Which one of following is a stataic system?
-
y(n) = x(n) - x(n - 1) -
y(n) = x(2n) - x(2n-1) -
y(n) = x(n - 1) -
y(n) = ex(n)
If a complex voltage wave is applied to a pure inductance, the resulting current wave is much smoother than the voltage wave.
-
True -
False
Which one of the following is the correct statement? The region of convergence of z transform of x[n] consists of the values of z for which x[n] r-n is
-
absolutely integrable -
absolutely summable -
unity -
< 1
Fourier transform o the function f(t) = 1 is
-
2p δ (ω) -
p δ (ω) -
δ(ω)/2p -
δ(ω)/p
If v(t) = 0 for t < 0 and e-at for t ≥ 0 V(jω) = 1/(a + jω).
-
True -
False
The term 'energy spectral density' is associated with
-
periodic waveform -
non-periodic waveform -
both perodic and non -perodic waveform -
none of the above
unit step is a
-
energy signal -
power signal -
neither energy nor power signal -
none
For formation of state equations, resistance of the circuit
-
should be in tree -
should be in cotree -
may be in tree or cotree -
none of the above
In a Communication system, noise is most likely to affect the signal.
-
at the transmitter -
In the channel -
in Information source -
at the destination
If R(t) is autocorrelation of a waveform v(t) and R(is autocorrelation for t =then
-
R(0) > R(t) -
R(0) ≥ R(t) -
R(0) < R(t) -
R(0) ≤ R(t)
Which of the following is/are not a property/properties power spectral density function Sx(ω)?
-
Sx(ω) is real function of ω -
Sx(ω) is a even function of ω -
Sx(ω) is non-positive function of ωSx(ω) ≤ 0 for all ω -
All of the above
The discrete time system describes by y(n) = x(n2) is
-
casual, Linear, time varying -
casual, non-linear, timevari -
non-casual, Linear, time invariant -
non-casual, non-linear, time variant
A system is said to be static system, when present output depend upon
-
present I/P -
presrent and past -
present and future -
past and future
The function f(t) = E[u(t - a) - u(t - b)] is
-
a pulse function originating at t = a -
a step function orginating at t = 0 -
an exponential function originating at t = a -
a pulse function originating at t = a and duration (b - a)
If f(t) =F(jω) = 2p δ(ω).
-
True -
False
A function will have only sine terms if
-
f(t) = - f(t) -
f(-t) = f(t) -
f(-t) = -f(t) -
none of the above
Assertion (A): The function δ'(t - b) is equal to 0 for t ≠ b
Reason (R): A number of impulses spaced from one another form an impulse train.
-
Both A and R are correct and R is correct explanation of A -
Both A and R are correct but R is not correct explanation of A -
A is true, R is false -
A is false, R is true
Assertion (A): Impulse function is an important function in network analysis.
Reason (R): Convolution integral enables us to find the response of a network to an arbitary input in terms of the impulse response.
-
Both A and R are correct and R is correct explanation of A -
Both A and R are correct but R is not correct explanation of A -
A is true, R is false -
A is false, R is true
If average correlation between v1(t) and v2(t) is R12(t) and average correlation between v2(t) and v1(t) is R21(t) then
-
R12(t) = R21(t) -
R21(t) = R12(t) -
R12(t) = - R21(t) -
none of these
A casual LTI system is described by the difference equation
2y[n] = ay[n -- 2x[n] + βx[n -
The system is stable only if
-
|a| = 2 |β| < 2 -
|a| > 2 |β| > 2 -
|a| < 2 any value of β -
|β| < 2, any value of a
A system is stable if ROC
-
include the unit circle -
exclude the unit circle -
lies on Circle -
entire plane
If ROC of x[n] is R1 then ROC of an x[n] is
-
R1a -
R1/a -
a/R1 -
R1 + a
If two mutually exclusive events A and B can happen in m and n ways, then either A or B can happen in (m + n) ways.
