12 Biomedical Engineering Fundamentals
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individual systems for a linear system where the sum of these individual responses
is not equal to the overall response in a nonlinear system.
Example of a linear system is as follows:
y(t) = 7x(t)
(12.11)
Example of a nonlinear system is as follows:
y(t) = x(t) + 7
(12.12)
12.3.2.2 Time-Invariant and Time-Variant Systems
A system can be considered as time-invariant if input–output characteristics of the
system do not vary with time. On the other hand, a time-variant system does not
follow such characteristics.
A system with input signal x(t) and output signal y(t) is time-invariant when
L {x (t − τ )} = y (t − τ )
(12.13)
where τ is shifting a parameter.
Example of time-invariant system is
y(t) = cos {x(t)}
(12.14)
Example of time-variant system is
y(t) = x(3t)
(12.15)
12.3.2.3 Linear Time-Invariant and Linear Time-Variant Systems
If a system satisfies linear and time-invariant properties, then it is known as linear
time-invariant system and a system which satisfies linear and time-variant properties
is called a linear time-variant system.
12.3.2.4 Static and Dynamic Systems
A system which does not require memory is known as static system and a system
which requires memory is called as dynamic system.
Example for memory-less static system is as follows:
y(t) = 3x(t)
(12.16)