4. Find the convolution of $f(t)=\left\{\begin{array}{11}\frac{3}{2} t, & 0 \leqt \leq 3 \ 0, &\text { otherwise }\end{array}\right.$ and Sg(t)=\left\{\begin{array}{i1}4, & -i leg i \leg 3' e,& \text { otherwise }\end{array}\right. $Answer:$$f* g=\left\{\begin{array}{11}0 & t \leqslant-1 \\frac{4}{3}(t+1)^[2} & -16\end{array}\right.$$SP. SD. 330|

ANSWER: Convolution: When talking absolutely numerically, convolution is the interaction by which…

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4. Find the convolution of

Database System Concepts

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ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

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Problems on Growing Functions

For a given set of functions f and g, the growth of functions states that the function g grows as fast as the function f. The growth rate of algorithms helps determine the algorithm's efficiency and compare its performance to other algorithms.

Question

4. Find the convolution of $f(t)=\left\{\begin{array}{11}\frac{3}{2} t, & 0 \leqt \leq 3 \ 0, &
\text { otherwise }\end{array}\right.$ and Sg(t)=\left\{\begin{array}{i1}4, & -i leg i \leg 3' e,
& \text { otherwise }\end{array}\right. $
Answer:
$$
f* g=\left\{\begin{array}{11}
0 & t \leqslant-1 \
\frac{4}{3}(t+1)^[2} & -1<t \leqslant 2 W
12 & 2<t \leqslant 3 \
12-\frac{4}{3}(t-3)*(2} & 3<t \leqslant 6 \
O & t>6
\end{array}\right.
$$
SP. SD. 330|

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