Re: AUParametricEq Q parameter?
Re: AUParametricEq Q parameter?
- Subject: Re: AUParametricEq Q parameter?
- From: Kevin Boyce <email@hidden>
- Date: Tue, 4 Jan 2005 09:33:29 -0500
On Jan 4, 2005, at 7:29 AM, Felipe Baytelman wrote:
What does the AUParametricEq Q parameter controls? Q for Quality?
kParametricEQParam_CenterFreq = 0
kParametricEQParam_Q = 1
kParametricEQParam_Gain = 2
Yes indeed, Q does stand for quality, as in "quality of the
oscillator"; it comes from early physics, probably initially from
mechanical oscillators like spring-mass-damper systems, or pendulums.
When building a clock, you want your timekeeping resonator to have a
very narrow resonance (or equivalently, low damping). Hence the term
"Quality", to indicate narrowness of resonance.
Course, you see one resonance, you've seen them all, so the term has
carried over to electronic and DSP resonances. Only now we just say
"Q", because "quality" doesn't necessarily mean "narrow resonance" in
our case.
A Q of infinity is an infinitely narrow resonance, and a Q of 1/2 is
"critically damped". Q=1/2 is the point at which the resonance poles
become complex.
One practical way of stating it is that the Q of a resonator is the
number of "periods" under the exponential decay of its impulse
response. More precisely, for Q>>1/2, the impulse response decays by
the factor exp(-pi) in Q cycles, which is about 96 percent decay, or
-27 dB.
I stole the above paragraph from
http://ccrma.stanford.edu/~jos/filters/Decay_Time_is_Q.html
Which has lots of details about Q on that page and the surrounding ones.
There, was that verbose enough?
-Kevin
--
Kevin Boyce
"Burn the land, and boil the sea; You can't take the sky from me."
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