A unit impulse function δ(t) is defined by∫ − ∞ ∞ δ ( t ) d t = 1
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Consider an LTI system subjected to a wide sense stationary input {x(n)}, which is a white noise sequence. The cross correlation Φxy [m] between input x(n) and output y(n) is:xx [m] = σ x 2 δ [ m ]
A. σ x 2 h [ m ]
B. σ x h [ m ]
C. 2 σ x 2 h [ m ]
D. 2 σ x h [ m ]
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If |H(ω)| = H(ω)H(-ω) then
A. h(n) has imaginary value
B. h(n) has real value
C. h(n) has any value
D. h(n) has positive value
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Let x(n) be a real-valued sequence that is a sample sequence of a wide-sense stationary discrete-time random process. The power density of this signal is
A. real, odd and non-negative
B. real, even and non-negative
C. purely imaginary, even and negative
D. purely imaginary, odd and negative
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Consider an impulse response h[n] = {-3, -1, 2, 1, 3}, system is . . . . . . . . phase and . . . . . . . . pass filter.
A. Linear, low
B. Linear, high
C. Linear, band
D. Non linear, all band
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If the input x(t) = u(t) + u(t - 1) is applied to a LTI system whose impulse response is given by h(t) = δ(t), then the response of the system y(t) is
A. u(t) + 2u(t + 1)
B. u(t) + u(t - 1)
C. u(t) + u(t + 1)
D. u(t) + 2u(t - 1)
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A system is defined by its impulse response h(n) = 5n u(n - 5). The system is
A. Unstable & non-causal
B. Stable & causal
C. Unstable & causal
D. Stable & non-causal
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Let X ( e j ω ) = ∑ n = − ∞ ∞ x [ n ] e − j ω n x [ n ] = 2 π 1 − π ∫ π X ( e j ω ) e j ω n d ω . X ( e j ω ) = ( 1 − 0.2 e − j ω ) ( 1 − 0.1 e − j ω ) 1 ,
A. 2(0.2)n u(n) - (0.1)n u(n)
B. 2(0.1)n u(n) - (0.2)n u(n)
C. (0.2)n u(n) - (0.1)n u(n)
D. (0.1)n u(n) - (0.2)n u(n)
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Sampling theorem denoted as
A. Δ T 1 > 2 μ m a x
B. T 1 > 2 μ m a x
C. Δ T 1 < 2 μ m a x
D. Δ T 1 > 1 μ m a x
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Given y .. ( t ) + 3 y . ( t ) + 4 y ( t ) = 2 x .. ( t ) + 7 x . ( t ) + 8 x ( t )
A. H ( s ) = 2 s 2 + 7 s + 8 s 2 + 3 s + 4
B. H ( s ) = s 2 + 3 s + 4 2 s 2 + 7 s + 8
C. H ( s ) = 2 s 2 + 3 s + 4 s 2 + 7 s + 8
D. H ( s ) = 2 s 2 + 3 s + 4 s 2 + 8 s + 7
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Which of the following is a non-recursive system?
A. y(n - 1) + 2y(n - 2 )
B. y(n - 3)
C. y(n) + 2y(n + 2)
D. 5y(n - 3)
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The amplitude spectrum of a Gaussian pulse is
A. uniform
B. a sine function
C. Gaussian
D. an impulse function
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Two random processes X and Y are such that RXY (t1 , t2 ) = 0 for all t1 and t2 and further one of them has zero mean. The processes are
A. Uncorrelated but not orthogonal
B. Orthogonal but not uncorrelated
C. Statistically independent and orthogonal
D. Orthogonal and uncorrelated
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The Z - transform of a-n u(-n - 1) is,
A. z − a 1 − z
B. z − a 1 z
C. z − a z
D. z − a − z
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What are poles and zeros of a system having following transfer function?H ( z ) = ( 1 + 1.3 z − 1 + 0.36 z − 2 ) ( 1 − z − 2 )
A. Zeros = -1, 1; poles = -0.4, -0.9
B. Zeros = -1, 1; poles = 0.4, 0.9
C. Zeros = 1; poles = 0.4, 0.9
D. Zeros = 1, 1; poles = 0.4, 0.9
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The auto-correlation function Rx (τ) of a random process has the property that Rx (0) is equal to
A. The square of the mean value of the process
B. The mean squared value of the process
C. The smallest value of Rx (τ)
D. 2 1 x (τ) + Rx (-τ)]
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Match
List-I with
List-II and select the correct answer using the options given below:
List-I [Function in time domain f(t)]List-II [Property]
a. sin ω 0 t u ( t − t 0 )
1. s 2 + ω 0 2 ω 0
b. sin ω 0 ( t − t 0 ) u ( t − t 0 )
2. { s 2 + ω 0 2 ω 0 } e − t 0 s
c. sin ω 0 ( t − t 0 ) u ( t )
3. s 2 + ω 0 2 e − t 0 s sin ( ω 0 t 0 + tan − 1 s ω 0 )
d. sin ω 0 t u ( t )
4. − s 2 + ω 0 2 1 sin ( ω 0 t 0 − tan − 1 s ω 0 )
A. a-3, b-1, c-4, d-2
B. a-4, b-2, c-3, d-1
C. a-3, b-2, c-4, d-1
D. a-4, b-1, c-3, d-2
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Which one of the following operations is not commutative?
A. Scaling and reversal of a signal x[n]
B. Scaling and folding of a signal x[n]
C. Folding and time reversal of a signal x[n]
D. Folding and time delaying of a signal x[n]
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The signals x1 (t) are band limited to 4π rad/sec and 10π rad/sec respectively. The minimum sampling rate required for sampling the signal x1 (2t) + x2 ( 2 t )
A. 16π rad/sec
B. 8π rad/sec
C. 40π rad/sec
D. 2π rad/sec
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A random variable X is defined by the double exponential distribution ρx (X) = ae-b|x| - ∞ < x < ∞x (X) is a probability density function?
A. a = 2 b
B. b = 2 a
C. a = b
D. a = b 1
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