Electrical Engineering - Signals and Systems
Exam Duration: 45 Mins Total Questions : 30
The laplace transform of signal sin 5t is
- (a)
\(\frac { 5 }{ s^{ 2 }+5 } \)
- (b)
\(\frac { s }{ s^{ 2 }+5 } \)
- (c)
\(\frac { 5 }{ s^{ 2 }+5 } \)
- (d)
\(\frac { s }{ s^{ 2 }+5 } \)
The laplace transform of signal u(t)-u(t-2) is
- (a)
\(\frac { e^{ -2s }-1 }{ s } \)
- (b)
\(\frac { 1-e^{ 2s } }{ s } \)
- (c)
\(\frac { 2 }{ s } \)
- (d)
\(\frac { -2 }{ s } \)
Which one of the following is true?
- (a)
A finite signal is always bounded
- (b)
A bounded signal always possesses inite energy
- (c)
A bounded signal;is always zero outside the interval \([-t_{ 0 },t_{ 0 }]\) for some \(t_{ 0 }\)
- (d)
A bounded signal is always finite
Fourier Transform of function is
- (a)
2sinc(\(2\pi f)\)-sin\(c^{ 2 }\)(\(\pi f\))
- (b)
\(2sinc^{ 2 }(2\pi f)-sinc(\pi f)\)
- (c)
\(2sinc(2\pi f)--sinc(\pi f)\)
- (d)
\(sinc(2\pi f)-sinc^{ 2 }(\pi f)\)
The time signal corresponding to \(\frac { s+3 }{ s^{ 2 }+3s+2 } \) is
- (a)
\((2e^{ -2t }+e^{ -t })u(t)\)
- (b)
\((2e^{ -2t }+e^{ -2t })u(t)\)
- (c)
\((2e^{ -2t }+e^{ -t })u(t)\)
- (d)
\((2e^{ -t }+e^{ -2t })u(t)\)
Given the Z-transform pair
\(X[n]\overset { z }{ \leftrightarrow } \frac { 32 }{ z^{ 2 }-16 } |z|<4\)
The Z-transform of the signal \(y[n]=\frac { 1 }{ 2^{ n } } x[n]\)
- (a)
\(\frac { (z+2)^{ 2 } }{ (z+2)^{ 2 }-16 } \)
- (b)
\(\frac { z^{ 2 } }{ z^{ 2 }-4 } \)
- (c)
\(\frac { (z-2)^{ 2 } }{ (z-2)^{ 2 }-16 } \)
- (d)
\(\frac { z^{ 2 } }{ z^{ 2 }-64 } \)
Given the Z-transform pair
\(3^{ n }n^{ 2 }u[n]\overset { z }{ \leftrightarrow } X(z)\)
The time of signal corresponding to \(X(z^{ -1 })\) is
- (a)
\(n^{ 2 }3^{ -n }u[-n]\)
- (b)
\(n^{ 2 }3^{ -n }u[-n]\)
- (c)
\(\frac { 1 }{ n^{ 2 } } 3^{ \frac { 1 }{ n } }u[n]\)
- (d)
\(\frac { 1 }{ n^{ 2 } } 3^{ \frac { 1 }{ n } }u[-n]\)
The Fourier transform of signal \({ e }^{ -4|t| }\) is
- (a)
\(\frac { 8 }{ 16+{ w }^{ 2 } } \)
- (b)
\(\frac { -8 }{ 16+{ w }^{ 2 } } \)
- (c)
\(\frac { 4 }{ 16+{ w }^{ 2 } } \)
- (d)
\(\frac { -4 }{ 16+{ w }^{ 2 } } \)
Consider a continuous-time periodic signal x(t) with fundamental period T and Fourier series coefficients X[k] Determine the Fourier series coefficient of the signal y(t) given in question and choose the correct option
The Fourier series coefficient of the signal y(t)=Ev [x(t)] is
- (a)
\(\frac { X[k]+X[-k] }{ 2 } \)
- (b)
\(\frac { X[k]-X[-k] }{ 2 } \)
- (c)
\(\frac { X[k]-X*[-k] }{ 2 } \)
- (d)
\(\frac { X[k]-X*[-k] }{ 2 } \)
The inverse Fourier transform of \(2\pi (1-cos4\pi t)\) +\(\pi \delta ((\omega +4\pi ) \) is
- (a)
\(2\pi (1-cos4\pi t)\)
- (b)
\(\pi (1-cos4\pi t)\)
- (c)
\(1-cos4\pi t\)
- (d)
\(2\pi (1+cos4\pi t)\)
Consider a continuous-time periodic signal x(t) with fundamental period T and Fourier series coefficients X[k] Determine the Fourier series coefficient of the signal y(t) given in question and choose the correct option
