Continuous Time Linear Invariant System Question 2 English 1 GATE ECE 2000 Signals and Systems - Continuous Time Linear Invariant System Question 2 English 2
3
GATE ECE 2000
MCQ (Single Correct Answer)
+2
-0.6
A system has a phase response given by $$\phi \,(\omega )$$ where $$\omega $$ is the angular frequency. The phase delay and group delay at $$\omega $$ = $${\omega _0}$$ are respectively given by
A
$$ - {{\phi ({\omega _0})} \over {{\omega _0}}}, - {{d\phi (\omega )} \over {d\omega }}\left| {\omega = {\omega _0}} \right.$$
B
$$\phi ({\omega _0}), - {{{d^2}\phi (\omega )} \over {d{\omega ^2}}}\left| {\omega = {\omega _0}} \right.$$
C
$${{{\omega _0}} \over {\phi ({\omega _0})}}, - {{d\phi (\omega )} \over {d\omega }}\left| {\omega = {\omega _0}} \right.$$
D
$${\omega _0}\,\phi \,({\omega _0})\,,\,\int_{ - \infty }^{{\omega _0}} \phi (\lambda )\,d\,\lambda $$
4
GATE ECE 2000
Subjective
+5
-0
A band limited signal x(t) with a spectrum X(f) as shown in Fig. a is processed as shown in Fig.b. p(t) is a periodic train of impulses as in Fig. c. The ideal band pass filter has a pass band from 26 KHz to 34 KHz.
(a) Calculate the Fourier series coefficients $${c_n}$$ in the Fourier expansion of p(t) in form $$p(t) = \sum\limits_{n = - \infty }^{ + \infty } {{c_n}} \,\exp \,\,(j\,n\,2\pi \,t/T)$$.
(b) Find the Fourier Transform of p(t).
(c) Obtain and sketch the spectrum of $${x_s}(t)$$.
(d) Obtain and sketch the spectrum of y(t). GATE ECE 2000 Signals and Systems - Sampling Question 9 English 1 GATE ECE 2000 Signals and Systems - Sampling Question 9 English 2 GATE ECE 2000 Signals and Systems - Sampling Question 9 English 3
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