Rane DEQ 60L Manual page 16

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Figure 7. Constant-Q Nonlinear Response.
The setting is adjusted in linear steps: 4, 8, and 12 dB, and
we see the resulting response curves. Symbols are shown at
1/3-octave intervals. For a constant-Q filter, the level 1/3-octave
away (shown as 1) is not a linear function of the setting, as
we see by the uneven spacing.
Linear Response Changes
Although not particularly obvious, graphic equalizer
bandpass response is, in general, not linear. This means
that when the center frequency amplitude is changed,
the filter skirts do not necessarily change in a linear
manner. If it were a linear response then boosting the
center frequency amplitude would result in a boost-
ing of the skirts a known and predictable (key words)
amount that was a linear factor of the amount of center
boost. Figure 7 shows boosting the center in 4-dB
steps results in points located 1/3-octave away being
boosted, first around 1-dB, then about 2-dB and for
the last 4-dB step nearly 3-dB. Contrast this with the
Perfect-Q linear response shown in Figure 8, where the
same points increase the same amount for each 4-dB
increase.
In previous graphic equalizer designs the interaction
acts like a linear system for small settings, but not for
large ones. The results are good as long as the filters are
not boosted or cut by large amounts; in that case the
result is a compromise, but it is better than uncorrect-
ed. To linearize the system the filters must be cascaded.
This results in the dB (logarithmic level) responses of
the filters summing together to form the composite
response; otherwise phase shifts between filter sections
complicate things.
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Figure 8. Perfect-Q Linear Response.
The Q has been adjusted such that the level 1/3-octave away
(shown as 1) is a linear function of the setting.
Perfect-Q takes a different approach. It adjusts
the filter Q, or bandwidth, as a function of boost/cut
amount, in such a way as to make the interaction
linear, and thereby much easier to correct. The fre-
quencies of the two filters directly adjacent to a given
filter are given priority. The interactions at those two
frequencies are made perfectly linear, which makes the
interactions at more distant frequencies more nearly
linear, and so on. Once the response is linear it is a
straightforward, although complex, mathematical mat-
ter to check the user setting and subtract the resultant
interaction so only the intended change is made.
Perfect-Q Availability
First use of this technology was the DEQ 60 Digital
Graphic Equalizer — a 2-channel 30-band 1/3-octave
design with conventional slider controls (part of Rane's
analog-controlled digital series). Perfect-Q is employed
in these fine products:
• DEQ 60L Graphic Equalizer
• Halogen software for the HAL Multiprocessors
Proprietary Rights
All techniques and algorithms discussed in this
article are covered by U.S. Patent 7,266,205 granted to
inventor Ray Miller and assigned to Rane Corporation.
International patent pending.
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