- #1
phoenixy
I have some trouble wrapping my head around singularity
One of assignment question is to show that the unit function is not defined at 0. To do that, I need to show
[tex]\lim_{\Delta\to0}[u_{\Delta}(t)\delta(t)]=0[/tex]
[tex]\lim_{\Delta\to0}[u_{\Delta}(t)\delta_{\Delta}(t)]=\frac{1}{2}\delta(t)[/tex]
Also, I need to show that the following is identical to u(t)
[tex]g(t)=\int u(t)\delta(t-\tau)d\tau[/tex]
integrating from negative infinity to positive infinity
One more question, what's the derivative of the impulse function?
PS: what's the tex code for integration from infinity to infinity? I tried \int_-\infty^+\infty, but the tex output is messed up
One of assignment question is to show that the unit function is not defined at 0. To do that, I need to show
[tex]\lim_{\Delta\to0}[u_{\Delta}(t)\delta(t)]=0[/tex]
[tex]\lim_{\Delta\to0}[u_{\Delta}(t)\delta_{\Delta}(t)]=\frac{1}{2}\delta(t)[/tex]
Also, I need to show that the following is identical to u(t)
[tex]g(t)=\int u(t)\delta(t-\tau)d\tau[/tex]
integrating from negative infinity to positive infinity
One more question, what's the derivative of the impulse function?
PS: what's the tex code for integration from infinity to infinity? I tried \int_-\infty^+\infty, but the tex output is messed up