# Proper transfer function

In control theory, a proper transfer function is a transfer function in which the degree of the numerator does not exceed the degree of the denominator. A strictly proper transfer function is a transfer function where the degree of the numerator is less than the degree of the denominator.
The difference between the degree of the denominator and degree of the numerator is the relative degree of the transfer function.

## Example

The following transfer function:
is proper, because
is biproper, because
but is not strictly proper, because
The following transfer function is not proper
because
A not proper transfer function can be made proper by using the method of long division.
The following transfer function is strictly proper
because

## Implications

A proper transfer function will never grow unbounded as the frequency approaches infinity:
A strictly proper transfer function will approach zero as the frequency approaches infinity :
Also, the integral of the real part of a strictly proper transfer function is zero.