Determining system response to a superposition of sinusoids
Since the response to a LTI system to a sinusoid is so easy to characterize, a
general technique for finding the response to a more general class of input
signals is as follows. If we can decompose the inputs signal as a superpositon
of sinusoids, then we can find the response of the system to each constituent
sinusoid. By linearity, the system output is the superposition of these
individual responses.
Up to Systems and Linearity
Example: continuous-time differentiator