Re: Please help on the signal and system problem [Homework help]
It can be proved that h(t)*cos(wt) = Acos(wt + θ) for all finite energy signal h(t) for some A and θ
a). Prove this result.
b). Find the relationship between A, θ, and h(t)
c). Finally, use this results and the Fourier Series definition to show that any periodic function x(t), after passing through a linear system with impulse
response h(t), the output y(t) is also periodic.
d). Use the results in the earlier parts to find the relationship between Fourier Series of input x(t) and the Fourier Series of the output y(t) of a linear
system with impulse response h(t).
Thanks!
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Should be h(t) convolute with cos(wt) = Acos(wt + θ)
It can be proved that h(t)*cos(wt) = Acos(wt + θ) for all finite energy signal h(t) for some A and θ
a). Prove this result.
b). Find the relationship between A, θ, and h(t)
c). Finally, use this results and the Fourier Series definition to show that any periodic function x(t), after passing through a linear system with impulse
response h(t), the output y(t) is also periodic.
d). Use the results in the earlier parts to find the relationship between Fourier Series of input x(t) and the Fourier Series of the output y(t) of a linear
system with impulse response h(t).
Thanks!
-----------
Should be h(t) convolute with cos(wt) = Acos(wt + θ)
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