# Thread: How to evaluate these convolutions:

1. ## How to evaluate these convolutions:

How to evaluate these convolutions:

a) y(t) = (u(t) - u(t-2)) * u(t)

b) z(t) = cos(pi*t)(u(t+1) - u(t-1)) * u(t)

c) n(t) = (e^at)u(t) * (u(t+2) - u(t))

where * represents convolution symbol

2. ## Re: How to evaluate these convolutions:

Originally Posted by essedra
How to evaluate these convolutions:

a) y(t) = (u(t) - u(t-2)) * u(t)

b) z(t) = cos(pi*t)(u(t+1) - u(t-1)) * u(t)

c) n(t) = (e^at)u(t) * (u(t+2) - u(t))

where * represents convolution symbol
Use the basic L-transform property...

$\displaystyle y(t)=f(t)*g(t) \implies \mathcal{L}\{y(t)\}= \mathcal{L}\{f(t)\}\ \mathcal{L}\{g(t)\}$ (1)

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$

3. ## Re: How to evaluate these convolutions:

Originally Posted by chisigma
Use the basic L-transform property...

$\displaystyle y(t)=f(t)*g(t) \implies \mathcal{L}\{y(t)\}= \mathcal{L}\{f(t)\}\ \mathcal{L}\{g(t)\}$ (1)

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$
Dear Sir,

In this class, we haven't started using Laplace Transform yet...The only way is to use convolution integral, I would be glad if you could help me...

With my kind regards,

4. ## Re: How to evaluate these convolutions:

Originally Posted by essedra
Dear Sir,

In this class, we haven't started using Laplace Transform yet...The only way is to use convolution integral, I would be glad if you could help me...

With my kind regards,
What have you tried and where do you get stuck? Please show all working.

5. ## Re: How to evaluate these convolutions:

a)
y(t) = (u(t) - u(t-2)) * u(t)
y(t) = u(t) * u(t) - u(t-2) * u(t)

and then I couldn't continue because I don't know how to evaluate this convolution.

6. ## Re: How to evaluate these convolutions:

Originally Posted by essedra
a)
y(t) = (u(t) - u(t-2)) * u(t)
y(t) = u(t) * u(t) - u(t-2) * u(t)

and then I couldn't continue because I don't know how to evaluate this convolution.
You said in an earlier post that "The only way [you're allowed to do them] is to use convolution integral"

Surely you can set up the integrals ....? So, again - what have you done and where do you get stuck?

7. ## Re: How to evaluate these convolutions:

( integral from T= minus infinity to T=infinity u(T) . u(t-T)dT ) - ( integral from T= minus infinity to T=infinity u(T) . u(t-2-T)dT )
I know that when we integrate with u(t), the integral starts from zero to infinity...Then, I couldn't solve the rest...

8. ## Re: How to evaluate these convolutions:

Originally Posted by essedra
( integral from T= minus infinity to T=infinity u(T) . u(t-T)dT ) - ( integral from T= minus infinity to T=infinity u(T) . u(t-2-T)dT )
I know that when we integrate with u(t), the integral starts from zero to infinity...Then, I couldn't solve the rest...
What is the function u(t)? How is it defined?