- #1
mym786
- 11
- 0
If one has input x(t), then convolving x(t) with impulse response of the system would give the zero-state of the system.
For example, we have a system described as :
(D[tex]^{2}[/tex] + 4D + 3)y(t) = (D+5)f(t).
I computed system impulse response which is :
h(t) = 2e[tex]^{-t}[/tex] - e[tex]^{-3t}[/tex]
Now if say f(t) = e[tex]^{t}[/tex]
f(t) (convolved) h(t) does not equal the particular solution of D.E. (Particular solution is zero-state) .
Why ??
For example, we have a system described as :
(D[tex]^{2}[/tex] + 4D + 3)y(t) = (D+5)f(t).
I computed system impulse response which is :
h(t) = 2e[tex]^{-t}[/tex] - e[tex]^{-3t}[/tex]
Now if say f(t) = e[tex]^{t}[/tex]
f(t) (convolved) h(t) does not equal the particular solution of D.E. (Particular solution is zero-state) .
Why ??