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>>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
I'm working, I'm working! ;-)
>>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.
Quite. Might build one of them too...
> 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..
A FIR can sound like *anything*. Even an IIR. (If you give it enough
points - but, uh, why?) But it does give more control.
> that brings us to additive synthesis.
Yeah - nice idea, but... how to control it all?
FM synthesis generates lots of frequencies, but you don't have to
control them individually. (They're controlled by some heavy-metal
mathematics involving Bessel functions and such things.)
>>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.
OK, a basic 3x3 pixel "blur" is basically a 2D version of an "averaging"
FIR. Since the kernel is all 1s (well, actually scaled for unity gain,
but...) the frequency responce is a sinc function. (Remember - the time
and frequency domains are "duals" of each other! The perfect lowpass
filter has a sinc kernel to the exact same reason.)
Now this sunc function will have a couple of zeros across the frequency
spectrum - the more points you average, the more zeros you have. A 3x3
blur would have 2 zeros in each direction - that means your
deconvolution would tend to have 2 poles in it's frequency responce.
IOW, it will try to insert waves which may or may not have been there in
the first place. Oh dear...
Now, if you had an uneven "blur" - like if the camera slipped in one
direction during the shot - the frequency responce on each axis would
have "holes" in it in different places. That at least admits the
possibility that you *might* be able to do "something" with it...
>>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.
I read about the Laplace transform to design IIRs. But apparently, it
turns differential and difference equations into polynomials (which are
*much* easier to solve), and integration and differentiation become
multiplication and division. (Again, *much* easier.) Also, rather like a
logarithm, multiplication becomes addition...
BTW... apparently named after Laplace, but invented 100 years earlier. :-|
> where would we be now without all those 17th/18th century
> mathematicians...? :D
...the 16th century? ;-)
The Orchid - converting povray.binaries.images into povray.freaky.maths :-D
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> Is it just me or are the two peaks in fact slightly tilted? In a
> representation of a function, they shouldn't!
It's the camera angle - or rather, a perspective distortion. (Makes it
look more "3D" though.) If you switch to othographic camera and point it
parallel to the axis, they are quite straight.
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