>>>>> "HM" == Hans Mikelson  writes:

 HM> Magnus Danielson writes:
 >> This formula is rather useless really, you migth get more interesting
 >> results out of
 >> 
 >> b1Y+b2Y'+b3Y"=a1X+A2X'+a3X"

 HM> Ooops.  Yes since the frequency response of the other = 1.  Actually I meant 
 HM> the more general:

 HM>     b1Y+b2Y'+b3Y"+...=a1X+a2X'+a3X"+...

Yes, I assumed you meant to expand it further... and we all type too
fast from times to times ;)

 >> and apply the LaPlace transform to it. You will need to do a touch of
 >> z-transform due to the sampling properties involved.

 >> I must admitt I haven't follwed all the twists of this thread but I
 >> have gotten the feeling that it is the filters in csound being discussed.

 HM> Well yes, I took a tangent and started talking about some filters I am 
 HM> working on in Csound, but not the built in filters.

The two filter curves that I saw earlier in the thread where quite
simple cases of pole and zero positioning and I had a long reply
comming up with z-plane plots in ASCII but I droped it in /dev/null
instead.

 >> 
 HM> I'm in the process of doing some more work with filters and have
 HM> been having some success with getting a more  analog sound by
 HM> "enveloping" the resonance so it doesn't jump up so suddenly. 
 >> 
 >> One of the real reasons that digital/sample base filter fail in making
 >> near emulation is that the sampling frequency creep to close the work
 >> area. If one would let the sampling frequency become very much larger
 >> things would become more and more closer, but this cost hardware and
 >> money.

 HM> This was the point I was trying to address by "solving" the filter equation 
 HM> numerically.  You could do the same thing by using a really big sample rate 
 HM> but that would be even more numerically intensive and would not have checks 
 HM> built in to make sure it was as close as you wanted it.  By solving the diff. 
 HM> eq. you could specify to make it as close as the 16 bit resolution of the 
 HM> output and fit in the sample rate so it should be indistinguishable from a 
 HM> sample of a continuous filter.  Since I'm mainly doing rendering not 
 HM> real-time the cost is not so bad.

Have you looked in some decent filter books? I can recommend a few of
them if you are intereted.

There has been extensive work on mapping analog filters into the
digital domain and there is several methods to use with diffrent
artifacts. Still having these fine methods I argue that the
samplingrate is far to small for either of these methods to preform as
well as they need. The basic problem is really that the frequency
curve follows a diffrent geometry in a sampled based system compared
to a continous system. By increasing the samplingrate will they become
closer and closer to each other in properties for a limited frequency
range.
                  st
The mapping is z=e   which will bend the jw axis into an circle.

 >> Digital stuff can do a lot of neat stuff, but you can't get at the
 >> same marks as analog filters, just more or less close. It's just isn't
 >> the same stuff theoretically. Similar, but not the same.

 HM> Analog filters also are only an approximation of the filter differential 
 HM> equation of course.

Sure, but analog filters will approximate continous systems better
than a sampled system may for contious signals. There is limits on
what you may do with analog systems thougth, component values may
become critical and all that, but it is a continous system.

Hey, I'm not in here for an analog vs. digital debate, I just want to
point out where digital systems fail to be true to analog systems.

 >> PS. Hans, you type very long lines there, use enter a little more
 >> often or have your emailer insert them for you.

 HM> I'm still getting used to a new mail program.  I checked the box that says 
 HM> force hard returns now so hopefully this will come through OK.

That's it! Now I don't need to hand-reedit your text when I quote you ;)

Cheers,
Magnus