a) If f(t)=tmandg(t)=tn, where m and n are positive integers. show that f∗g=tm+n+1∫01um(1−u)ndu b) Use...
a) If , where m and n are positive integers. show that
b) Use the convolution theorem to show that
c) Extend the result of part b to the case where m and n are positive numbers but not necessarily integers.
Answer & Explanation
Skilled2021-01-31Added 95 answers
Since we must get , we can try with the substitution :
(b) and (c)
where B is function. Recall that,
where function. When m and n are positive integers,
The finally result for (a), consider the subtitution .
For (b) and (c), notice that this integral is a function
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