In control theory

Control theory

Control theory is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems. The desired output of a system is called the reference...

, a strictly proper transfer function

Transfer function

A transfer function is a mathematical representation, in terms of spatial or temporal frequency, of the relation between the input and output of a linear time-invariant system. With optical imaging devices, for example, it is the Fourier transform of the point spread function i.e...

 is a transfer function where the degree

Degree (mathematics)

In mathematics, there are several meanings of degree depending on the subject.- Unit of angle :A degree , usually denoted by ° , is a measurement of a plane angle, representing 1⁄360 of a turn...

of the numerator is less than the degree of the denominator.

Example

The following transfer function is not strictly proper
because.

The following transfer function however, is strictly proper
because.

Implications

A strictly proper transfer function will approach zero as the frequency approaches infinity.
which is true for all physical processes.