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I had written in another thread:
>> One performance measure might be the attenuation one octave and two
>> octaves from the 3dB cutoff frequency (more attenuation = higher
>> score). That's a frequency domain measurement.
Dennis responded:
>In the frequency domain, the -3 dB point is more or less irrelevant. A
>2-pole filter will be 12 dB down an octave above Fc (Fc*2). How far down
>it is at Fc will depend on the Q or the damping factor (1/2Q) of the
>filter. Its behavior (overshoot, undershoot) in the time domain will be
>determined by Q.
For a 2-pole filter, yes, but not for higher order filters, where
you can have inflection points in the frequency response curve. For
example, I recently constructed a 6-pole highpass filter that had
a more "desirable" (to me) temporal response to a step function.
The frequency response was such that it leveled off at 14 dB about
an octave away from the 3 dB point, stayed there for another half
octave or so, and then fell off further from there. Actually the
plateau was more of a slight hump. The filter had, essentially, two
roll-off frequencies, at different attenuation levels.
I don't think a measure like Q has any meaning in that case, with
respect to desired filter performance -- the Q of my filter was
basically the same as a 6-pole filter of some traditional type, but
the frequency and time responses were quite different.
--
,|___ Alex Matulich -- alex@xxxxxxxxxxxxxx
// +__> Director of Research and Development
// \
// __) Unicorn Research Corporation -- http://unicorn.us.com
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