belovedbayareaboy
New member
- Joined
- May 17, 2010
- Messages
- 1
Hey all,
Need help with a convolution problem involving the Dirac Delta function...
Construct \(\displaystyle f(t) = (g * k) (t)\) , where \(\displaystyle g(t) = e^t\) and \(\displaystyle k(t) = \delta(t-2)\)
Then we can rewrite as:
\(\displaystyle \int_0^t \! \delta(\tau-2) e^{t-\tau} \, d\tau\)
Can I then use the sifting property of the delta function to evaluate the integral and arrive at \(\displaystyle e^{t-2}\) ? Or does it only apply to an infinite range? (i.e. -inf to inf)
Thanks!
Need help with a convolution problem involving the Dirac Delta function...
Construct \(\displaystyle f(t) = (g * k) (t)\) , where \(\displaystyle g(t) = e^t\) and \(\displaystyle k(t) = \delta(t-2)\)
Then we can rewrite as:
\(\displaystyle \int_0^t \! \delta(\tau-2) e^{t-\tau} \, d\tau\)
Can I then use the sifting property of the delta function to evaluate the integral and arrive at \(\displaystyle e^{t-2}\) ? Or does it only apply to an infinite range? (i.e. -inf to inf)
Thanks!