We can also speak of the transient response and steady-state response
given any fixed sum of sinewaves as input, since a sum of
sinewaves can be regarded as a ``steady-state signal'' (after it is
switched on). Of course, any practical signal whatsoever, including a
switch-on transient, can be represented by an infinite sum of
sinusoids (just consider its inverse Fourier transform
representation [83]). However, we're speaking in this section about
practical engineering terms--not pure mathematics. Therefore, we'll
consider a valid ``steady state input signal'' to be any fixed linear
combination of a finite number of sinusoids (allowing dc as a
zero-Hz sinusoid).^{6.6} Under this constraint, the turn-on transient
cannot be represented by a finite sum of sinusoids. Generally
speaking, any discontinuity in an input signal must be regarded as a
transient, and transients will always disturb the steady-state
operation of a filter, resulting in a transient response at the filter
output.

In summary, a filter transient response is caused by suddenly
switching on a filter input signal, or otherwise disturbing a
steady-state input signal away from its steady-state form. After the
transient response has died out, we see the steady-state response,
provided that the input signal itself is a steady-state signal (a
fixed linear combination of sinusoids) and the filter is LTI.