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:<math> \textbf{G}(s) = \frac{\textbf{N}(s)}{\textbf{D}(s)} = \frac{s^{4} + n_{1}s^{3} + n_{2}s^{2} + n_{3}s + n_{4}}{s^{4} + d_{1}s^{3} + d_{2}s^{2} + d_{3}s + d_{4}}</math>
because
:<math> \deg(\textbf{N}(s)) = 4 \leq \deg(\textbf{D}(s)) = 4 </math>.
The following transfer function however, is '''not proper'''
:<math> \textbf{G}(s) = \frac{\textbf{N}(s)}{\textbf{D}(s)} = \frac{s^{4} + n_{1}s^{3} + n_{2}s^{2} + n_{3}s + n_{4}}{d_{1}s^{3} + d_{2}s^{2} + d_{3}s + d_{4}}</math>
because
:<math> \deg(\textbf{N}(s)) = 4 \nleq \deg(\textbf{D}(s)) = 3 </math>.
==Implications==
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