Linear system
A linear system is a system that will produce the same output for both of the following actions:
1. One puts signals through the system, multiplies the outcomes by a constant, and add the results together.
2. One multiplies the same signals by the same constants, adds the results together, and sends that outcome through the system.
An example of a linear system is as follows:
$ y(t) = 15x(t)\!<\math> The proof for this is rather simple. Suppose you put <math>x(t) = t + 12\!<\math> and end up with <math>15t + 180\!<\math>. You also send <math>z(t) = t - 2\pi\!<\math> through the system and get <math>15t - 30\pi\!<\math>. You multiply the first outcome by <math>2\!<\math> and get <math>30t + 360\!<\math>. You multiply the second result by <math>3\!<\math> and you get <math>45t - 90\pi\!<\math>. After summing the two, you get <math>75t + 360 - 90\pi\!<\math>. $
