Electronics and Communication Engineering - Signals and Systems
Exam Duration: 45 Mins Total Questions : 30
Consider the following signals:
x(t) = cos \(\pi\)t + 2 cos 3\(\pi\)t + 3 cos 5 \(\pi\)t
y(t) = sin2t + 6cos 2\(\pi\)t
z(t) = sin 3t cos 4t
Periodic signals are
- (a)
x(t) and y(t)
- (b)
y(t) and z(t)
- (c)
x(t) and z(t)
- (d)
All of the these
Tthe system y(t) = x(t-5) = x(3-t) has the properties
- (a)
K, L, M, N
- (b)
L, M, N
- (c)
K, L, N
- (d)
K, M, L
The system y(t) = x\(\left( \frac { t }{ 2 } \right) \) has the properties
- (a)
K, L, M, N
- (b)
K, L
- (c)
K, M
- (d)
K, N
The system t\(\frac{d}{dt}\) y(t) - 8y(t) = x(t) has the prioperties
- (a)
K, L, M, N
- (b)
K, L, M
- (c)
K, M
- (d)
K, N
The impulse response of a continuous-time LTI system is \(h(t)=\left( { 2e }^{ -2t }-{ e }^{ \frac { t-100 }{ 100 } } \right) u(t)\). The system is
- (a)
causal and stable
- (b)
causal bu8t not stable
- (c)
stable but not causal
- (d)
neither causal norstable
The continuous time convolution integral y(t) = e-3(t+3) u(t)*u(t+3) is
- (a)
\(\frac { 1 }{ 3 } \left[ 1-{ e }^{ -3\left( t+3 \right) } \right] u\left( t+3 \right) \)
- (b)
\(\frac { 1 }{ 3 } \left[ 1-{ e }^{ -3\left( t+3 \right) } \right] u\left( t \right) \)
- (c)
\(\frac { 1 }{ 3 } \left[ 1-{ e }^{ -3t } \right] u\left( t \right) \)
- (d)
\(\frac { 1 }{ 3 } \left[ 1-{ e }^{ -3t } \right] u\left( t+3 \right) \)
The Laplace transform of signal \(t\frac { d }{ dt } \left\{ { e }^{ -t }cost\ u\left( t \right) \right\} \) is
- (a)
\(\frac { -\left( { s }^{ 2 }+4s+2 \right) }{ \left( { s }^{ 2 }+2s+2 \right) ^{ 2 } } \)
- (b)
\(\frac { \left( { s }^{ 2 }+4s+2 \right) }{ \left( { s }^{ 2 }+2s+2 \right) ^{ 2 } } \)
- (c)
\(\frac { \left( { s }^{ 2 }+2s+2 \right) }{ \left( { s }^{ 2 }+4s+2 \right) ^{ 2 } } \)
- (d)
\(\frac { -\left( { s }^{ 2 }+2s+2 \right) }{ \left( { s }^{ 2 }+4s+2 \right) ^{ 2 } } \)
The discrete time Fourier coefficients of \(\sum _{ m=-\infty }^{ \infty }{ \delta \left[ n-4m \right] } \) is
- (a)
\(\frac { -1 }{ 4 } \), for all k
- (b)
\(\frac { 1 }{ 4 } \), for all k
- (c)
\(\frac { 1 }{ 4 } |k|\), for all k
- (d)
\({ e }^{ j\frac { \pi }{ 2 } k }\)
\(H(z)=\frac { 1 }{ 1-\frac { 1 }{ 2 } Z^{ -1 } } +\frac { 1 }{ 1-2Z^{ -1 } } \left| Z \right| >2\) is
- (a)
causal
- (b)
non-causal
- (c)
anti-causal
- (d)
Cannot be determined
The Fourier transform of signal te-1 u(t) is
- (a)
\(\frac { 1 }{ 1+{ \omega }^{ 2 } } \)
- (b)
\(\frac { -1 }{ 1+{ \omega }^{ 2 } } \)
- (c)
\(\frac { 1 }{ (1+{ j\omega })^{ 2 } } \)
- (d)
\(\frac { 1 }{( 1-{ \omega })^{ 2 } } \)
As the period of the periodic signal increases, the fundamental frequency
- (a)
increases
- (b)
decreases
- (c)
remains same
- (d)
depends on T
Consider the z-transform X(z)=5z2+4z-1+3, 0<|z|<\(\infty \). The inverse z-transfom x[n] is
- (a)
\(5\delta \left[ n+2 \right] +3\delta \left[ n \right] +4\delta \left[ n-1 \right] \)
- (b)
\(5\delta \left[ n-2 \right] +3\delta \left[ n \right] +4\delta \left[ n+1 \right] \)
- (c)
5u[n+2]+3u[n]+4u[n+1]
- (d)
5u[n-2]+3u[n]+4u[n+1]
The Fourier of a real periodic function has only
P: Cosine terms if it is even
Q: Sine terms if it is even
R: Cosine terms if it is odd
S: Sine terms if it is odd
Which of the above statements are correct?
