# Signals & Systems Questions and Answers – Discrete Time Convolution – 1

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This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “Discrete Time Convolution – 1”.

1. Is discrete time convolution possible?
a) True
b) False

Explanation: Yes, like continuous time convolution discrete time convolution is also possible with the same phenomena except that it is discrete and superimposition occurs only in those time interval in which signal is present.

2. How is discrete time convolution represented?
a) x[n] + h[n]
b) x[n] – h[n]
c) x[n] * h[n]
d) x[n] + h[n]

Explanation: Discrete time convolution is represented by x[n]*h[n]. Here x[n] is the input and h[n] is the impulse response.

3. What are the tools used in a graphical method of finding convolution of discrete time signals?
a) Plotting, shifting, folding, multiplication, and addition in order
b) Scaling, shifting, multiplication, and addition in order
c) Scaling, multiplication and addition in order
d) Scaling, plotting, shifting, multiplication and addition in order

Explanation: The tools used in a graphical method of finding convolution of discrete time signals are basically plotting, shifting, folding, multiplication and addition. These are taken in the order in the graphs. Both the signals are plotted, one of them is shifted, folded and both are again multiplied and added.

4. Choose the correct equation for finding the output of a discrete time convolution?
a) y[n] = ∑x[k]h[n-k], k from 0 to ∞
b) y[n] = ∑x[k]h[n-k], k from -∞ to +∞
c) y[n] = ∑x[k]h[k], k from 0 to ∞
d) y[n] = ∑x[k]h[n], k from -∞ to +∞

Explanation: y[n]=∑x[k]h[n-k], k from -∞ to +∞
Is the correct equation, where x[n] is the input and h[n] is the impulse response of the ∂[n] input of an LTI system. This is referred to as the convolution sum.

5. What is a convolution sum?
a) ∑x[k]h[n-k], k from -∞ to +∞
b) ∑x[k]*∑h[n-k], k from -∞ to +∞
c) ∑x[k]+∑h[n-k], k from -∞ to +∞
d) ∑∑x[k]h[n-k], k from -∞ to +∞

Explanation: y[n]=∑x[k]h[n-k], k from -∞ to +∞, y[n] is the output of the summation of the components on the right hand side. Where x[n] is the input of an LTI system and h[n] is the impulse response of the ∂[n] input of an LTI system. The response is due to superposition, in short.

6. What is the convolution of x[n]=e-n2 and h[n]=n2?
a) 5.318n2 + .123
b) 6.318n2 + .123
c) 5.318n+.88
d) 5.318n2+.8846

Explanation: x[n]*h[n]=∑x[k]h[n-k] =∑e-k2[(n-k)2] =3n2∑e-k2 + ∑k2 e-k2
=5.318n2+.8846.

7. Choose the properties which are followed by a discrete time convolution?
a) Associative, commutative, distributive
b) Associative
c) Commutative and distributive
d) Distributive and associative

Explanation: The properties which are followed by a discrete time convolution are same as continuous time convolution. These are – associative, commutative, distributive property.

8. What is the convolution of a signal with an impulse?
a) Signal itself
b) Impulse
c) A new signal
d) Signal multiplied by impulse

Explanation: The convolution of a signal x(n) with a unit impulse function ∂(n) results in the signal x(n) itself:
x(n)* ∂(n)=x(n).

9. What is the commutative property?
a) x(n)*h(n)=h(n)*x(n)
b) x(n)+h(n)=h(n)+x(n)
c) x(n)**h(n)=h(n)**x(n)
d) x(n)h(n)=h(n)x(n)

Explanation: The commutative property is x(n)*h(n)=h(n)*x(n), where x(n) is the input and h(n) is the impulse response of the ∂(n) input of an LTI system.
∑x[k]h[n-k], when we change the variables to n-k to k-n makes it equal to LHS and RHS.

10. What is the associative property of discrete time convolution?
a) [x1(n) * x2(n)]*h(n) = x1(n)* [x2(n)*h(n)]
b) [x1(n) * x2(n)]+h(n) = x1(n) + [x2(n)*h(n)]
c) [x1(n) + x2(n)]*h(n) = x1(n)* [x2(n)+h(n)]
d) [x1(n) * x2(n)]h(n) = x1(n) [x2(n)*h(n)]

Explanation: [x1(n)* x2(n)]*h(n)= x1(n)* [x2(n)*h(n)], x1(n) and x2(n) are inputs and h(n) is the impulse response.
This can be proved by considering two x1(n)* x2(n) as one output and then using the commutative property proof.

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