Consider a four point moving average filter defined by the equation y [ n ] = ∑ i = 0 3 α i x [ n − i ] . The condition on the filter coefficients that results in a null at zero frequency is
A. α1 = α2 = 0; α0 = -α3
B. α1 = α2 = 1; α0 = -α3
C. α0 = α3 = 0; α1 = α2
D. α1 = α2 = 0; α0 = α3
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Which one of the following is correct?
Energy of a power signal is
A. finite
B. zero
C. infinite
D. between 1 and 2
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Consider this variant of the Fibonacci system:
y[n] = y[n - 1] - y[n - 2] + x[n], where x[n] represents the input and y[n] represents the output. The poles of the given system will be:
A. 1, 2
B. 0, 1, 2
C. e j 3 π , e − j 3 π
D. e j 3 π , e − j 3 π , 0
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For a random signal (continuous time) x(t) defined for t ≥ 0, its probability density function (pdf) at t = t0 is such that
A. It is non-negative and its integral equals 1
B. Need not be non-negative, but integral equals 1
C. It is non-negative, but integral is not 1
D. None of the above
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If the unit step response of the network is (1 - e-at ), then its impulse response is:
A. a-1 e-at
B. ae-at
C. (1 - a-1 )e-at
D. (1 - a)e-at
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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 is
A. |a| < 1, |b| > 1
B. |a| < 1, |b| < 1
C. |a| > 1, |b| > 1
D. |a| > 1, |b| < 1
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Given h[n] = {1, 2, 3, 2, 1}. It is a linear phase FIR filter because
A. h[n] = h[N - 1 - n]
B. h[n] has finite number of samples
C. h[n] = -h[N - 1 - n]
D. h[n] = h[N - n]
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In a trigonometric Fourier series representation of a signal; ao (or Ao ) is:
A. The average value
B. The RMS value
C. The Mean square value
D. The peak value
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If a sequence is circularly shifted in time by 8 units, the magnitude response will
A. remain constant
B. increase by 8
C. remain unchanged
D. shift by 8 units
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A function of one or more variables which conveys information on the nature of physical phenomenon is called
A. Noise
B. Interference
C. System
D. Signal
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According to Shanon's theorem, the output from any source of rate R can be coded and transmitted over channel capacity C with the condition that
A. C < R
B. C < R2
C. C > R
D. C > R2
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A discrete time signal is given as x [ n ] = cos 9 π n + sin [ − 7 π n + 2 1 ] .
The period N for the periodic signal is
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A stable and casual digital infinite impulse response filter has its pole location at
A. unit circle on z - plane
B. inside the unit circle on z - plane
C. outside the unit circle on z - plane
D. anywhere on z - plane
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Which of the following is/are not a property/properties of a power spectral density function Sx (ω)?
A. Sx (ω) is a real function of ω
B. Sx (ω) is an even function of ω
C. Sx (ω) is a non-positive function of ω i.e. Sx (ω) ≤ for all ω
D. All of the above
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Which one of the following is a periodic signal?
A. x 1 ( t ) = 2 e j ( t + 4 π ) u ( t )
B. x 2 ( n ) = u [ n ] + u [ − n ]
C. x 3 [ n ] = k = − ∞ ∑ ∞ { δ [ n − 4 k ] − δ [ n − 1 − 4 k ] }
D. x 4 ( t ) = e ( − 1 + j ) t
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A network consisting of a finite number of linear resistor (R), inductor (L), and capacitor (C) elements, connected all in series or all in parallel, k = 1 ∑ 3 a k cos ( k ω 0 t ) , where ak ≠ 0, ω0 ≠ 0. The source has nonzero impedance. Which one of the following is a possible form of the output measured across a resistor in the network?
A. k = 1 ∑ 3 b k cos ( k ω 0 t + ϕ k ) , where b k = a k , ∀ k
B. k = 1 ∑ 3 b k cos ( k ω 0 t + ϕ k ) , where b k = 0 , ∀ k
C. k = 1 ∑ 3 a k cos ( k ω 0 t + ϕ k )
D. k = 1 ∑ 2 a k cos ( k ω 0 t + ϕ k )
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The direct form structure of an FIR (finite impulse response) filter is shown in the figure.
The filter can be used to approximate a
A. low-pass filter
B. high-pass filter
C. band-pass filter
D. band-stop filter
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Let x(t) be the input to linear, time invariant system the required output is 4x(t - 2). The transfer function of the system should be
A. 4ej4πf
B. 2ej8πf
C. 4e-j4πf
D. 2ej8πf
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If a discrete time signal x[n] is filtered by a ideal low pass filter with cut-off frequency . . . . . . . . then the output of the filter can be sampled by a factor of 'M' (is and integer) without aliasing.
A. π/Μ
B. π/M + 1
C. π/M - 1
D. π/M2
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x(t) is a periodic signal with even symmetry. Then, its trigonometric fourier series expansion will have
A. Only sinusoidal component
B. Only cosine component
C. A dc component
D. Only even harmonic components
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