Signals	Systems	System Response
Frequency Representation	Fourier Series / Transforms	Background Material

Once we have established that y(t) = h(t) ** x(t), where the ** symbol represents convolution, combined with the commutative property of convolution, y(t) = h(t) ** x(t) , we see that the “system” can be the “signal” or vice versa, the “signal” can be the “system.” This may sound confusing at first, but let’s take it apart and analyze it slowly.

We know that when we have a system with an input x(t) with a system transfer function (or impulse response function) h(t), the output is represented by y(t), which is the convolution of x(t) and h(t). However, since x(t) and h(t) are just arbitrary function “names” (For ex, we could potentially call the input h(t) and the transfer function x(t)), either one could be the “signal” and the counterpart the “system.” This is illustrated clearly as the associative property (on the previous link Convolution) of convolution. Essentially, what we are saying can be represented by figure 2 below.

The associative property of convolution dictates f **g = g ** f. Figure 1 above is the equivalent of saying y = x ** h (The output is the convolution of the input with the transfer function). Figure 2, on the other hand, is saying y = h ** x (Also, the output is the convolution of the input with the transfer function where this time the input is h(t) and the transfer function is x(t)). 

Example:

System Flow Diagram
Input, x(t)
Transfer Function, h(t)
Output, y(t)
Solve!
Convolution Solution
System Flow Diagram with Solution