# Signals & Systems Questions and Answers – Continuous Time Convolution – 2

This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “Continuous Time Convolution – 2”.

For all the following problems, h*x denotes h convolved with x. \$ indicates integral.

1. Find the value of [d(t) – d(t-1)] * -x[t+1].
a) x(t+1) – x(t)
b) x(t) – x(t+1)
c) x(t) – x(t-1)
d) x(t-1) – x(t+1)

Explanation: The delta function convolved with another function results in the shifted function.

2. If h1, h2 and h3 are cascaded, find the overall impulse response
a) h1 * h2 * h3
b) h1 + h2 + h3
c) h3
d) all of the mentioned

Explanation: The resultant impulse response will be the convolution of all the subsequent impulse responses.

3. Find the value of [d(t-3) – d(t-1)] * x[t+3].
a) x(t+3) – x(t+2)
b) x(t) – x(t+1)
c) x(t) – x(t+2)
d) x(t-1) – x(t+2)

Explanation: The delta function convolved with another function results in the shifted function.

4. If h1, h2 and h3 are cascaded, and h1 = u(t), h2 = d(t) and h3 = d(t), find the overall impulse response
a) s(t)
b) d(t)
c) u(t)
d) all of the mentioned

Explanation: The resultant impulse response will be the convolution of all the subsequent impulse responses.
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5. Find the value of [d(t) – u(t-1)] * x[t+1].
a) x(t+1) – \$x(t)
b) \$x(t) – x(t+1)
c) x(t) – \$x(t-1)
d) \$x(t-1) – x(t+1)

Explanation: The delta function convolved with another function results in the shifted function.

6. If h1, h2 and h3 are cascaded, and h1 = u(t+4), h2 = d(t-3) and h3 = d(t-5), find the overall impulse response
a) u(t-4)
b) u(t-6)
c) u(t-8)
d) all of the mentioned

Explanation: The resultant impulse response will be the convolution of all the subsequent impulse responses.

7. Find the value of [u(t) – d(t-1)] * -x[t+1].
a) \$x(t+1) – x(t)
b) x(t) – \$x(t+1)
c) \$x(t) – x(t-1)
d) \$x(t-1) – x(t+1)

Explanation: The delta function convolved with another function results in the shifted function.

8. If h1, h2 and h3 are parallelly summed, find the overall impulse response
a) h1 + h2 + h3
b) h1 – h2 + h3
c) h1*h2*h3
d) all of the mentioned

Explanation: The resultant impulse response will be the convolution of all the subsequent impulse responses.

9. Find the value of [u(t) – u(t+1)] * x[t+1].
a) \$x(t+1) – \$x(t+3)
b) \$x(t) – \$x(t+2)
c) \$x(t) – \$x(t-1)
d) \$x(t+1) – \$x(t+2)

Explanation: The delta function convolved with another function results in the shifted function.

10. If h1, h2 and h3 are cascaded, and h1 = u(t), h2 = exp(t) and h3 = sin(t), find the overall impulse response
a) sin(t)*exp(t)*u(t)
b) sin(t) + exp(t) + u(t)
c) u(t)*sin(t)
d) all of the mentioned

Explanation: The resultant impulse response will be the convolution of all the subsequent impulse responses.

11. Who started the Convolution theorem?
a) Sylvestre François Lacroix
b) Vito Volterra
c) Pierre Simon Laplace
d) D’Alembert

Explanation: One of the earliest uses of the convolution integral appeared in D’Alembert’s derivation of Taylor’s theorem, 1754.Sylvestre François Lacroix, has also used convolution on page 505 of his book entitled Treatise on differences and series.

12. What is periodic convolution?
a) Continuous type superposition
b) Periodic type summation
d) Summation of both continuous and periodic type

Explanation: When a function g is periodic, with period T, then for functions, f, such that f∗g exists, the convolution is also periodic. This is called a periodic convolution.
Example: f*g=∫∑[f(e+kT)]g(t-e).

13. What is a circular or cyclic convolution?
a) Convolution of a periodic and continuous time function
b) Convolution of a periodic and discrete time function
c) Superposition of periodic and periodic function
d) Summation of continuous time and a convolution of a periodic function convolution

Explanation: The circular convolution is done of two aperiodic functions (i.e. Schwartz functions) happens when one of them is convolved in the normal way with a periodic summation of the other given function.
(Xn*h)[n]=∑h[m].xn[n-m], for discrete sequences n.

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