Proper transfer function
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If the degree of the numerator equals the degree of the denominator, the transfer function is biproper.
The difference between the order of the denominator (number of poles) and order of the numerator (number of zeros) is the relative degree of the transfer function.
The following transfer function:
is proper, because
is biproper, because
but is not strictly proper, because
The following transfer function is not proper (or strictly proper)
The following transfer function is strictly proper
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 (which is true for all physical processes):
Also, the integral of the real part of a strictly proper transfer function is zero.