Chapter 3 Signals and systems Part II
Properties of systems
Memoryless
The output at any time only depends on the input at that time
Invertability
For any output, there’s only one input that can cause this output
Causality
The output at any time only depends on the input at past and present, namely, the system cannot anticipate the future input
If x1(t) = x2(t) when t <= t0
Then y1(t0) = y2(t0)
The impulse response h(t) is 0 when t < 0
The Region of Convergence of H(s) is at the right side of the right most pole
Stability
If the input is bounded, the output is also bounded
The impulse response h(t) is absolute integrable.
The Region of Convergence of H(s) must include the jw-axis
Time invariance
If x(t) -> x(t - t0)
Then y(t) -> y(t - t0)
Linearity
If x(t) -> ax1(t) + bx2(t)
Then y(t) -> ay1(t) + by2(t)