# Homework Help: Convolution of delta

1. May 31, 2012

### error 401

hi

I really need your help ....

for linear time invariant system

f(t) =f1(t) (convolution) f2(t)
f(t) = ∫f1(t).f2 ( t-T)
or f(t) = ∫f1(t-T).f2(t)

where f1(t) = delta function = δ(t).δ(t-2)
and f2(t) = sine wave = sin ( ∏t )

how i can solve this .... my problem is : how can i make this integration with impulse ??

thanks in advance

2. May 31, 2012

### error 401

i forget that ... the limits of integration from (0 ) to (2)

3. May 31, 2012

### rude man

First, you need to get your convolution integral right.
Then, what do you mean by " f1(t) = delta function = δ(t).δ(t-2) "? It's not an equation I can make sense of ...

4. May 31, 2012

### error 401

i mean how can i solve this integral

∫δ(t).δ(t-2)sin(∏t)

5. May 31, 2012

### RoshanBBQ

$$\delta(t)\delta(t-2) = 0$$

And the convolution of a function with zero is zero. Your definition of the convolution integral appears incorrect. I suspect you are not giving us all the details, because the problem makes no sense. What was the original problem? (I know there was one since the limits of integration have already simplified from -inf to inf to 0 to 2)

edit:
I'll go ahead and throw out a property that may be helpful, though what you've given us so far doesn't indicate you will use it. The sampling property states

$$\int\limits_{a}^{b}\delta(x-c)f(x)dx=f(c)$$

if b > c > a

This property leads to a very simple result when convolving some function f(t) with an impulse d(t - c).

Last edited: May 31, 2012
6. Jun 2, 2012

### error 401

the original problem is : convolution between 2 function ( sine wave and delta function ) but when he sketch delta function ..gives two vertical lines ..one of them at x=0 upward and the other at x=2 downward ...

so how can i solve this ?!

and I really appreciate your assistance :)

7. Jun 2, 2012

### RoshanBBQ

That is just the sum of two Dirac delta functions.

$$f_1(x) = \delta(x) + \delta(x-2)$$

Just write out the convolution integral and use the sampling rule.

8. Jun 3, 2012

### error 401

:D

thank you so much ..

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