-
True -
False
unit step is a
-
energy signal -
power signal -
neither energy nor power signal -
none
If a function f(t) is an odd, function, its Fourier series
-
contains only sine terms -
contains only cosine terms -
contains a constant and sine terms -
contains a constant and cosine
ROC of sequence x[n] = δ[n] is
-
Not exist -
z = 0 -
Entire Plane -
Entire Plane expect z = 0, z = ∞
If X(z) = (1 - a)z-1/[(1 - z-1)(1 - az-1)] and 1 < |z|, the final value of xk is
-
0 -
1 -
∞ -
2
The range of values of a and b for which the linear time invariant system with impulse response.
h(n) = an n ≥ 0
= bn n < 0
will be stable if
-
|a| > 1, |b| > 1 -
|a| < 1, |b| < 1 -
|a| < 1, |b| > 1 -
|a| > 1, |b| < 1
If f(- t) = f(t), the function f(t) has only cosine terms.
-
True -
False
The inverse Laplace transform of 1/(s - a)2 is
-
eat -
t eat -
t2 eat -
eat/t
A discrete LTI system is non-casual if its impulse response is
-
an ∪(n - 2) -
an-2 ∪(n) -
an+2 ∪(n) -
an ∪(n + 2)
A stationary process has
-
all statistical properties independent of time -
all statistical properties dependent of time -
zero variance -
ensemble average equal to time average
The Laplace transform of a unit step function is
-
1 -
1 / s -
s -
1 / s2
x = AX + Bu is a state equation.
-
True -
False
Which of the following can be impulse response of a casual system?
If two mutually exclusive events A and B can happen in m and n ways, then either A or B can happen in (m + n) ways.
-
True -
False
For a second order system, damping ratio ζ is such that 0 < ζ <. Then the roots of characteristic equation are
-
real but not equal -
real and equal -
complex conjugate -
imaginary
The function δ'(t - b) is a unit doublet.
-
True -
False
The standard deviation of a set of observations is the rms value of the deviation from the arithmetic mean.
-
True -
False
If the sequence |xn|1/n converges, then the series 
converages absolutely is
-
Ratio test -
Root test -
Convergence test -
Divergence test
The output of a linear system for any input can be computed in which of the following ways?
-
Only by summation of inpulse response by convolution integral -
Only by summation of step response by superposition integral -
Neither a nor b -
Either (a) or (b)
Which one is correct option about ROC?
-
ROC does not contain any pole -
ROC of finite duration sequence is entire plane expect z = 0, z = ∞ -
a and b -
only a
If f(t)↔ F(jω), and f(t) is real, then F(- jω)
-
F(jω) -
F*(j↔) -
F*(- jω) -
none of these
Final value theorem is used to find
-
steady state value of system output -
initial value of output -
transient beaviour of output -
none of these
Which one of following is correct condition to check the stability of sysytem in terms of impulse response?
-
Σ(x(n)) < ∞ -
Σx(n) < 0 -
Σx(n) = 0 -
Σx(n) = ∞
If xk = 0 for k < 0 and = 2k for k ≥ 0 X(z) = z/(z -2).
-
True -
False
Assertion (A): If an event A can happen in m ways and another event B can happen in n ways, both can happen in mn ways.
Reason (R): Two events are mutually exclusive if happening of either precludes the occurrence of other.
-
Both A and R are correct and R is correct explanation of A -
Both A and R are correct but R is not correct explanation of A -
A is true, R is false -
A is false, R is true
The signal m(t) =cospt is sampled at the rate of Fs =Hz, then determine signal after sampling.
-
4 cos 100 pt + 8 sin 200 pt -
4 cos 100 pt + 8 sin 200 pt + cos 75 pt -
4 cos 25 pt + 8 sin 50 pt + cos 75 pt -
none
A function will have only sine terms if
-
f(t) = - f(t) -
f(-t) = f(t) -
f(-t) = -f(t) -
none of the above
Fourier transform o the function f(t) = 1 is
-
2p δ (ω) -
p δ (ω) -
δ(ω)/2p -
δ(ω)/p