Properties of Systems
Given Below are the Properties of Systems :
- Periodicity
- Even and Odd
- Linearity
- Time Invariant
- LTI Systems
- BIBO Stability
- Causality
- Reflection
Periodicity
The signal’s behavior/graph repeats after every T. Therefore,
Here, T is the fundamental period
So we can say signal remains unchanged when shifted by multiples of T.
Even and Odd
An even signal is symmetric about the Y-axis.
x(t)=x(-t) even
x(t)=-x(-t) odd
A signal can be broken into it’s even and odd parts to make certain conversions easy.
Linearity
It constitutes of two properties-
(i) Additivity/Superposition
if x1(t) -> y1(t)
and x2(t) -> y2(t)
(ii) Property of scaling
if x1(t) -> y1(t)
then
If both are satisfied, the system is linear.
Time Invariant
Any delay provided in the input must be reflected in the output for a time invariant system.
Here, x2(t) is a delayed input.
We check if putting a delayed input through the system is the same as a delay in the output signal.
LTI Systems
A linear time invariant system. A system that is linear and time-invariant.
BIBO Stability
The bounded input bounded output stability. We say a system is BIBO stable if-
Causality
Causal signals are signals that are zero for all negative time.
If any value of the output signal depends on a future value of the input signal then the signal is non-causal.
Reflection
If a signal is given by x(t) then the reflected signal is described by x(-t). Thus, the reflected signal assumes at time –t the value of the original signal that occurs at time t.
Introduction to Signals and Systems: Properties of systems
In this article, we will go through Signal and systems, First, we will define what is a signal and what is a system, then we will go through the calculation of the Energy and Power of Signals with their transformation, At last we will conclude our article with Properties, Applications and some FAQs.
Table of Content
- What are Signals ?
- What is a System ?
- Calculating the Energy and Power
- Properties of Systems
- Applications