Digital filtering

[Paolo Predonzani]

> > a week ago I followed my first class of DSP. It's mainly about digital
> > filtering. It isn't quite as hard as I would have imagined it to be.

My class of DSP and DIP(Digital image processing) was not easy at all :(

> > Actually it isn't hard at all. One chapter of the book we're studying from

What book? Oppenheim & Shafer?

> > is about how to make analog filters digitally!!! Sounds pretty interesting
> > to me.
> 
> No, it's not hard... in principle... however there are several traps to fall
> into and keep awake and learn those... there is also a number of nice
> optimations that can be used...

Some of the traps are:
-stability: no poles outside the unit circle are allowed. You want to make
 your filter self-oscillate, don't you?
-Finite register length effects: the `signal' and the `coefficients' are
 quantized. Sometimes the closest approximation of a stable pole is  outside
 the unit circle. Moreover the quantization error can be seen as a noise source.
-limited dynamics: how can clipping be handled? 

As to optimizations: yes they're possible but not always useful. As I said above,
the distribution of poles is discrete; The problem is that some optimizations
produce unuseful (all possible poles concentrated in a small zone) distibutions.
Sometimes suboptimal filter configurations are preferred to obtain a
regular distribution of possible poles.
> 
> Mapping of analog filter into the digital domain may not allways be a success
> story, so redesign migth be better.
> 
I think the mapping is always possible but in no case the frequency response
is identical to the analog filter (below Fs/2, of course).
Simple mappings (approximation of derivative by means of difference) have
freq. response aliasing problems. Bilinear transformations are more interesting
(good mapping of s-plane onto z-plane) but have a strange frequency response.

> > Another thing, this afternoon we're having a new practical experience. The
> > coming nine weeks we'll have to design a digital synthesizer with a group of
> > eight. At least that's what I've heard. Anything rolling out of this shall
> > be reported to the list to discuss or whatever.
> 
Let us know.


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| Paolo Predonzani  |  email: predo at dist.dist.unige.it |
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