By far the most frequent purpose for using a filter is extracting either
the low-frequency or the high-frequency portion of an audio signal, attenuating
the rest. This is accomplished using a
*low-pass* or
*high-pass*
filter.

Ideally, a low-pass or high-pass filter would have a frequency response of one up to (or down to) a specified cutoff frequency and zero past it; but such filters cannot be realized in practice. Instead, we try to find realizable approximations to this ideal response. The more design effort and computation time we put into it, the closer we can get.

Figure 8.2 shows the frequency response of a low-pass
filter. Frequency is divided into three bands, labeled on the
horizontal axis. The
*passband*
is the region (frequency band) where the filter should pass its input through
to its output with unit gain.
For a low-pass filter (as shown), the passband reaches from a frequency of
zero up to a certain frequency limit. For a high-pass filter, the passband
would appear on the right-hand side of the graph and would extend from the
frequency limit up to the highest frequency possible. Any
realizable filter's passband will be only approximately flat;
the deviation from flatness is called the
*ripple*,
and is often specified by giving the ratio between the highest and lowest gain
in the passband, expressed in decibels. The ideal low-pass or high-pass filter
would have a ripple of 0 dB.

The
*stopband*
of a low-pass or high-pass filter is the frequency
band over which the filter is intended not to transmit its input.
The
*stopband attenuation*
is the difference, in decibels, between the lowest gain in the passband
and the highest gain in the stopband. Ideally this would
be infinite; the higher the better.

Finally, a realizable filter, whose frequency response is always a
continuous function of frequency, must have a frequency
band over which the gain drops from the passband gain to the stopband
gain; this is called the
*transition band*.
The thinner this band can be made, the more nearly ideal the filter.