Date: Tue, 15 Oct 91 15:11:31 EDT
From: burgess@cc.gatech.edu (David Burgess)
Message-Id: <9110151911.AA08238@warhol.cc.gatech.edu>
To: glove-list@karazm.math.uh.edu
Subject: Re: LPC vs. polynomial predicting

I normally just listen to this list, but since I'm up to my neck in filters and predictors right  
now, I couldn't help but run my mouth:
Linear predictive coding predicts with a linear filter: a differential equation, or, in the digital  
domain, a difference equation.  Implementation is easy: you just feed the signal into the  
filter and take the result.  The trick is picking the right filter.
Low pass filters will control jitter, but may give sluggish response.
A properly tuned second order filter is good for many control/conditioning applications,  
like the suspension system of your car.  It will reduce jitter, but still can be tuned to give a  
quick response.  A second order difference equation looks like:
y[n] = x[n] + ax[n-1] + bx[n-2] + cy[n-1] + dy[n-2]
where x is the input, y is the output, n is the time index, any all the other things are  
coefficiants.  choose a,b,c,d carefully, because bad choices will give unstable filters that  
can oscillate uncontrolably or go racing off into infinity.
I once experimented with polynomial prediction on my mouse driver, and found the first  
order prediction was ok, but higher order (quadratic, cubic, etc.) resulted in really bad  
overshoot.
Disclaimers: I've never used a power-glove.  I'm not a professional DSP engineer.

--david