filter waveform question

[Ingo Debus]

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

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

> 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...

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

> 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!

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

Ingo