Question

Find the convolution of

Answer 1

fa=1 0<=x<=a, 0 otherwise

fb=1 0<=x<=b, 0 otherwise



fa*fb?

Answer 2

an integral that expresses the amount of overlap one function is shifted over the other

Answer 3

I understand that, but i dont know how to do the integral


is fa*fb=\[\int\limits_{0}^{t}1*1*dt=t?\]

Answer 4

i see something about \(\large \tau\)

Answer 5

is that f(a) = 1 on the interval [0,a]
and f(b) = 1 on the interval [0,b]

??

Answer 6

\[\int\limits_{0}^{t}f(u)g(t-u)du\]

Answer 7

yes

Answer 8

u is fine as well

Answer 9

do we assume a < b ?

Answer 10

just a gut feeling, but im curious if this amounts to F(b) - F(a)

Answer 11

i dont think so
\[\int\limits_{0}^{t}f _{a}(u)f_{b}(u-t)du=\int\limits_{0}^{\min(a,b)}1*1*du=\min(a,b)?\]

Answer 12

that is correct, the amount of overlap of the functions, they are y = 1 after all; is the minimum of a and b