Signal Processing MCQs with Answers 2027

Q61

The z-transform of a system is

H (z) = \frac{z}{z - 0.2} .

If the ROC is |z| < 0.2, then the impulse response of the system is

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Q62

Open question

The Dirac-delta function δ(t) is defined as

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Q63

Open question

Let h(t) be the impulse response of a linear time invariant system. Then the response of the system for any input u(t) is

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Q64

Open question

The response of an initially relaxed linear constant parameter network to a unit impulse applied at t = 0 is 4e^-2tu(t). The response of this network to a unit step function will be

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Q65

Open question

Consider the signal x(t) = cos(6πt) + sin(8πt), where t is in seconds. The Nyquist sampling rate (in samples/second) for the signal y(t) = x(2t + 5) is

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Q66

Open question

The impulse response h[n] of a linear time invariant system is given as

h [n] = {\matrix - 22, 42, 0, \matrix n = 1, - 1 n = 2, - 2 otherwise

If the input to the above system is the sequence

e^{\frac{j π n}{4}},

the output is

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Q67

Open question

If

F (s) = L [f (t)] = \frac{2 ( s + 1 )}{s ^{2} + 4 s + 7}

then the initial and final values of f(t) are respectively

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Q68

Open question

A causal LTI system is described by the difference equation
2y[n] = αy[n - 2] - 2x|n| - βx[n - 1].
The system is stable only if

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Q69

Open question

The function f(t) has the Fourier transform f(ω)
The Fourier transform of

g (t) = - \infty \int \infty g (t) e^{- j ω} d t

is

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Q70

Open question

The z-transform of a signal is given by

C (z) = \frac{1}{4} \frac{z ^{- 1} ( 1 - z ^{- 4} )}{( 1 - z ^{- 1} ) ^{2}} .

Its final value is

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Q71

Open question

Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let {a_k} be the complex Fourier series coefficients of x(t), where k is integer valued. Consider the following statements about x(3t):
1. The complex Fourier series coefficients of x(3t) are {a_k} where k is integer valued.
2. The complex Fourier series coefficients of x(3f) are {3a_k} where k is integer valued.
3. The fundamental angular frequency of x(3t) is 6π rad/s.
For the three statements above, which one of the following is correct?

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Q72

Open question

Let x(t) = cos(10πt) + cos(30πt) be sampled at 20 Hz and reconstructed using an ideal low-pass filter with cut-off frequency of 20 Hz. The frequency/frequencies present in the reconstructed signal is/are

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Q73

Open question

Consider a four point moving average filter defined by the equation

y [n] = \sum_{i = 0}^{3} a_{i} x [n - i] .

The condition on the filter coefficients that results in a null at zero frequency is

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Q74

Open question

The Fourier transform of y(2n) will be

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Q75

Open question

The Fourier series of a real periodic function has only
P. Cosine terms if it is even
Q. Sine terms if it is even
R. Cosine terms if it is odd
S. Sine terms if it is odd
Which of the above statements are correct?

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Q76

Open question

For a function g(t), it is given that

- \infty \int + \infty g (t) e^{- j ω t} d t = ω e^{- 2 ω^{2}}

for any real value

ω

. If

y (t) = - \infty \int t g (τ) d τ, then - \infty \int + \infty y (t) d t

is. . . . . . . .

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Q77

Open question

A linear discrete-time system has the characteristics equation, z³ - 0.81 z = 0. The system

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Q78

Open question

A function is given by f(t) = sin²t + cos 2t. Which of the following is true?

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Q79

Open question

Two systems H₁(z) and H₂(z) are connected in cascade as shown below. The overall output y(n) is the same as the input x(n) with a one unit delay. The transfer function of the second system H₂(z) is

x (n) \to H_{1} (z) = \frac{( 1 - 0.4 z ^{- 1} )}{( 1 - 0.6 z ^{- 1} )} \to H_{2} (z) \to y (n)

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Q80

Open question

Consider the z-transform X(z) = 5z² + 4z^-1 + 3; 0 < |z| < ∞. The inverse z-transform x[n] is

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