Signal Processing MCQs with Answers 2027

Q101

The auto-correlation function of an energy signal has

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Q102

Let x(t) be a periodic function with period T = 10. The Fourier series coefficients for this series are denoted by

a_{k}

, that is

x (t) = k = - \infty \sum \infty a_{k} e^{j k \frac{2 π}{T} t} .

The same function x(t) can also be considered as a periodic function with period T' = 40. Let b_k be the Fourier series coefficients when period is taken as T'. If

k = - \infty \sum \infty ∣ a_{k} ∣ = 16,

then

k = - \infty \sum \infty ∣ b_{k} ∣

is equal to

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Q103

Open question

A periodic signal x(t) of period T₀ is given by

x\left( t \right) = \left\{ {\matrix{ {1,} & {\left| t \right| < {T_1}} \\ {0,} & {{T_1} < \left| t \right| < {{{T_0}} \over 2}} \\ } } \right.

the dc component of x(t) is

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Q104

Open question

The Laplace transform of a unit ramp function starting at t = a, is

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Q105

Open question

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\{ \matrix{ \matrix{ {x\left( n \right),} & {n \ge 1} \\ } \hfill \\ \matrix{ {0,} & {n = 0} \\ } \hfill \\ \matrix{ {x\left( {n + 1} \right),} & {n \le - 1} \\ } \hfill \\} \right.

where x(n) is the input and y(n) is the output.
The above system has the properties

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Q106

Open question

Which of the following cannot be the Fourier series expansion of a periodic signal?

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Q107

Open question

Let x(t) be a wide sense stationary (WSS) random with power spectral density S_x(f). If Y(t) is the process defined as y(t) = x(2t - 1), the power spectral density S_Y(f) is

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Q108

Open question

The Fourier series expansion of a real periodic signal with fundamental frequency f₀ is given by

g_{p} (t) = n = - \infty \sum \infty c_{n} e^{j 2 π f_{0} t};

it is given that c₃ = 3 + j5. Then c₃ is

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Q109

Open question

The input x(t) and output y(t) of a system are related as

y (t) = - \infty \int t x (τ) cos (3 τ) d τ .

The system is

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Q110

Open question

Consider the sequence x[n] = aⁿu[n] + bⁿu[n], where u[n] denotes the unit-step sequence and 0 < |a| < |b| < 1. The region of convergence (ROC) of the z-transform of x[n] is

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Q111

Open question

Laplace transforms of the functions tu(t) and u(t)sin(t) are respectively

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Q112

Open question

If

x [n] = (\frac{1}{3})^{∣ n ∣} - (\frac{1}{2})^{n} u [n],

then the region of convergence (ROC) of its z-transform in the z-plane will be

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Q113

Open question

A 1 kHz sinusoidal signal is ideally sampled at 1500 samples/sec and the sampled signal is passed through an ideal low-pass filter with cutoff frequency 800 Hz. The output signal has the frequency

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Q114

Open question

Consider a system whose input r and output y are related by the equation

y (t) = - \infty \int \infty x (t - τ) h (2 τ) d τ

Where h(t) is shown in the graph
Which of the following four properties are possessed by the system? BIBO: Bounded input gives a bounded output
Causal: The system is causal.
LP : The system is low pass.
LTI: The system is linear and time-invariant.

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Q115

Open question

A Hilbert transformer is a

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Q116

Open question

The trigonometric Fourier series of a periodic time function can have only

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Q117

Open question

The Fourier transform of a signal
h(t) is

H (j ω) = \frac{( 2 cos ω ) ( sin ω )}{ω}

The value of h(0) is

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Q118

Open question

The output y(t) of a linear time invariant system is related to its input x(t) by the following equation:
y(t) = 0.5x(t - t_d + T) + x(t - t_d) + 0.5x(t - t_d -T).
The filter transfer function H(ω) of such a system is given by

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Q119

Open question

Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?

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Q120

Open question

Consider a six-point decimation-in-time Fast Fourier Transform (FFT) algorithm, for which the signal-flow graph corresponding to X[I] is shown in the figure. Let

W_{6} = exp (- \frac{j 2 π}{6}) .

In the figure, what should be the values of the coefficients a₁, a₂, a₃ in terms of W₆ so that X[I] is obtained correctly?
Signal Processing mcq question image

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