27 Mar
2010
27 Mar
'10
9:57 p.m.
On Sat, Mar 27, 2010 at 11:47:04AM -0700, Ken Restivo wrote:
I've been looking a bit deeper into the peculiar shelf
filter shown on that page.
What is shown there is actually a second order shelf
filter - the sum of the input + a second order highpass
with some gain.
This correspons to the blue curve, the one that 'dips'
the most before starting to rise. The other curves are
the result if you move the two sections of the highpass
apart in frequency, gradually turning it into 1st order
for the part that matters - this is the yellow curve.
Now what is the origin of this 'dip' ? For a 2nd order
highpass the part below the cutoff frequency has a phase
that tends towards 180 degrees as frequency goes down and
the slope of the filter approaches 12 dB/oct. At the point
where the highpass_with_gain curve intersects the 0dB line,
the phase shift has not yet reached 180 degrees, but it is
well beyond 90 degrees so the real part is in antiphase
with input signal it is added to, and that causes the 'dip'.
In an analog implementation this would be difficult to
avoid. So this 'dip' may well be an unwanted side effect
rather than a wanted feature, with the real feature being
the 2nd order nature of the filter giving it a slope that
is almost double the normal value for a shelf filter.
(look at the blue line: 11 dB difference from 2 to 4 kHz).
This is relatively easy to implement, maybe I'll do it
one of these days.
Ciao,
--
FA
O tu, che porte, correndo si ?
E guerra e morte !