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Test: Properties of Systems


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21 Questions MCQ Test Signals and Systems | Test: Properties of Systems

Test: Properties of Systems for Electrical Engineering (EE) 2022 is part of Signals and Systems preparation. The Test: Properties of Systems questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: Properties of Systems MCQs are made for Electrical Engineering (EE) 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Properties of Systems below.
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Test: Properties of Systems - Question 1

Is the system y(t) = Rx(t), where R is a arbitrary constant, a memoryless system?

Detailed Solution for Test: Properties of Systems - Question 1

The output of the system depends on the input of the system at the same time instant. Hence, the system has to be memoryless.

Test: Properties of Systems - Question 2

Construct the inverse system of y(t) = 2x(t)

Detailed Solution for Test: Properties of Systems - Question 2

Now, y(t) = 2x(t) => x(t) = 0.5*y(t)
Thus, reversing x(t) <-> y(t), we obtain the inverse system: y(t) = 0.5x(t)

Test: Properties of Systems - Question 3

Comment on the linearity of y[n] = n*x[n].

Detailed Solution for Test: Properties of Systems - Question 3

The function obeys the scaling/homogeneity property, but doesn’t obey the additivity property, thus not being linear.

Test: Properties of Systems - Question 4

Does the following discrete system have the parameter of memory, y[n] = x[n-1] + x[n] ?

Detailed Solution for Test: Properties of Systems - Question 4

y[n] depends upon x[n-1], i.e at the earlier time instant, thus forcing the system to have memory.

Test: Properties of Systems - Question 5

Comment on the causality of y[n] = x[-n].

Detailed Solution for Test: Properties of Systems - Question 5

For positive time, the system may seem to be causal. However, for negative time, the output depends on time at a positive sign, thus being in the future, enforcing non causality.

Test: Properties of Systems - Question 6

 y[t]= ∫x[t],t ranges from 0 to t. Is the system a memoryless one?

Detailed Solution for Test: Properties of Systems - Question 6

While evaluating the integral, it becomes imperative to know the values of x[t] from 0 to t, thus making the system requiring memory.

Test: Properties of Systems - Question 7

y(t) = x2(t). Is y(t) = sqrt(x(t)) the inverse of the first system?

Detailed Solution for Test: Properties of Systems - Question 7

We cannot determine the sign of the input from the second function, thus, the output doesn’t replicate the input. Thus, the second function is not an inverse of the first one.

Test: Properties of Systems - Question 8

y(t) = sin(x(t-1)) : Comment on its memory aspects.

Detailed Solution for Test: Properties of Systems - Question 8

The output at any time t = A, requires knowing the input at an earlier time, t = A – 1, hence making the system require memory aspects.

Test: Properties of Systems - Question 9

 y(t) = x(t-2) + x(2-t). Comment on its causality:

Detailed Solution for Test: Properties of Systems - Question 9

For a time instant existing between 0 and 1, it would depend on the input at a time in the future as well, hence being non causal.

Test: Properties of Systems - Question 10

Which of the following systems is linear?

Detailed Solution for Test: Properties of Systems - Question 10

Only d satisfies both the scaling and the additivity properties.

Test: Properties of Systems - Question 11

Comment on the causality of y[n] = n*x[n].

Detailed Solution for Test: Properties of Systems - Question 11

For positive time, the system may seem to be causal. For negative time, the output depends on the same time instant, thus making it causal.

Test: Properties of Systems - Question 12

 What is the following type of system called? y[n] = x[n] + y[n-1].

Detailed Solution for Test: Properties of Systems - Question 12

If we write for n-1, n-2, .. we will obtain y[n] = x[n] + x[n-1] + x[n-2] …,
thus obtaining an adder system.

Test: Properties of Systems - Question 13

 Which of the following systems is stable?

Detailed Solution for Test: Properties of Systems - Question 13

Stability implies that a bounded input should give a bounded output. In a, b, d there are regions of x, for which y reaches infinity/negative infinity. Thus the sin function always stays between -1 and 1, and is hence stable.

Test: Properties of Systems - Question 14

Which of the following systems is time invariant?

Detailed Solution for Test: Properties of Systems - Question 14

In each of b and c there is a negative sign of t involved, which means a backward shift of t-0 in time, would mean a forward shift in each of them. In option a twice of t leads to time variant. However, only in d, the backward shift will remain as backward, and undiminished.

Test: Properties of Systems - Question 15

Which property of delta function indicates the equality between the area under the product of function with shifted impulse and the value of function located at unit impulse instant ?

Detailed Solution for Test: Properties of Systems - Question 15

Sampling  indicates the equality between the area under the product of function with shifted impulse and the value of function located at unit impulse instant

Test: Properties of Systems - Question 16

State whether the differentiator system is a stable system or not.

Detailed Solution for Test: Properties of Systems - Question 16

 The derivative of a function can be unbounded at some bounded inputs, like tan(x) at x=pi/2, hence the differentiator system is unstable in general, when the input is not specified.

Test: Properties of Systems - Question 17

Which of the following systems is memoryless?

Detailed Solution for Test: Properties of Systems - Question 17

A system possessing no memory has its output depending upon the input at the same time instant, which is prevalent only in option b.

Test: Properties of Systems - Question 18

 For what value of k, will the following system be time invariant?y(t) = x(t) + x(kt) – x(2t) + x(t-1)

Detailed Solution for Test: Properties of Systems - Question 18

A system possessing no memory has its output depending upon the input at the same time instant, which is prevalent only in option b.

Test: Properties of Systems - Question 19

State if the following system is periodic or not. y(t) = sin(√(2)*x(t))

Detailed Solution for Test: Properties of Systems - Question 19

The function y = sin(nx) is periodic only for rational ‘n’.

Test: Properties of Systems - Question 20

State whether the following system is periodic or not. y(t) = log(sin(x(t)).

Detailed Solution for Test: Properties of Systems - Question 20

Sin x is a periodic function, but log x is not a periodic function. Thus y is log t, where t= sin x, thus y is not periodic.

Test: Properties of Systems - Question 21

Comment on the linearity of y[n] = n*x[n].

Detailed Solution for Test: Properties of Systems - Question 21

The function obeys the scaling/homogeneity property, but doesn’t obey the additivity property, thus not being linear.

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