- (a)
P and S
- (b)
P and R
- (c)
Q and S
- (d)
Q and R
A function is given by f(t) = sin2 t + cos 2t. Which of the following is true?
- (a)
f (t) has frequency components at 0 and 1/2\(\pi\) Hz
- (b)
f (t) has frequency components at 0 and 1/\(\pi\) Hz
- (c)
f (t) has frequency components at 1/2\(\pi\) and 1/\(\pi\) Hz
- (d)
f (t) has frequency components at 0, 1/2\(\pi\) and 1/\(\pi\) Hz
If the Laplace transform of a signal y(t) is Y(s) = \(\frac { 1 }{ s\left( s-1 \right) }\) then, its final value is
- (a)
-1
- (b)
0
- (c)
1
- (d)
unbounded
The N-point discrete Fourier transform of a signal x[n] is XDFT[k] = X*DFT[k], then which of the following is true?
- (a)
y[n] = x*[n]
- (b)
y[n] = Nx*[n]
- (c)
y[n]=\(\frac{1}{N}\) x*[n]
- (d)
y[n]=-x*[n]
Which one is causal system?
- (a)
y(n) = 3x(n) - 2x(n-1)
- (b)
y(n) = 3x(n) + 2x(n+1)
- (c)
y(n) = 3x(n+1) + 2x(n-1)
- (d)
y(n) = 3x(n+1) + 2x(n-1) + x(n)
The Transfer function of an LTI system may be expressed as H(z) = K\(\frac { \left( z-{ z }_{ 1 } \right) .....\left( z-{ z }_{ m } \right) }{ \left( z-{ P }_{ 1 } \right) ....\left( z-{ P }_{ n } \right) } \) .
Following are the statements made.
1. poles of H(z) are called natural modes.
2. poles of H(z) are called natural frequencies.
Choose the correct option.
- (a)
1-true, 2-false
- (b)
1-false, 2-true
- (c)
1-true, 2-true
- (d)
1-false, 2-false
The Nyquist sampling rate for the signal s(t) = \(s\left( t \right) =\frac { sin\left( 500 \right) \pi t }{ \pi t } \times \frac { sin\left( 700 \right) \pi t }{ \pi t } \) is given by
- (a)
400 Hz
- (b)
600 Hz
- (c)
1200 Hz
- (d)
1400 Hz
The minimum sampling frequency (in sample/s) required to reconstruct the following signal from its samples without distortion. x(t)=\(5\left( \frac { sin\ 2\pi \ 1000t }{ \pi t } \right) +7\left( \frac { sin\ 2\pi 1000\ t }{ \pi t } \right) ^{ 2 }\)would be
- (a)
\(2\times { 10 }^{ 3 }\)
- (b)
\(4\times { 10 }^{ 3 }\)
- (c)
\(6\times { 10 }^{ 3 }\)
- (d)
\(8\times { 10 }^{ 3 }\)
A signal x(n) = sin\(\left( { \omega }_{ 0 }n+\phi \right) \) is the input to a linear time-invariant system having a frequency response H(ej\(\omega\) ). If the output of the system is A(n-n0), then the most general form of \(\angle \)H( e j\(\omega\) ) will be
- (a)
\(-{ n }_{ 0 }{ \omega }_{ 0 }+\beta \) for any arbitrary real \(\beta \)
- (b)
\(-{ n }_{ 0 }{ \omega }_{ 0 }+2k\) for any arbitrary integer k
- (c)
\({ n }_{ 0 }{ \omega }_{ 0 }+2k\) for any arbitrary integer k
- (d)
\(-{ n }_{ 0 }{ \omega }_{ 0 }+\phi \)
The impulse response functions of four linear system s1, s2, s3, s4 are given respectiively by
h 1(t) = 1
h2(t) = u(t)
\(h_{ 3 }\left( t \right) =\frac { u\left( t \right) }{ t+1 } \)
h4(t) = e-3t u(t)
where, u(t) is the unit step function. Which of these systems is time- invariant, causal and stable?
