Simplistically, filters and amplifiers can be considered as four-terminal networks described by a transfer function as follows:
Figure 3.1 shows some ideal transfer functions.
If 
is a real constant then we call
the network an ideal amplifier.
If 
is a heavyside step
function we refer to the circuit as an ideal low-pass filter, and if
an ideal high-pass
filter.
Figure 3.1: a) Ideal amplifier, b) Ideal low-pass
filter, c) ideal high-pass filter, d) low-pass filter and e) high-pass
filter.