>>>How does it sound? :)
>>
>>With a fixed cutoff frequency... almost inaudable. But if you *sweep* the 
>>cutoff frequency, it sounds mostly like a phaser.
> 
> 
> Nice, i like to 'explore' a sound with filters like that, afterwards
> it's easier to identify the different sources from which the sound is built

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!]

>>FIR filters are much easier to design, and can give a more exact frequency 
>>responce.
> 
> i especially was stunned by the idea that you can make up an arbitrary
> freq.-response and get the corresponding filter-kernel by FFT-ing it.

Indeed. It looks so complicated, but it's really so simple... I love it 
when that happens in mathematics! ;-)

Of course, the numbers you put into an inverse FFT are for frequency 
*bands*. So while the whole band is guaranteed to total up to the number 
you demand, individual frequencies within that band might be above or 
below the requested gain... herein lies the complexity of designing 
FIRs. It's not as simple as it looks. ;-)

[Of course, usually the answer is just "use more points"... :-/  ]

>>IIR filters are harder to design, and don't give quite such exact 
>>frequency characteristics... but they run *much* faster!
> 
> yes, the feedback-idea behind IIRs is cool. i have to learn more about
> that some time.

 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...

(Close enough that a 5-pole Butterworth IIR filter utterly kicks bottom 
compared to any 5-point FIR you could design. But different enough that 
a very big FIR filter works better, if you have the CPU power.)

>>Anyway, I learned everything I know here:
>>http://www.dspguide.com/
> 
> 
> i know this book, it's a real gem, i have never seen the basics of
> convolution, fft, etc. explained clearer than in this one

I have played with the FFT a lot. This book explains *why* it does some 
of the strange things it does...

> or briefly said: i think polar coords.
> would be more useful than rectangular coordinates

Yes, you're exactly right.

I only used grid cordinates because it looks cooler. ;-)

Now, if this were the s-domain...


[Side note: Actually, if you take away the gridlines, it's quite hard to 
see the zero next to the front pole. It just looks like a patch of 
shadow that shouldn't exist. With the gridlines there, you can see that 
it's actually a dip in the surface.]

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