Theorem:

Statement :If a causal system is either additive or homogeneous ,then y(t) can not be non zero before x(t) is non-zero .

Proo f:

Say x(t) = 0 for all t less than or equal to t₀.

We have to show that the system response y(t) = 0 for all t less than or equal to t₀.

Since the system is either additive or homogeneous the response to the zero input signal is the zero output signal. The zero input signal and x(t) are identical for all t less than or equal to t₀.

Hence, from causality, their output signals are identical for all t less than or equal to t₀.

We conclude the discussion on system properties by noting that this is not an end, but merely a beginning! Through much of our further discussions, we will be looking at an important class of systems - Linear Shift-Invariant (LSI) Systems.