Not sure if this is the right forum. This is a mathematical question, but it is from signals.(adsbygoogle = window.adsbygoogle || []).push({});

An LTI system is a mapping from one function space to another that is both linear and time invariant.

Given this, how might I show that if the input is a sinusoid, the output, is also a sinusoid? Similarly for complex exponentials? If one can show that a spectral decomposition can be performed on an LTI system, then this is trivial, but that requires analysis of the eigenvalues and eigenfunctions of the system, which I am not very familiar with.

Furthermore, it turns out that complex exponentials are eigenfunctions of any LTI system. Are they the only eigenfunctions? If so, is the frequency response of an LTI system equivalent to its spectrum (set of eigenvalues)?

I'd appreciate it if someone could provide insight on these matters, and perhaps recommendation of a textbook that would explain these concepts very well.

BiP

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# LTI system and sinusoids/complex exponentials

**Physics Forums | Science Articles, Homework Help, Discussion**