# Signals & Systems Questions and Answers – Properties of Systems – II

This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “Properties of Systems – II”.

1. What is the following type of system called? y[n] = x[n] + y[n-1].
a) Subtractor system
c) Product System
d) Divisor System

Explanation: If we write for n-1, n-2, .. we will obtain y[n] = x[n] + x[n-1] + x[n-2] …,

2. Which of the following systems is linear?
a) y(t) = sin(x(t))
b) y(t) = log(x(t))
c) y(t) = cos(x(t))
d) y(t) = dx(t)/dt

Explanation: Only d satisfies both the scaling and the additivity properties.

3. Which of the following systems is stable?
a) y(t) = log(x(t))
b) y(t) = exp(x(t))
c) y(t) = sin(x(t))
d) y(t) = tx(t) + 1

Explanation: 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.

4. Which of the following systems is time invariant?
a) y(t) = x(2t) + x(t)
b) y(t) = x(t) + x(1-t)
c) y(t) = -x(t) + x(1-t)
d) y(t) = x(t) + x(t-1)

Explanation: In each of a, 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. However, only in d, the backward shift will remain as backward, and undiminished.

5. State whether the differentiator system is causal or not.
a) True
b) False

Explanation: The derivative of a function can be written in forward difference and in backward difference form, hence the derivative would depend on a slightly forward value of the function, thus making it non causal.
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6. State whether the differentiator system is a stable system or not.
a) True
b) False

Explanation: 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.

7. Which of the following systems is memoryless?
a) y(t) = x(2t) + x(t)
b) y(t) = x(t) + 2x(t)
c) y(t) = -x(t) + x(1-t)
d) y(t) = x(t) + 2x(t+2)

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

8. For what value of k, will the following system be time invariant?
y(t) = x(t) + x(kt) – x(2t) + x(t-1)
a) 1
b) 2
c) 3
d) 2.5

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

9. State if the following system is periodic or not. y(t) = sin(sqrt(2)*x(t))
a) No
b) Yes

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

10. State whether the following system is periodic or not. y(t) = log(sin(x(t)).
a) Yes
b) No

Explanation: 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.

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