filter waveform question

[Magnus Danielson]

>>>>> "ID" == Ingo Debus <debus at cityweb.de> writes:

Hi!

As there where talk about filters I could not resist to interfear...

 ID> Toni Jovanovski wrote:
 >> >On a second-order filter (12dB/oct) it is the Q parameter that
 >> >determines whether the filter is a Butterworth or Chebysheff or
 >> >whatever.
 >> 
 >> Well,I'm not so sure.I'm must check this

 ID> Let's look at it this way (correct me if I'm wrong):
 ID> The order of a low pass filter is equal to the number of parameters
 ID> which can be varied independently. A first order filter has only one
 ID> parameter, the cutoff frequency (Juergen mentioned a 6dB/oct filter with
 ID> resonance recently, this cannot be a first order filter then). A second
 ID> order filter has two parameters, these can be fc and Q. The terms
 ID> "Chebysheff" or "Butterworth" etc. describe how much ripple there is in
 ID> the pass band. For a second order filter, the "ripple" consists only of
 ID> one peak. The height of the peak is controlled by Q. For instance,
 ID> Q=0.58 for Bessel, 0.71 for Butterworth, 0.96 for Chebysheff with 1dB
 ID> ripple, 1.30 for Chebysheff with 3dB ripple (numbers from
 ID> Tietze-Schenk).
 ID> A fourth order filter has four independent parameters, although most
 ID> synthesizer 24dB/oct VCFs still only have controls for fc and Q. Any
 ID> fourth order filter can be made from two second order filters in series.
 ID> Thus you have two fc and two Q parameters. Some synths (e.g Yamaha
 ID> SY/TG77) have their 24dB/oct filter implemented this way.

The order is strictly connected to the number of poles, not the dB/oct
number not the number of parameters. The number of parameters is
actually greater than the number of poles, it is up to about the
double. The reason for this is that you can have zero's that also can
be varied. One example of this is the fully parametric equalizer which
uses a 2-pole filter but has three variable properties (Frequency,
width and amplification grade). The parametric equalizer use a balance
between the 2 poles and 2 zeros. The poles and zeroes have the same
frequency but their relative distance to eachother controls the
amplification and the distance of them from the jw-axis controls the
width. So, the number of variable parameters is a bad measure.
For larger filters one changes a number of paramters in bulk.

Bessel, Chebychev, Butterworth, Gauss, LaGrange etc. are all diffrent
approximations to the brickwall idealized model of a filter. These
approximations have their respective properties (Butterworth have a
maximum flat frequency response, Besselhave a maximum flat groupdelay
etc).

 >> filter.There is a another class of filters FIR  ( finite impulse response
 >> )filters.I say this because I wanna show how complex is Filter design.It's
 >> not just electronics...

 ID> But FIR filters cannot be made only of resistors, capacitors, inductors
 ID> and amplifiers. You need delay lines. Not necessarily digital, BBDs (or
 ID> tape echo machines :-)) can also be used. The difference to a
 ID> conventional RLC filter is obvious when a square wave is applied to a
 ID> FIR low pass: There's not only overshoot after the rising edge but also
 ID> "undershoot" *before* it! This can never be achieved with a RLC filter.

Well, you *can* make FIR filters which has both pre and post
ringing. The possibilities for preringing is as large for any
filtering concept, they start when the signal enters the filter. The
postringing effect will strictly end at a certain point in time for
FIR filters (thus the name Finite Impulse Responce) where as IIR
(Infinite Impulse Responce) and normal analog filters can
theoretically go on forever (where they in reality would disintegrate
or the signal be swallowed in the noise).

 >> Yes , of course!!!I forgot to mentiot it.When there isn't resonance ( Q )
 >> the poles are simple ( real numbers ) and when you put resonance , poles
 >> become complex-conjugate numbers.Changing the Q factor poles are moving in
 >> complex-plane!

 ID> Yes, and because poles are either single real poles or complex-conjugate
 ID> pole pairs the number of poles is the number of parameters which can be
 ID> varied independently.

Well, no... a pole is allways resonant! The real poles are only
resonant at DC for some exponential change. DC is as much as a
frequency as 440 Hz or 1 kHz in theory.

The resonance (Q) property is the real component of any pole
position. A resonant filter normally has one or two poles near the
jw-axis (and thus appears resonant for stable sines) where as the
others will make more subtle changes in the sound.

There are many measures on filters, many which are more or less
derivate properties on the pole and zero positions of the filter. Some
measures seems like generically correct where they may only hold for a
very tight frequency range for instance. The dB/oct measure is
sometimes a very confusing term where it may be a good term for some
cases, it is a derivate property and not a real direct property.

Cheers,
Magnus