EE5410 Signal Processing : From the eigenfunction property to frequency response

EE5410 Signal Processing : From the eigenfunction property to frequency response

1. One of the most important properties of Fourier series is a direct consequence of the eigenfunction property of complex exponentials.

2. if a PERIODIC signal is applied to an LTI system, then the output will be periodic with the SAME period,

and EACH of the coefficients of the output is the corresponding Fourier coefficient of the input MULTIPLIED by a complex number whose value is a function of the frequency corresponding to that Fourier coefficient.

3. This function of frequency is characteristic of the LTI system and is referred to as the frequency response of the system.

4. By examining th frequency response, we were led directly to the idea of filtering using LTI systems.