The units of the spectrum obtained by Fourier transforming the covariance function of a stationary stochastic process is
A. power per Hertz
B. energy per Hertz
C. power per second
D. energy per second
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Zero padding are
A. zero appearing in the X(k) sequence
B. value of X(k) is zero
C. dummy sample added with value 0 in X(k)
D. both A and B
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In Digital Filters, how many interpolated data points are inserted between samples when performing 4X over sampling?
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Which of the following statement is not true
A. Autocorrelation function and energy spectral density form a Fourier transform pair
B. Autocorrelation function of a real valued energy signal is a real valued odd function
C. The value of autocorrelation function of a power signal at the origin is equal to the average power of the signal
D. Autocorrelation function is the inverse Fourier transform of power spectral density
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Which of the following is not a periodic function of φ?
A. sinφ + π cosφ
B. sin(πφ) + cos(πφ)
C. sin(φ) + cos(πφ)
D. sin(π) + cos(π + φ)
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Which of the following cannot be the Fourier series expansion of a periodic signal?
A. x(t) = 2cost + 3cos3t
B. x(t) = 2cosπt + 7cost
C. x(t) = cost + 0.5
D. x(t) = 2cos 1.5πt + sin 3.5πt
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A system with input x[n] and output y[n] is given as y [ n ] = ( sin 6 5 π n ) x ( n ) .
The system is
A. linear, stable and invertible
B. non-linear, stable and non-invertible
C. linear, stable and non-invertible
D. linear, unstable and invertible
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Let F(ω) be the Fourier transform of a function f(t), then F(0) is
A. − ∞ ∫ ∞ f ( t ) d t
B. − ∞ ∫ ∞ ∣ f ( t ) ∣ 2 d t
C. − ∞ ∫ ∞ ∣ t f ( t ) ∣ 2 d t
D. − ∞ ∫ ∞ t f ( t ) d t
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Let P be linearity, Q be time-invariance, R be causality and S be stability. A discrete-time system has the input-output relationship,
y\left( n \right) = \left\{ {\begin{array}{*{20}{c}}
{x\left( n \right),}&{n \geqslant 1} \\
{0,}&{n = 0} \\
{x\left( {n + 1} \right)}&{n \leqslant - 1}
\end{array}} \right.
Where x(n) is the input and y(n) is the output.
The above system has the properties
A. P, S but not Q, R
B. P, Q, S but not R
C. P, Q, R, S
D. Q, R, S but not P
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Consider a random sinusoidal signal x(t) = sin(ω0 t + φ), where a random variable 'φ' is uniformly distributed in the range ± 2 π . The mean value of x(t) is
A. zerp
B. π 2 sin (ω0 t)
C. π 2 cos (ω0 t)
D. π 2
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Match
List-I with
List-II and select the correct answer using the options given below:
List-I (x[n])
List-II (X(z))
a. a n u [ n ]
1. ( z − a ) 2 a z
b. a n − 2 u [ n − 2 ]
2. z e − j − a z e − j
c. e j n a n
3. z − a z
d. n . a n u [ n ]
4. z − a z − 1
A. a-3, b-2, c-4, d-1
B. a-2, b-3, c-4, d-1
C. a-3, b-4, c-2, d-1
D. a-1, b-4, c-2, d-3
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The minimum number of delay elements required in realizing a digital filter with the transfer function H ( z ) = 1 + c z − 1 + d z − 2 + e z − 3 1 + a z − 1 + b z − 2 is
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An input x[n] with length 3 is applied to a linear time invariant system having an impulse response h[n] of length 5 and Y(ω) is the DTFT of the output y[n] of the system. If |h[n]| ≤ L and |x[n]| ≤ L for all n, the maximum value of Y(0) can be:
A. 15 LB
B. 12 LB
C. 8 LB
D. 7 LB
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The complex exponential power form of Fourier series of x(t) is: x ( t ) = ∑ k = − ∞ ∞ a k . e j T 0 2 π . k t
If x ( t ) = ∑ b = − ∞ ∞ δ ( t − b ) , then the value of ak is:
A. 1 - (-1)k
B. 1 + (-1)k
C. 1
D. -1
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If x(t) = 10 rect ( 2 t ) , the zero-frequency value of its spectrum is given by
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FIR filters can be designed using
A. windowing method
B. bilinear transformation
C. impulse invariant transformation
D. windowing and frequency sampling method
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The auto correlation function Rx (τ) satisfies which one of the following properties?
A. Rx (τ) = -Rx (-τ)
B. Rx (τ) = Rx (-τ)
C. Rx (τ) ≥ Rx (0)
D. Rx (τ) ≥ 1
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If a random process X(t) is ergodic then, statistical averages
A. and time averages are different
B. and time averages are same
C. are greater than time averages
D. are smaller than time averages
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Which one of the following systems described by the following input-output relation is non-linear?
A. y(n) = nx(2n)
B. y(n) = x(n2 )
C. y(n) = n2 x(n)
D. y(n) = x2 (n)
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Let h(t) denote the impulse response of a causal system with transfer function s + 1 1 . Consider the following three statements:
S1 : The system is stable.
S2 : h ( t ) h ( t + 1 ) is independent of t for t > 0.
S3 : A non-causal system with the same transfer function is stable.
For the above system,
A. only S1 and S2 are true
B. only S2 and S3 are true
C. only S1 and S3 are true
D. S1 , S2 and S3 are true
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