Question 9.P.6: Obtain the continuous convolution of the two time function s...
Obtain the continuous convolution of the two time function shown in Figure P9.6. Next, with a sampling interval of 0.5 s, obtain the discrete convolution of the two functions. Compare the two sets of results and note the errors introduced in the discrete convolution. What is the cause of these errors and what can be done to improve the accuracy of the results.
\begin{aligned}&\text { Continuous convolution } \\&\qquad g(t) * h(t)= \begin{cases}t-1+e^{-t} & 0<t \leq 1.5 \\-2 e^{(1.5-t)}+e^{-t}+4-t & 1.5<t \leq 3 \\-2 e^{(1.5-t)}+e^{(3-t)}+(4-t) e^{-3} & 3<t \leq 4.5 \\e^{(3-t)}+(t-7) e^{-3} & 4.5<t \leq 6 \\0 & 6<t\end{cases}\end{aligned}
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