The Fourier series coefficient of the signal y(t)-Re[x(t)] is
- (a)
\(\frac { X[k]+X[-k] }{ 2 } \)
- (b)
\(\frac { X[k]-X[-k] }{ 2 } \)
- (c)
\(\frac { X[k]+X*[-k] }{ 2 } \)
- (d)
\(\frac { X[k]-X*[-k] }{ 2 } \)
Power spectral density of signal x(t) is shown below The average power is
- (a)
zero
- (b)
6
- (c)
Infinite
- (d)
-6
A signal g(t)=10 sin \((12\pi t)\) is a
- (a)
periodic signal with period 6 s
- (b)
periodic signal with period 10/6 s
- (c)
periodic signal with period 1/6 s
- (d)
a periodic signal
Find the autocorrelation of the x(t)=e-atu(t)
- (a)
\(\frac { e^{ -at } }{ 2a^{ 2 } } \)
- (b)
\(2\lambda e^{ -a\lambda }\)
- (c)
\(\frac { e^{ -a\lambda } }{ 2a^{ 2 } } \)
- (d)
\(\frac { e^{ -a\lambda } }{ 2a } \)
Unit impulse response of a system is given as
c(t)=-4-t+6e-2t
The step response of the same system for \(t\ge 0\) is equal to
- (a)
3e-2t+4e-t-1
- (b)
-3e-2t+4e-t-1
- (c)
-3e-2t-4e-t-1
- (d)
-3e-2t+4e-t+1
The Laplace transform of x(t) can be interpreted as the transform of x(t) after multiplication by real ......... signal
- (a)
Fourier, exponential
- (b)
z-transform, impulse
- (c)
z-transform, exponential
- (d)
Fourier, impulse
\(X(s)=\frac { 1 }{ \left( s+1 \right) \left( s+2 \right) } \) with ROC between -1, -2 then x(t) is given by
- (a)
(e2t - e-t) u(t)
- (b)
e2t - e-t u(t)
- (c)
- e-t u (t) - e-t u(t)
- (d)
None of these
System function H(s) =\(\frac { 1 }{ s+3 } \) For a signal sin 2t, the 5+3 steady state response is
- (a)
1/8
- (b)
infinite
- (c)
zero
- (d)
8
The transfer function of an LTI system may be expressed as
\(H(z)=K.\frac { \left( Z-Z_{ 1 } \right) ...\left( Z-Z_{ m } \right) }{ \begin{matrix} \left( Z-P_{ 1 } \right) & \left( Z-P_{ n } \right) \end{matrix} } \)
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
A continuous time signal x(t) is applied to the input of a continuous time LTI system with unit impulse response h(t). Find the output y(t). Given that x(t)=e2tu(-t) and h(t) = u(t - 3)
- (a)
1/2
- (b)
-1/2
- (c)
0
- (d)
2
A system with x(t) and output y(t) is defined by the input output relation \(Y(t)=\int _{ -\infty }^{ -2t }{ X\left( \tau \right) d\tau } \) The system wi II be
- (a)
causal, time invariant and unstable
- (b)
causal, time invariant and stable
- (c)
non-causal, time invariant and unstable
- (d)
non-causal, time variant and unstable
The Fourier series coefficients for a discrete time signal \(x\left[ n \right] =\left\{ \underset { \uparrow }{ 1 } ,1,0,0 \right\} \) periodic with N =4 is given by
- (a)
\(C_{ k }=\frac { 1 }{ 2 } \left[ 1+e^{ -j\pi k/2 } \right] \)
- (b)
\(C_{ k }=\frac { 1 }{ 4 } \left[ 1+e^{ -j\pi k/2 } \right] \)
- (c)
\(C_{ k }=\frac { 1 }{ 2 } \left[ 1+e^{ -j\pi k } \right] \)
- (d)
\(C_{ k }=\frac { 1 }{ 4 } \left[ e^{ 2\pi k }+e^{ -j\pi k/4 } \right] \)
