Test: Introduction to Systems

# Test: Introduction to Systems - Electrical Engineering (EE)

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## 10 Questions MCQ Test GATE Electrical Engineering (EE) 2024 Mock Test Series - Test: Introduction to Systems

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Test: Introduction to Systems - Question 1

### A function f(t) is an even function, if for all values of (t) ( T is the time-period of the function)

Detailed Solution for Test: Introduction to Systems - Question 1

For even function, f(t) = f(-t)

For odd function, f(t) = -f(-t)

Test: Introduction to Systems - Question 2

### A control system transfer function is H(s) = 1/s3. Express its impulse response in terms of unit step signal

Detailed Solution for Test: Introduction to Systems - Question 2

Convolution in the time domain implies multiplication in S(or frequency) domain

The Laplace transform of any signal h(t) is given by

So we observe that the H(s) = 1/s3, corresponds to a unit step signal convoluted with itself thrice.

Therefore the correct answer is option 1

Test: Introduction to Systems - Question 3

### The unit impulse response of a linear time invariant system is the unit step function u(t) for t > 0, the response of the system to an excitation e-at u(t), a > 0 will be

Detailed Solution for Test: Introduction to Systems - Question 3

Given: h(t) = u(t)
x(t) = e–at u(t)

∴ Y(s) = X(s) H(s) =

y(t) = 1/a (1 – e– at) u(t)

Test: Introduction to Systems - Question 4

A system with an input x(t) and output y(t) is described by the relation: y(t) = tx(t). This system is

Detailed Solution for Test: Introduction to Systems - Question 4

y(t) = tx(t)

y1(t) = t.x1(t) = r1(t)

y2(t) = tx2(t) = r2(t)

y1(t) + y2(t) = t(x1(t) + x2(t))

= r1(t) + r2(t)    ∴ linear

y(t) = t.x(t)

y( t - to) = (t - to) x ( t - to)

and for delayed input signal,

y(t) = t x (t - to)

y(t) ≠ y( t-to)

∴ Time varying signal

Test: Introduction to Systems - Question 5

If a function f(t) u(t) is shifted to the right side by t0, then the function can be expressed as

Detailed Solution for Test: Introduction to Systems - Question 5

Since f(t) u(t) = f(t) for t > 0 also we know

u ( t - to) = 1, for t > to

Here in right side shifting that means to > 0

by property on shifting right side,

Test: Introduction to Systems - Question 6

The impulse response of a causal, linear, time- invariant, continuous time system is h(t). The output y(t) of the same system to an input x(t). Where x(t) = 0 for t < -2 is

Detailed Solution for Test: Introduction to Systems - Question 6

Since, causal system

h(t) = 0 for t < 0

Input y(t) = x(t) * h(t)

h(τ) = 0 for τ < 0

x ( t - τ) = 0, for t - τ < - 2

∴ τ > f + 2

Test: Introduction to Systems - Question 7

The unit step response of a system is given by (1 - eαt) u(t), the impulse response is given by

Detailed Solution for Test: Introduction to Systems - Question 7

Test: Introduction to Systems - Question 8

Figure I and Figure II, shows the input x(t) to a linear time invariant system and the impulse response h(t) of the system

the output of the system is zero everywhere except for the time interval.

Detailed Solution for Test: Introduction to Systems - Question 8

Given x(t) and h(t) y(t) = x(t) * h(t)

y(t) =x(τ) h(t – τ)dτ– ∞

Thus, we conclude that the output of the system is zero everywhere except for the time interval.
1 < t < 5

Test: Introduction to Systems - Question 9

A signal f(t) = cos8πt + 0.5cos4πt is instantaneously sampled. The maximum allowable value of sampling interval Ts in sec is

Test: Introduction to Systems - Question 10

The impulse response. h[n] of a linear time invariant system is given by h[n] = u[n + 3] + u[n - 3] - 2u[n - 7], the above system is

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## GATE Electrical Engineering (EE) 2024 Mock Test Series

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