>> Of course, it's not quite the same. With electronics, you have to 
>> remember that your "10 Ohm" resisters are actually 10 Ohm +/- 10%. ;-)
> 
> Right, unless you have 1% resistors.

Even then, you have to be careful that your design won't malfunction 
wildly if one of the two "identical" resistors isn't quite "identical", 
for example.

With digital IIR, you just have to be careful about numerical stability.

>> And also, it seems you cannot make a digital IIR with *exactly* the 
>> same frequency response as the corresponding analogue IIR - although 
>> it's a pretty close match. But analogue IIRs are designed in the 
>> s-domain, which is a different "shape" to the z-domain. It's quite 
>> easy to map coordinates from one domain to the other, but the 
>> resulting function doesn't behave in exactly the same way.
> 
> That was one of things that threw me, if you look at poles and zeros 
> diagrams, many of them are in the s domain, so you have to remember to 
> wrap them around a unit circle. when you look at them.

Yeah, it's tricky. There are several possibly ways to map the s-domain 
to the z-domain - including advanced techniques where one specific 
frequency maps exactly while the rest are all approximate. (E.g., so you 
end up with a correct cutoff frequency even if the rolloff angle is 
different.)

>> Oh yeah - you have a wife, don't you?
>>
>> [I'm not jelous. Much.]
>>
> 
> Oh, don't be. I have a son, too. :) He's getting to the "human parrot" 
> stage, now.. Gotta watch myself. He's great fun now. Can't wait till 
> he's old enough to take an interest in some of the things I do.

Yeah, I think I have a picture somewhere on my harddrive of him doing 
his "it's time to ****ing FEED ME!" expression. Except that, of course, 
you can never tell if he means "feed me" or something else - just "I'M 
NOT FRIGGIN HAPPY!"

I just hope he doesn't grow up to be an idiot. Because, man, that would 
be seriously upsetting as a parent, I imagine... o_O

>>> Its kind of nice knowing enough to predict what will happen when 
>>> moving a pole or a zero on the chart (Custom IIR)
>>
>> I tried to build a unit for Reaktor that does this, but without much 
>> success. (Again, the mathematics isn't "hard", it's just fiddly. And 
>> Reaktor isn't terrifically flexible...)
> 
> I thought about downloading the demo to play around with.

What, Reaktor?

> What was 
> interesting was dragging a pole ever so slightly out of the unit circle 
> at certain angles (frequency) would cause it to give a screeching 
> feedback then go unstable. Of course a pole beyond the unit circle is 
> obviously not a stable configuration. It was interesting to see just how 
> far I could push it before the applet would decide not to render.

The numerical stability depends on the exact kind of arithmetic you use. 
(Integer, fixed-point, floating-point, single-precision, 
double-precision, denormals...) A Chebyshev LP filter with high-order 
basically involves turning the feedback path gain up higher and higher, 
and the input gain lower and lower (to keep the passband at unit gain), 
until the whole thing becomes completely unworkable.

Still, I gather that with analogue electronics, anything much beyond 6 
poles is basically hopeless...

> The JVM has come a long way, too. If I understand correctly much of the 
> code in the VM gets translated to native machine code for the platform 
> its on. CLR is much the same way.

...CLR is on more than one platform? :-P

>> If you want a digital filter to precisely disect a signal (e.g., for 
>> technical analysts), you want the most accurate filter you can get. 
>> But if you just want to make interesting noises, precision is not 
>> important. Indeed, resonance, ripple, and other "artifacts" that are 
>> usually to be avoided suddenly become useful and interesting! :-D
> 
> Of course. Much like guitarists discovered an interesting artifact of 
> their amplifiers. Turn up the gain so the signal starts clipping makes 
> the guitar sound much more interesting. :)

Indeed. ;-) Distortion is the new hifi.

> Dunno why, synthesizers have always fascinated me. More the 
> waveform-based, rather than sample-based. Twisting tones into 
> instruments is just cool. :)

I've always loved synthesizers because... I like the crazy music they 
make! :-D My dad has some old Moog recordings on LP. Obviously the 
synthesizer itself is pretty lame, but some of the compositions people 
put together... they don't make recordings like that any more.

>> Ever heard of the Kurplus-Strong algorithm?
> 
> Nope :) I'm sure wikipedia has. It has, and looks like I read the 
> article, so Yes. :)
> 
> Very much the IIR plucked string in the applet.

And then you get into the whole "waveguide synthesis" thing, like 
Reaktor's Steampipe instrument. Very neat...

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