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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The Fourier transform of a voltage signal x(t) is X(f). The unit of |X(f)| is
A. Volt
B. Volt-sec
C. Volt/sec
D. Volt2
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An excitation is applied to a system at t = land its response is zero for -∞ < t < T. Such a system is a
A. Non-causal system
B. Stable system
C. Causal system
D. Unstable system
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A realization of a stable discrete time system is shown in figure. If the system is excited by a unit step sequence input x[n], the response y[n] is
A. 4 ( − 3 1 ) n u [ n ] − 5 ( − 3 2 ) n u [ n ]
B. 5 ( − 3 2 ) n u [ n ] − 3 ( − 3 1 ) n u [ n ]
C. 5 ( − 3 1 ) n u [ n ] − 3 ( − 3 2 ) n u [ n ]
D. 5 ( − 3 2 ) n u [ n ] − 5 ( − 3 1 ) n u [ n ]
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Match the following and choose the correct combination.
Group I
Group II
E. Continuous and aperiodic signal
1. Fourier representation is continuous and aperiodic.
F. Continuous and periodic signal
2. Fourier representation is discrete and aperiodic.
G. Discrete and aperiodic signal
3. Fourier representation is continuous and periodic.
H. Discrete and periodic signal
4. Fourier representation is discrete and periodic.
A. E-3, F-2, G-4, H-1
B. E-1, F-3, G-2, H-4
C. E-1, F-2, G-3, H-4
D. E-2, F-1, G-4, H-3
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If L[f(t)] = F(s), then L[f(t - T)] is equal to
A. esT F(s)
B. e-sT F(s)
C. 1 + e s T F ( s )
D. 1 − e − s T F ( s )
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The impulse response h(t) of a linear time-invariant continuous time system is described by h(t) = exp(αt)u(t) + exp(βt)u(-t), where u(t) denotes the unit step function, and α and β are real constants. This system is stable if
A. α is positive and β is positive
B. α is negative and β is negative
C. α is positive and β is negative
D. α is negative and β is positive
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Given that
L [ f ( t ) ] = s 2 + 1 s + 2 , L [ g ( t ) ] = ( s + 3 ) ( s + 2 ) s 2 + 1 , h ( t ) = 0 ∫ t f ( τ ) g ( t − τ ) d τ
L[h(t)] is
A. s + 3 s 2 + 1
B. s + 3 1
C. ( s + 3 ) ( s + 2 ) s 2 + 1 + s 2 + 1 s + 2
D. None of the above
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An FIR system is described by the system function
H ( z ) = 1 + 2 7 z − 1 + z 3 z − 2
The system is
A. Maximum phase
B. Minimum phase
C. Mixed phase
D. Zero phase
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For a signal x(t) the Fourier transform is X(f). Then the inverse Fourier transform of X(3f + 2) is given by
A. 2 1 x ( 2 t e j 3 π t )
B. 2 1 x ( 2 t ) e − 3 j 4 π t
C. 3x(3t)e-j4πt
D. x(3t + 2)
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The region of convergence of the z-transform of a unit step function is
A. |z| > 1
B. |z| < 1
C. (Real part of z) > 0
D. (Real part of z) < 0
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The region of convergence of the z-transform of a unit step function is
A. |z| > 1
B. |z| < 1
C. (Real part of z) > 0
D. (Real part of z) < 0
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Poles of Butterworth and Chebyshev low pass filters are located on . . . . . . . . and . . . . . . . . respectively in s-plane.
A. Ellipse, circle
B. Circle, ellipse
C. Circle, circle
D. Standard ellipse, tilted ellipse
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Let function A = sinω0 t and B = sin(ω0 t + φ). The power of two signals; PA and PB is related as
A. PB = φPA
B. PB = ϕ 1 PA
C. PB = tanφPA
D. PB = PA = P
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Match
List-I with
List-II and select the correct answer using the options given below:
List-I (Time Function)
List-II (Fourier Spectrum/Fourier Transform)
a. Periodic Function
1. Continuous spectrum at all frequencies
b. Aperiodic Function
2. -jπ{δ(ω - ω0 ) - δ(ω + ω0 )}
c. Unit Impulse δ(t)
3. Line discrete spectrum
d. sin ω(t)
4. 1
A. a-4, b-2, c-3, d-1
B. a-3, b-1, c-4, d-2
C. a-4, b-1, c-3, d-2
D. a-3, b-2, c-4, d-1
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Which of the following is introduced in the frequency sampling realization of the FIR filter?
A. Poles are more in number on unit circle
B. Zeros are more in number on the unit circle
C. Poles and zeros at equally spaced points on the unit circle
D. None of the above
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The convolution of f(t) with itself is given to be ∫ 0 t f ( τ ) d τ . Then what is f(t)?
A. The unit ramp function
B. Equal to 1
C. The unit step function
D. The unit impulse function
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If x[n] = -x[-n], then
A. n = − ∞ ∑ ∞ x [ n ] = 1
B. n = − ∞ ∑ ∞ x [ n ] = 0
C. n = 0 ∑ ∞ x [ n ] = 1
D. n = 0 ∑ ∞ x [ n ] = 0
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A signal x(t) is band-limited to 2Hz, and y(t) = x3 (t) + x(t) + 1. The Nyquist sampling frequency of y(t) is:
A. 3 Hz
B. 6 Hz
C. 12 Hz
D. 27 Hz
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The output of a system with impulse response δ[n - 2] to an input signal, u[n + 2] is:
A. u[n + 2]
B. u[n]
C. u[n - 2]
D. u[n] - u[n - 2]
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