By definition:
and so for scalars and :
Again by definition:
Which should allow you to write down the result you require (there may be a problem if is discontinuous at ).
CB
Hey guys. just wondering if anyone can help me with this piece of convolution integral.
i am asked to convolute f(t) and g(t) where
f(t) = 2r(t-1) - 2r(t-2) - u(t-2) - u(t-3) where r is a ramp function and
u is a unit step function
and
g(t) = d(t-2) - d(t-3) where d is the unit impulse
function or delta dirac function
i use the graphical approach and make use of the sifting property of the impulse function. does that sound right? i have an answer but i'm not sure if rite. any help or input would be much appreciated.
thanks for the quick response CaptainBlack. this is my answer
for t <3, y(t) = 0
for 3<t<4, y(t) = 2(t-1)
for 4<t<5, y(t) = 2(t-1) + 1
for 5<t<6,y(t) = 1
where y(t) is the convolution of f(t) and g(t).
there is a discontinuity of f(t) at t=2 but i have taken that into consideration in the answer above. can you confirm if this is correct?