System Properties
Classification system according to its behavior
1) system with memory or not
System is said to have a memory if its output signal depends on past value of the input signal. The
temporal of past value on which the output depends is defines how far the memory of the system into the
past. Normally energy storing elements have memory like capacitor, inductor etc.
In case of capacitor
In case of accumulator
In contrast to this, a system is said to be memory less if its output signal depends only on the present value
of the input signal. Resistor is the example of the memory less system since the current flowing through it
depends only on the value of voltage across it.
So in system without memory we can say:
2) Causality
System is said to be causal if the present value of the output signal depends only on the present and or the
past value of the input signal. Such a system is often referred to as being nonanticipatory, as the output
doesn’t anticipate future value of the input. The if the resistor and capacitor are connected in series then
such system is called causal because the capacitor voltage responds only to the present and past value of
the source voltage.
In discrete signal
Average filtering
In contrast to this if the output signal depends on present past and future value then such system is called
non causal system. And system is said to be anti causal if the output of the system depends only on future
value.
3) linearity
A system is said to be linear if it satisfies the principle of superposition. That is, the response of the linear
system to a weighted sum of input signal is equal to the same weighted sum of output signal, each output
being associated with the particular input signal acting on the system independently of all the other input
signal. System that violet principle of superposition is said to be nonlinear. If system is linear it holds the
property of scaling and homogeneity.
For single input single output, if system holds property of
Then
This property is called superposition and this will happen only when the system is linear.
This property is called scaling and homogeneity.
Linear system doesn’t create new frequency.
4) Stability
Stable system is one in which small input lead to response that do not diverge the output. A system is
said to be bounded input bounded output stable if and only if every bounded input result in a bounded
output. Output of such system does not diverge if the input does not diverge.
If pole of the system lie on right half plane than system is unstable. Unstable system is physically non
realizable. And if pole of the system lie on the left half plane then system is stable system and only the
stable system are realizable which is shown in above figure.
Here x(t) is limited to certain limit. i.e. here input is bounded to certain limit hence the output also
bounded so the about system is stable system.
This system is unstable system because as t tends to infinity y(t) becomes infinity.
5) Invertibility
A system is said to be invertible if the input of the system can be recovered from the system output.
Invertible system produces finite output for finite input. If a system is invertible then an inverse
system exist that, when cascaded with the original system, yields an output w[n] equal to the input x[n]
to the first system. Thus, the series connection has an overall input output relationship which is the
same as that for the identity system.