1. The problem statement, all variables and given/known data
The unit impulse response of an LTIC system is h(t) = [itex]e^{-t}u(t)[/itex]. Find the system's (zero-state) response y(t) if the input f(t) is [itex]e^{-2t}u(t-3)[/itex].
2. Relevant equations
y(t) = f(t) * h(t) = [itex]∫^{∞}_{-∞}f(t)h(t-\tau)d\tau[/itex]
[itex]f_{1}(t) * f_{2}(t - T) = c(t)[/itex]
[itex]f_{1}(t) * f_{2}(t - T) = c(t - T)[/itex]
3. The attempt at a solution
I'm not sure how to apply the shifting property because here in f(t) I have the unit step function only which is shifted and not the exponential. Is it possible to apply the shifting property above for this problem? I don't see how I can apply it for the reason mentioned above.
Thanks for any help.
The unit impulse response of an LTIC system is h(t) = [itex]e^{-t}u(t)[/itex]. Find the system's (zero-state) response y(t) if the input f(t) is [itex]e^{-2t}u(t-3)[/itex].
2. Relevant equations
y(t) = f(t) * h(t) = [itex]∫^{∞}_{-∞}f(t)h(t-\tau)d\tau[/itex]
[itex]f_{1}(t) * f_{2}(t - T) = c(t)[/itex]
[itex]f_{1}(t) * f_{2}(t - T) = c(t - T)[/itex]
3. The attempt at a solution
I'm not sure how to apply the shifting property because here in f(t) I have the unit step function only which is shifted and not the exponential. Is it possible to apply the shifting property above for this problem? I don't see how I can apply it for the reason mentioned above.
Thanks for any help.
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