The discrete time Fourier coefficients X[k] for \(x\left[ n \right] =2sin\left( \frac { 4 }{ 19 } n \right) +cos\left( \frac { 10 }{ 19 } n \right) +1\) will be
- (a)
\(-j\delta \left[ k+2 \right] +j\delta \left[ k-2 \right] +\frac { 1 }{ 2 } \delta \left[ k+5 \right] +\frac { 1 }{ 2 } \delta \left[ k-5 \right] +1\)
- (b)
\(-j\delta \left[ k+2 \right] +j\delta \left[ k-2 \right] +\frac { 1 }{ 2 } \delta \left[ k+5 \right] +\frac { 1 }{ 2 } \delta \left[ k-5 \right] +\delta \left[ k \right] \)
- (c)
\(-j\delta \left[ k-2 \right] +j\delta \left[ k+2 \right] +\frac { 1 }{ 2 } \delta \left[ k+5 \right] +\frac { 1 }{ 2 } \delta \left[ k+5 \right] +\delta \left[ k \right] \)
- (d)
None of the above
Fourier series coefficient y(t) =x(t -t0) + x(t + t0) will be
- (a)
\(2cos\left( \frac { 2\pi }{ T } kt_{ 0 } \right) X\left[ k \right] \)
- (b)
\(e^{ -t_{ 0 } }X\left[ -k \right] +e^{ t_{ 0 } }X\left[ k \right] \)
- (c)
\(e^{ -t_{ 0 } }X\left[ k \right] +e^{ t_{ 0 } }X\left[ -k \right] \)
- (d)
\(2sin\left( \frac { 2\pi }{ T } kt_{ 0 } \right) X\left[ k \right] \)
Find 3 terms of the Fourier series of a periodic 1 kHz rectangular waveform symmetrical about t =0 and having a pulse width of 500 us and amplitude as 5 V.
- (a)
\(2.5+3.18cos(2\pi \times 10^{ 3 }t)-1.06cos(6\pi \times 10^{ 3 }t)\)
- (b)
\(2.5+3.18cos(2\pi \times 10^{ 3 }t)+1.06cos(6\pi \times 10^{ 3 }t)\)
- (c)
\(2.5-3.18cos(2\pi \times 10^{ 3 }t)-1.06cos(6\pi \times 10^{ 3 }t)\)
- (d)
\(2.5-3.18cos(2\pi \times 10^{ 3 }t)+1.06cos(6\pi \times 10^{ 3 }t)\)
The signal \(n\left( \frac { t }{ c } \right) +n\left( \frac { t }{ 2c } \right) \) is
- (a)
energy signal
- (b)
power signal
- (c)
Both (a) and (b)
- (d)
None of these
Obtain the Fourier transform of a rectangular pulse of duration 2 s and having a magnitude of 10 V as shown in figure.
- (a)
\(20e^{ -j\omega }sinc(\omega )\)
- (b)
\(20e^{ -j\omega }\frac { sinc(\omega ) }{ \omega } \)
- (c)
\(e^{ -j\omega }sinc\omega \)
- (d)
\(20^{ -j\omega }sinc(\omega )\)
Find the system function H(z) and unit sample response h(n) of the system whose difference equation is described as under \(y(n)=\frac { 1 }{ 2 } y(n-1)+2x(n)\) where, y(n) and x(n) are the output and input of the system respectively.
- (a)
\(2\left( \frac { -1 }{ 2 } \right) ^{ n }u(n)\)
- (b)
2(1)nu(n)
- (c)
\(2\left( \frac { 1 }{ 2 } \right) ^{ n }u(n)\)
- (d)
\(\left( \frac { 1 }{ 2 } \right) ^{ n }u(n)\)
Let P be linearity, Q be time invariance, R be causality and S be stability.
The system \(y\left[ n \right] =\sum _{ m=0-\infty }^{ n+1 }{ u\left[ m \right] } \) has the properties
- (a)
P, Q, R and S
- (b)
R and S
- (c)
P and Q
- (d)
Q and R
Let P be linearity, Q be time invariance, R be causality and S be stability.
The system y [n] = rect (x [n]) has the properties
- (a)
P, Q and R
- (b)
Q, R and S
- (c)
R, S and P
- (d)
S, P and Q