- (a)
s1
- (b)
s2
- (c)
s3
- (d)
s4
The Hilbert transform of cos \({ \omega }_{ 1 }\)t + sin \({ \omega }_{ 2 }\)t 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
The bilateral Laplace transform \({ e }^{ -\frac { t }{ 2 } }u\left( t \right) +{ e }^{ -t }u\left( t \right) +{ e }^{ t }u\left( -t \right) \) is
- (a)
\(\frac { 6{ s }^{ 2 }+2s-2 }{ \left( 2s+1 \right) \left( { s }^{ 2 }-1 \right) ' } \) ; Re(s)<-0.5
- (b)
\(\frac { 6{ s }^{ 2 }+2s-2 }{ \left( 2s+1 \right) \left( { s }^{ 2 }-1 \right) ' } \) -1>Re(s)>1
- (c)
\(\frac { 1 }{ s+0.5 } +\frac { 1 }{ s+1 } +\frac { 1 }{ s-1' } \) ; -1<Re(s)<1
- (d)
\(\frac { 1 }{ s+0.5 } +\frac { 1 }{ s+1 } +\frac { 1 }{ s-1' } \) ; -0.5<Rre(s)<1
The bilateral Laplace transform of a signal x(t) is \(X\left( s \right) =\left( \frac { 1 }{ s } -\frac { { e }^{ -s } }{ s } -{ e }^{ -2s } \right) \)Roc : Re(s)<0. The signal x(t) is
- (a)
u(-t)+u(-t+1)+\(\delta \)(t+2)
- (b)
u(-t)-u(-t+1)-\(\delta \)(t+2)
- (c)
u(-t)-u(-t+1)-\(\delta \)(t+2)
- (d)
-u(-t)+u(-t-1)+\(\delta \)(t+2)
The impulse response of an ideal band-pass filter is
- (a)
4fc sin c (2fc t).cos(\({ \omega }_{ 0 }\)t)
- (b)
2fc sin c (2fc t)
- (c)
rect (2fc t)
- (d)
fc sin c (2fc t)
The impulse response of an LTI system is h(t) = u(t-4). The step response is
- (a)
tu(t)+(4-t) u(t-4)
- (b)
tu(t) + (1-t) u(t-4)
- (c)
1+t
- (d)
(1+t) u(t)
Consider the transform pair given below
\(cos2tu(t)\underleftrightarrow { L } X(s)\)
The time signal corresponding to (s+1) X(s) is
- (a)
[cos 2t-2sin 2t)
- (b)
\(\left( cos\quad 2t+\frac { sin2t }{ 2 } \right) u(t)\)
- (c)
[cos 2t+2sin 2t]u(t)
- (d)
\(\left( cos\quad 2t-\frac { sin2t }{ 2 } \right) u(t)\)
Consider the signals x[n] and y[n] given below figure:
The signal x[n + 2] y[n - 2] is
- (a)
-Q.png)
- (b)
-Q.png)
- (c)
-Q.png)
- (d)
-Q.png)
Let p be linearity Q be time Invariance R be casualty and S be stability.
The system y[n]=nx[n] has the properties
- (a)
P,Q,R,S
- (b)
Q,R,S
- (c)
P,Q
- (d)
Q,R
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