"Orchid XP v2" <voi### [at] devnull> schrieb im Newsbeitrag 
news:42ff61ca$1@news.povray.org...
>>>Yes... I'm currently building a realtime Java IIR filter system which 
>>>will hopefully let me filter arbitrary sounds and see what happens... 
>>>[This is assuming it ever works!]
>>
>>
>> Oh nice, you could do a nice z-plane-GUI to position the poles and zeros
>> in Realtime, too =)
>
> Yeah, something like that. ;-)
>
> In my lunch break at work, I built a little thing out of Tcl then allows 
> you to pick pole and zero coordinates, and then launches GNUplot and 
> graphs it for you. :-D (Sadly, GNUplot itself can't create filters with an 
> arbitrary number of poles because there's no looping capabilities.)
>
> It could then also spit out the IIR coeficients, and even get GNUplot to 
> graph the impulse and frequency responce. (Again, GNUplot can't run the 
> filter to get the impulse responce because that requires looping. As would 
> doing an FFT. So Tcl does that and writes it to file, than GNUplot graphs 
> it.)
>
> I'm currently attempting to do the same thing with Java...

a realtime update of the impulse- and freq.response would be very cool.
Be sure to post someting in p.o-t about it, when you've made progress


> Another advantage of IIRs over FIRs is that you can *change* the frequency 
> responce quickly and easily - just gotta change a handful of coeficients. 
> (An FIR would require an entire FFT step for this!) Plus they can emulate 
> the old analogue synthesiser sound. (All analogue filters are IIRs!)

that's definately a good argument to use them in virtual analog 
synthesizers.
i wonder if we would choose the FIR-sound as more 'natural' if analog
filters sounded like FIRs or if it's really because we sense the sound
itself as more pleasing to the ear..


> In fact, IIRs are *so* fast that it's quicker to take a pure sawtooth tone 
> and IIR filter it down than it is to calculate half a dozen sine waves 
> from the Fourier series and add them all together... [Well, in trueth, 
> there will be come crossover point at which one becomes better than the 
> other. But I wouldn't think it would take too long to reach!]

that brings us to additive synthesis. I remember there actually was a
hardwaresynth that took this approach and could generate the first 64
harmonics in realtime AFAIR and control each harmonic with it's own
envelope but apparently it sounded not too different or special to get
wide attention. I think the main problem was that it's not easy to
make an easy interface to control so many oscs in parallel in a way
that gives interesting results. Without noise to spice it up it
sounded rather sterile.

>>>Indeed. It looks so complicated, but it's really so simple... I love it 
>>>when that happens in mathematics! ;-)
>>
>>
>> yes, me too :)
>> some time ago i had the idea to use the deconvolution idea (that is also
>> described a bit in the 'dspguide') to undo the blur in photos that is
>> the result from jiggling the camera during the exposure. I think if you
>> knew the motion of the camera you could guess a blurring filterkernel
>> from that, which can emulate the camwiggling. now just use to 
>> deconvolution
>> on the blurred image with that filterkernel and perhaps you can regain
>> most of it's original sharpness back (that is, what the noise didn't 
>> eat..)
>
> ...and the ADC quantinization noise, and the JPEG compression. ;-)
>
> You could probably *improve* the image significantly. However, if the 
> original convolution actually _eliminated_ any frequencies, you aren't 
> going to get them back, no matter /how/ high the gain. Deconvolution is 
> effectively passing the signal through a filter who's frequency responce 
> is the reciprocol of the first one - and taking the reciprocol of zero 
> isn't wise. ;-)

yeah, that's the problem. I think i should just try it to see if
the zeros in the freq-response of a realworldcase render deconvolution
useless or not.


>>>From FIRs we know that longer impulse responce = better. So you would 
>>>imagine that an *infinite* impulse responce would be the best! :-D
>>>
>>>But, alas, feedback can only create certain waveforms. In particular, the 
>>>impulse responce for a "perfect" low-pass filter would be an infinite 
>>>sinc function - basically a sine wave that decays as the reciprocol of 
>>>time. Using IIRs, I can make a sine wave that decays *exponentially* with 
>>>time... which is close... but not *quite* the same...
>>
>>
>> ah, thanks for the explanation. That sounds like an interesting
>> optimization-task to tune the IIR-coefficients though i fear someone
>> has already done this before me..
>
> As I said, it's all down to pole-zero plots. (The incredible thing is that 
> somebody figured out that if you take the problem and put it through the 
> Laplace transform, it becomes very much simpler!)

yes, the laplace transform is really a cool idea.
Take a differential equation and get an algebraic equation in return,
it's always great to find such unexpected relations in math.
where would we be now without all those 17th/18th century
mathematicians...? :D

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