Handbook for Sound Engineers

Filters and Equalizers 785

23.1 Filter and Equalizer Definitions

A filter is a device or network for separating signals on
the basis of their frequency. Filters can either be defined
in terms of their pass band only where, the frequencies
of interest are allowed through, or in term of their stop
band, where certain frequencies are removed. The
default design mode for most filters is as a low pass
where all frequencies below a cutoff frequency, and
extending down to dc, are allowed to pass. A simple
re-arrangement usually allows for a high pass to be
made, where all frequencies above a cutoff frequency,
and extending upward, are transmitted. Other mode
complex responses such as bandpass are constructed
from these basic elements.
Passive filters have no amplification components in
the circuit. They cannot add energy to the signal so can
only act to attenuate signals.
Active filters use transistor or operational amplifier-
based gain stages allowing the option of boosting some
of the, or the whole, spectrum.
An equalizer is a device that uses filters to compen-
sate for undesirable magnitude or phase characteristics
of a systems response.

23.1.1 Pass Band

The pass band is a band of frequencies that pass
through a filter with a loss of less than 3 dB relative to
the nominal gain of the filter.

23.1.2 Stop Band

The stop band is a band of frequencies that pass through
a filter with a loss of greater than 3 dB relative to the
nominal gain of the filter.

23.1.3 Cutoff Frequency

A cutoff frequency is the frequency at which the gain
first falls to 3 dB below the nominal gain of the filter, as
you move out of the pass band.

23.1.4 Corner Frequency

A corner frequency is the frequency at which the rate of

change of a response makes a noticeable change. In the

case of a low-pass or high-pass filter, this is the same as

a the cutoff frequency, but other filters such as shelving

filters may have additional corner frequencies.

23.1.5 Bandwidth

The bandwidth is the difference between the upper and

lower cutoff frequencies on either side of the pass band.

23.1.6 Transition Band

The transition band is the range of frequencies over

which the gain the filter falls from its level at the cutoff

frequency to the nominal attenuation level in the stop

band.

23.1.7 Center Frequency

The center frequency of a band of frequencies is defined

as the geometric mean of the lowest and highest

frequencies of the band.

(23-1)

where,

f 1 is the cutoff frequency of the high-pass filter,

f 2 is the cutoff frequency of the low-pass filter.

23.1.7.1 Geometric Symmetry

A response showing mirror image symmetry about the

center frequency when plotted on a log scale is said to

have geometric symmetry. This is the natural response

of many electrical circuits as the response function

tends to contain multiplicative terms.

23.1.7.2 Arithmetic Symmetry

A response showing mirror image symmetry about the

center frequency when plotted on a linear scale is said

to have arithmetic symmetry. A bandpass filter with a

constant envelope delay will have arithmetic symmetry

in both phase and amplitude. The center frequency in

this case will be given by the arithmetic mean

(23-2)

Figure 23-1. Pass bands and Stop bands of a filter.

Stopband Stopband

Cutoff frequency

Bandwidth or passband

0 dB

3 dB fm= f 1 uf 2

fc

f 1 +f 2

2

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