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Sinusoids are Eigenfunctions of CT LTI Systems

Module by: Richard Baraniuk. E-mail the author

Figure 1
Figure 1 (f1.png)
yt= V ω tτhτd τ =hτeiω(tτ)d τ =eiωthτe(iωτ)d τ =Hωeiωt y t τ V ω t τ h τ τ h τ ω t τ ω t τ h τ ω τ H ω ω t
where Hω H ω is the eigenvalue (scale factor) and eiωt ω t is V ω t V ω t , which is the eigenfunction.

Summary: Figure 2.

Figure 2: Hω H ω is the eigenvalue and eiωt ω t is the eigenfunction.
Figure 2 (f2.png)
Hω=|Hω|eiHω H ω H ω H ω
where |Hω| H ω changes the amplitude of eiωt ω t and eiHω H ω changes the phase of eiωt ω t .
output=|Hω|ei(ωt+Hω) output H ω ω t H ω

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