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(1) Fourier showed that periodic signals can be represented as a sum of complex exponentials known as Fourier series. (2) Complex exponentials are the eigenfunctions of linear time-invariant systems. The response of an LTI system to a complex exponential is another complex exponential with only an amplitude change. (3) Therefore, if a signal is represented by a Fourier series, the output of an LTI system can also be represented by the same Fourier series with the amplitudes scaled by the system
- Author
- Alper Karacakaya
- Language
- EN