Digital filtering

[Erik Schuijers]

> 
> > > 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 :(
> 

Hmmm, I must say it's not THAT easy. But in accordance to the mathemagic
I've been following lately it's pretty easy!

> > > Actually it isn't hard at all. One chapter of the book we're studying from
> 
> What book? Oppenheim & Shafer?
> 

No, it's a scriptum by some professor at the University.

> > 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? 

First of all I want my filter to just not self-oscillate in order to stay
away from instability problems. 
The approximation of the filter coefficients is definitely going to be one of 
the worst problems. Especially because writing an algorithm into the DSP
program will cost a lot of time. That's why I've been thinking of dumping a
lot of these coeffecients into an EPROM, only if an EPROM is fast enough.
Clipping is a problem indeed. You'll just have to make sure the input, at
least that's what I think you're talking about, must be prohibited from
clipping.

Another thing I've thought about. Is to make some extra free bits free for
calculations (LSB's that is) in order to get more accurate approximations.

> 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.

Perhaps this might be something to think of when poles get in those places
where the effect is minimal.

> > 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.

I don't think I would want to use the approximation of derivative method
because it's really hard to implement the voltage control. I've already
thought about this. Also, how could you implement Q?

Erik