What is the relationship between filtering and eigenfunctions?

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SUMMARY

The discussion clarifies the relationship between filtering and eigenfunctions in the context of linear time-invariant (LTI) systems. An eigenfunction is defined as a waveform that is scaled by a constant, known as the eigenvalue, when processed through a filtering operation (A). The equation Af = Lf illustrates this relationship, confirming that filtering corresponds to scaling via the representation of a function by its eigenfunction.

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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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