This set of Signals & Systems online test focuses on “Continuous Time Convolution – 3”.

1. What is the full form of the LTI system?

a) Linear time inverse system

b) Late time inverse system

c) Linearity times invariant system

d) Linear Time Invariant system

View Answer

Explanation: LTI system stands for linear time Invariant system. It investigates the response of a linear and time variant system to an arbitrary input signal.

2. What is a unit impulse response?

a) The output of a linear system

b) The response of an invariant system

c) The output of an LTI system due to unit Impulse signal

d) The output of an input response signal

View Answer

Explanation: The impulse response is defined as the output of an LTI System due to a unit impulse signal input applied at time t=0 or n=0.

x(t)–>y(t)

∂(t)–>h(t)

Where ∂(t) is the unit impulse function and h(t) is the unit impulse response of a continuous time LTI system.

3. How are the convolution integral of signals represented?

a) x(t)+h(t)

b) x(t)-h(t)

c) x(t)*h(t)

d)x(t)**h(t)

View Answer

Explanation: We obtain the system output y(t) to an arbitrary input x(t) in terms of the input response h(t).

y(t)= ∫x(α)h(t-α)dα=x(t)*h(t).

4. How do you define convolution?

a) Weighted superposition of time shifted responses

b) Addition of responses of an input signal

c) Multiplication or various shifted responses of a stable system

d) Superposition of various outputs

View Answer

Explanation: This is defined as-

y(t)= ∫x(α)h(t-α)dα=x(t)*h(t), output y(t) to an arbitrary input x(t) in terms of the input response h(t).

This is defined as a weighted superposition of time shifted responses where the whole of the signals is taken into account i.e its full limits.

5. The Convolution of the continuous functions f(t)=e-t2 and g(t)=3t2 is 5.312t2.

a) True

b) False

View Answer

Explanation: f(t)=e-t2 and g(t)=3t2

f(t)*g(t)= ∫f(α)g(t-α)dα

=∫e-α2-3(t-α)2 dα

=3t2√π-0+3√π/2

=5.31t2+2.659.

6. What is the difference between convolution and multiplication?

a) Convolution leads to addition and multiplication leads to the multiplication

b) Convolution leads to a superposition of signals while multiplication does not consider all the signals

c) Convolution is multiplication but of signals

d) Convolution is a multiplication of added signals.

View Answer

Explanation: Convolution is defined as weighted superposition of time shifted responses where the whole of the signals is taken into account. But multiplication leads to loss of those signals which are after the limits.

7. Convolution leads to loss of signals.

a) True

b) False

View Answer

Explanation: False, convolution is superimposition hence it does not lead to loss of signals. But multiplication does. It keeps the signal intact while superimposing it.

8. Convolution is considered in case of ________

a) Discrete time systems only

b) Continuous time only

c) In both continuous time and discrete time

d) Superposition of various outputs

View Answer

Explanation: Convolution is considered in case of both continuous time and discrete time systems. In continuous time it is represented by x(t)*h(t) and in discrete time as x[n]*h[n], x is input and h is the response in both cases.

9. Choose the properties which are very important in case of LTI signals and systems?

a) Linearity and time invariance

b) Linearity and stability

c) Stability and invariance

d) Linearity and causality

View Answer

Explanation: Linearity and time invariance are the most important properties which are very important in case of LTI signals and systems as they even derive their name Linear time invariance from them. It is also because many physical properties possess these properties.

10. Why is a linear time invariant systems important?

a) They can be structured as wanted

b) They can be molded in any domain

c) They are easy to define

d) They can be represented as a linear combination of signals

View Answer

Explanation: A Linear time invariant system is important because they can be represented as linear combination of delayed impulses. This is in case of both continuous and discrete time signals. So, output can be easily calculated through superposition that is convolution.

11. What is a dummy variable?

a) Unused variable

b) Extra variable

c) Free variable

d) Something that is used to store extra numbers

View Answer

Explanation: A free variable or a dummy variable which are mostly used in LTI systems are notation that specifies places in an expression where substitution may take place. They are very useful for calculation of convolution.

12. When are dummy variables used in continuous time convolution?

a) To change the limits of integration

b) To change the domain of integration

c) To substitute time analysis

d) To substitute frequency analysis

View Answer

Explanation: Dummy variables are used in continuous time convolution to change the domain of integration i.e the input and response are first changed into a dummy variable domain before convolution.

Suppose x(t) is the input and h(t) is the impulse response so to find the convolution, the domain is changed to a dummy variable e(suppose).

So, x(t)*h(t)=x(τ)*h(τ).

13. After converting the input and output to a dummy variable, the next step of convolution is ________

a) Shifting any one of the signals to left side i.e towards the negative direction

b) Changing the dummy variables

c) Shift the impulse response

d) Shift the input

View Answer

Explanation: The next step of convolution after conversion to dummy variable is shifting any one of the input or response to the negative side. This is done for superimposition purposes.

14. Continuous time convolution is done from negative infinity to positive infinity.

a) True

b) False

View Answer

Explanation: Convolution is a superposition theorem hence we have to consider the signals from negative to positive infinity. We start at t, at−∞ and slide it all the way to +∞. Wherever the two functions intersect, we find the integral of their product.

15. It does not matter which one we shift, the input signal or the unit impulse response of a system during linear convolution in an integral.

a) True

b) False

View Answer

Explanation: It does not matter which one we shift input or output. We start at t at −∞ and slide it all the way to +∞. Wherever the two functions intersect, we find the integral of their product.

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