What is the relationship between filtering and eigenfunctions?

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Eigenfunctions are waveforms that maintain their form when processed by a linear time-invariant (LTI) system, only experiencing scaling. The relationship between filtering and eigenfunctions is established through the equation Af = Lf, where A represents the filter and L denotes the scaling factor. This indicates that filtering can be viewed as a scaling operation on the eigenfunction. The scaling constant in this context is referred to as the eigenvalue. Understanding this relationship is crucial for grasping the behavior of systems in signal processing.
hotel
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Hi,
I don’t know if I understand eigenfunction correctly, I hope someone can help me with it.
By definition of eigenfunction as
Af=Lf ;
Is it correct to say that filtering (A) is equal to scaling (L) through representation of a function by eigenfunction (f) ?
thanks
 
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An eigenfunction is a waveform that only gets scaled when going through a linear time-invariant (LTI) system. The scaling constant is the eigenvalue.
 

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