x y Response of an LTI system to a periodic input.

H(s) Multiply magnitudes, add phases. n n Attenuate higher frequencies: “lowpass filter”.

Back to rectifier example AC y=|x| DC + Idea: add a lowpass filter in cascade to attenuate the AC components, and get a “purer” DC source.

y=|x| + H(s) + Rectifier plus filter

What does z(t) look like?

Mean square approximation

Extension to Fourier

Example: Square Wave

Convergence in mean square

Mean square convergence for the square wave