What will be the Laplace transform for f(t) = e-bt u(t)?
A. F ( s ) = s + b s
B. F ( s ) = s ( s + b ) 1
C. F ( s ) = s + b 1
D. F ( s ) = 1 + b s
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The even and odd components of the signal x(t) = e-2t cos t are respectively,
A. cos 2t cos t and -sin 2t cos t
B. sinh 2t sin t and -cosh 2t cos t
C. cos 2t sin t and -sin 2t cos t
D. cosh 2t cos t and -sinh 2t cos t
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A band-limited lowpass signal is sampled at twice its Nyquist rate with fs = 2000 sps. The signal is band-limited to
A. 250 Hz
B. 1000 Hz
C. 500 Hz
D. 2000 Hz
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For a given transmitted pulse p(t), 0 ≤ t ≤ T, the impulse response of a filter matched to the received signal is
A. -p(t - T), 0 ≤ t ≤ T
B. -p(T - t), 0 ≤ t ≤ T
C. p(t - T), 0 ≤ t ≤ T
D. p(T - t), 0 ≤ t ≤ T
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If x ( n ) = { ( 2 1 ) n ; 0 ≤ n ≤ ( N − 1 ) 0 ; otherwise then x(z) is equal to
A. 1 − ( 2 1 ) z − 1 1 − 2 − N z − N
B. 1 − 2 z − 1 1 − ( 2 1 ) − N z − N
C. 1 − ( 2 1 ) z − 1 1 − 2 N z − N
D. 1 − ( 2 1 ) z − 1 1 − ( 2 1 ) N z − N
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Consider a single input single output discrete-time system with x[n] as input and y[n] as output, where the two are related as
y\left[ n \right] = \left\{ {\begin{array}{*{20}{c}}
{n\left| {x\left[ n \right]} \right|,}&{{\text{for }}0 \leqslant n \leqslant 10} \\
{x\left[ n \right] - x\left[ {n - 1} \right],}&{{\text{otherwise}}}
\end{array}} \right.
Which one of the following statements is true about the system?
A. It is causal and stable
B. It is causal but not stable
C. It is not causal but stable
D. It is neither causal nor stable
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The covariance function, Cx (τ), of a stationary stochastic process, x(t), is said to be positive definite. This means that
A. C x ( τ ) ⩾ 0 for all τ
B. − ∞ ∫ ∞ C x ( τ ) d τ ⩾ 0
C. − ∞ ∫ ∞ C x ( τ ) exp ( − j ω τ ) d τ ⩾ 0
D. C x ( 0 ) ⩾ 0
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A composed signal is given by x(t) = cos(ωt) + sin(ωt) + sin2 (ωt) + cos(ωt) + sin2 (ωt). The odd component is
A. cos(ωt)
B. sin(ωt)
C. sin2 (ωt)
D. cos(ωt)sin2 (ωt)
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The signal x(n) shown in the above figure is a
A. periodic discrete time signal
B. periodic signal
C. non-periodic signal
D. periodic discrete time signal consisting of 3 non-zero samples
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Which of the following is NOT one of the representations of discrete-time signals?
A. Analytical representation
B. Tabular representation
C. Graphical representation
D. Sequence representation
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The first stage DIT-FFT of a sequence x(n) is given by:
A. X ( k ) = { G ( k ) + W N k H ( k ) 0 ≤ k ≤ ( 2 N − 1 ) G ( k + 2 N ) − W N k H ( k + 2 N ) 2 N ≤ k ≤ ( N − 1 )
B. X ( k ) = { G ( k ) − W N k H ( k ) 0 ≤ k ≤ ( 2 N − 1 ) G ( k + 2 N ) − W N k H ( k + 2 N ) 2 N ≤ k ≤ ( N − 1 )
C. X ( k ) = { G ( k ) − W N k H ( k ) 0 ≤ k ≤ ( 2 N − 1 ) G ( k ) + W N k H ( k ) 2 N ≤ k ≤ ( N − 1 )
D. X ( k ) = { G ( k + N ) − W N k H ( k ) 0 ≤ k ≤ ( 2 N − 1 ) G ( k ) + W N k H ( k ) 2 N ≤ k ≤ ( N − 1 )
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What is the value of magnitude frequency response of Butterworth low pass filter at Ω = 0 ?
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The input-output relationship of a causal stable LTI system is given as y[n] = αy[n - 1] + βx[n]
If the impulse response h[n] of this system satisfies the condition n = 0 ∑ ∞ h [ n ] = 2 , the relationship between α and β is
A. α = 1 − 2 β
B. α = 1 + 2 β
C. α = 2β
D. α = -2β
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The linear time invariant system h(t) = (e-4t + e4t ).u(t) is . . . . . . . . and . . . . . . . .
A. Causal, Unstable
B. Noncausal, Unstable
C. Causal, Stable
D. Noncausal, Stable
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The unit sample response of a discrete system is 1, 2 1 , 4 1 , 0, 0, 0 . . . For an input sequence 1, 0, 1, 0, 0, 0 . . ., what is the output sequence?
A. 1 , 2 1 , 4 1 , 2 1 , 4 1 , 0 , 0 ...
B. 1 , 0 , 4 1 , 0 , 0 ...
C. 2 , 2 1 , 4 5 , 0 , 0 ...
D. 1 , 2 1 , 4 5 , 2 1 , 4 1 , 0 , 0 ...
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The output w[n] of the system shown in figure is
x [ n ] y [ n ] = − ∞ ∑ n x [ k ] y [ n ] w [ n ] = y [ n ] − y [ n − 1 ] w [ n ] A. x[n]
B. x[n - 1]
C. x[n] - x[n - 1]
D. 2 1 (x[n - 1]) + x[n]
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A matched filter having a frequency response H ( f ) = j 2 π f 1 − e − j 2 π f T matches to:
A. s ( t ) = { 1 , 0 ≤ t ≤ T 0 , otherwise
B. s ( t ) = { − 1 , 0 ≤ t ≤ T 0 , otherwise
C. s ( t ) = { 1 − T t , 0 ≤ t ≤ T 0 , otherwise
D. s ( t ) = { − 1 + T t , 0 ≤ t ≤ T 0 , otherwise
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Auto-correlation function Rx (τ) of a stationary process X(t) is
A. a deterministic function with maximum value at τ = 0
B. a deterministic function which is periodic
C. a stationary random process
D. a periodic stationary process
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What is the ROC for the given signal?
x 1 [ n ] = ( 2 1 ) n u [ n − 3 ]
A. ∣ z ∣ > 2 1
B. ∣ z ∣ < 2 1
C. ∣ z ∣ < 3 1
D. ∣ z ∣ > 3 1
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If the step response of a causal, linear time-invariant system is a(t), then the response of the system to a general input x(t) would be
A. 0 + ∫ t d τ d a ( τ ) x ( t − τ ) d τ
B. a ( 0 ) x ( t ) + 0 + ∫ t d τ d a ( τ ) x ( t − τ ) d τ
C. x ( 0 ) a ( t ) + 0 + ∫ t x ( τ ) a ( t − τ ) d τ
D. x ( 0 ) a ( t ) + 0 + ∫ t d τ d a ( τ ) x ( t − τ ) d τ
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