Perfect-Q-3
Figure 1. Band interaction of 1/3-octave Proportional-Q filters
Figure 2. Band interaction of 1/3-octave Constant-Q filters
Figure 4. Graphic response of Perfect-Q filters
Figure 3. Band interaction of Interpolating Constant-Q filters
Figure 5. Phase response of Figures 1 and 4.
-14
+14
-12
-10
-8
-6
-4
-2
+0
+2
+4
+6
+8
+10
+12
-2
+2
-1.75
-1.5
-1.25
-1
-0.75
-0.5
-0.25
+0
+0.25
+0.5
+0.75
+1
+1.25
+1.5
+1.75
d
B
u
octaves
combined response
showing reduced
band interaction
increased ripple
individual responses
(actual slider settings)
-14
+14
-12
-10
-8
-6
-4
-2
+0
+2
+4
+6
+8
+10
+12
-2
+2
-1.75
-1.5
-1.25
-1
-0.75
-0.5
-0.25
+0
+0.25
+0.5
+0.75
+1
+1.25
+1.5
+1.75
d
B
u
octaves
decreased ripple
individual responses
(actual slider settings)
-14
+14
-12
-10
-8
-6
-4
-2
+0
+2
+4
+6
+8
+10
+12
-2
+2
-1.75
-1.5
-1.25
-1
-0.75
-0.5
-0.25
+0
+0.25
+0.5
+0.75
+1
+1.25
+1.5
+1.75
d
B
u
octaves
individual responses
(actual slider settings)
no band interaction or ripple
combined response
is perfect
-14
+14
-12
-10
-8
-6
-4
-2
+0
+2
+4
+6
+8
+10
+12
-2
+2
-1.75
-1.5
-1.25
-1
-0.75
-0.5
-0.25
+0
+0.25
+0.5
+0.75
+1
+1.25
+1.5
+1.75
d
B
u
octaves
individual responses
(actual slider settings)
combined response
showing effects of
band interaction
-80
+80
+70
+50
+30
+10
+90
+90
-60
-40
-20
-10
-30
-50
-70
+0
+20
+40
+60
-2
+2
-1.5
-1
-0.5
-0
+0.5
+1
+1.5
octaves
d
B
u
Proportional-Q
Perfect-Q
By the 1970s it was clear that a constant-Q design
would come a lot closer to the ideal. The use of active
filters greatly increased the designer’s ability to realize
new filter topologies and, in 1981, three constant-Q,
one-third-octave graphic equalizers were concurrently
designed. While a significant improvement, the results
were not ideal. Figure 2 shows the response of a con-
stant-Q design with two adjacent sliders boosted 6 dB.
While band interaction is significantly reduced, ripple
between bands is increased.
Interpolating Constant-Q, developed to reduce the
ripple, works quite well, however band interaction is
increased, and the overall output amplitude is nearly as
bad as proportional-Q. Figure 3 shows it is narrower,
more closely approximating the front panel’s 2/3-octave
width, but the amplitude is 9 dB.
It’s not Constant – It’s not Proportional –
It’s Perfect!
As stated earlier, DSP allows filter technology not
possible with analog designs. Ray Miller, one of Rane’s
distinguished DSP engineers extensively researched
filter band interaction and developed new ways of
preventing it.
Perfect-Q features virtually no band interaction
and extremely low ripple between adjacent bands. The
result: the world’s first graphic equalizer whose output
response precisely matches the front panel slider set-
tings dramatically shown in Figures 4 and 6.
