Static or Dynamic Systems

a)      Static systems:

Definition: It is a system in which output at any instant of time depends on input sample at the same time.

Example:

1)      y(n) = 9x(n)

In this example 9 is constant which multiplies input x(n). But output at nth instant that means y(n) depends on the input at the same (nth) time instant x(n). So this is static system.

2)      y(n) = x2(n) + 8x(n) + 17

Here also output at nth instant, y(n) depends on the input at nth instant. So this is static system.

Why static systems are memory less systems?

Answer:

Observe the input output relations of static system. Output does not depend on delayed [x(n-k)] or advanced [x(n+k)] input signals. It only depends on present input (nth) input signal. If output depends upon delayed input signals then such signals should be stored in memory to calculate the output at nth instant. This is not required in static systems. Thus for static systems, memory is not required. Therefore static systems are memory less systems.

b)      Dynamic systems:

Definition: It is a system in which output at any instant of time depends on input sample at the same time as well as at other times.

Here other time means, other than the present time instant. It may be past time or future time. Note that if x(n) represents input signal at present instant then,

1)      x(n-k); that means delayed input signal is called as past signal.

2)      x(n+k); that means advanced input signal is called as future signal.

Thus in dynamic systems, output depends on present input as well as past or future inputs.

Examples:

1)      y(n) = x(n) + 6x(n-2)

Here output at nth instant depends on input at nth instant, x(n) as well as (n-2)th instant x(n-2) is previous sample. So the system is dynamic.

2)      y(n) = 4x(n+7) + x(n)

Here x(n+7) indicates advanced version of input sample that means it is future sample therefore this is dynamic system.

Why dynamic system has a memory?

Answer:

Observe input output relations of dynamic system. Since output depends on past or future input sample; we need a memory to store such samples. Thus dynamic system has a memory.

For continuous time (CT) systems:

A continuous time system is static or memoryless if its output depends upon the present input only.

Example:

Voltage drop across a resistor.

It is given by,

v(t) = i(t)*R

Here the voltage drop depends on the value of the current at that instant. So it is static system.

On the other hand a CT system is dynamic if output depends on present as well as past values.