The signal defined by the equations f(t) = 0 for t < 0, f(t) = E for 0 ? t ? a and f(t) = 0 for t > a is

Numerator power will higher than denominator, and such transfer functions is not realizable.

All linear system possess the property of superposition i.e., if input u₁ gives output y₁ and input u₂ gives output y₂ then input u₁ + u₂ will give output y₁ + y₂.

Superposition implies homogencity i.e., if input u gives output y, then input ku gives output ky where k is a rational number.

In general a system is linear if a transformation T satisfies the relation

T(au₁ + ?u₂) = aT(u₁) + ?T(u₂)

where a and ? are constant.