Question

convolution

Answer 1

can someone explain how we get this?
\[(\delta * f)(t)=f(t)\]

Answer 2

\(\delta\) is the unit impulse function

Answer 3

Convolutions are joyous time. Hold on.

Answer 4

(also this isn't a convolution)

Answer 5

what is it then? :/

Answer 6

yea..i'm having a hard time with them :(

Answer 7

read 1.1 here

Answer 8

Wow, I'm so sorry that * is the convolution operator.
I missed that, and thought that we were just sampling.

If you still don't understand it, I'm happy to offer a little light.

Signals are *fun* stuff /s

Answer 9

of course :)
but give me some time... i'm a little slow

Answer 10

\[\int\limits f(t) \delta (t-a)=f(a) \\x(t) \delta (t-t_0)=x(t_0)\delta (t-t_0)\]

these i can understand,
but i dont see how \(\delta * f\) follows from them

Answer 11

That's the first integral!

Answer 12

you've shown that the convolution is commutative...

Answer 13

what i dont understand is specifically what the convolution of a function and an impulse function is

Answer 14

heyy

Answer 15

hey :)

Answer 16

Maybe consider an unit impulse function first

Answer 17

?
i dont follow

Answer 18

ok

Answer 19

What must be the height of that constant impulse for the area to be \(1\) ?

Answer 20

1/h

Answer 21

Yes, lets try and express this function in terms of "unit step function"

Answer 22

familiar with unit step functions right ?

Answer 23

yes

Answer 24

http://www.math.fsu.edu/~fusaro/EngMath/Ch5/TUSFSSTDDF_files/Image2251.gif

Answer 25

u'(t)=\(\delta (t)\)