stability of all pole filter for linear prediction
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- KVRist
- Topic Starter
- 167 posts since 12 May, 2012
i will consider all of this when i return from hiatus LOL
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- KVRer
- 11 posts since 6 Oct, 2018
One idea I've encountered is to multiply each coefficient a[ i ] by some damping factor d raised to the index of the coefficient
i.e. a'[ i ] = a[ i ] * d^i
originally found at line 116 here: https://github.com/xiph/vorbis/blob/master/lib/lpc.c
My observation is that LPC filters will generate curves that go above unit amplitude, when excited by an impulse. Their magnitude is the gain of the filter which is the theoretical numerator in the TF, something like
G
------------------
1-sum(a[k]*z^k)
The LPC texts also talk about 'reflection coefficients' which are supposed to be immune to exploding. I can't vouch for this because my matrix solver doesn't do it, and most LPC references I find hard to interpret due to optimisation and/or terminology.
'Pre-emphasis' i.e. difference/highpass before analysis is supposed to prevent the system from coding large swings
The way linear prediction can split a signal into auto-regressive and residual (whitened) components is amazing, experimenting with it beyond just the talkbox effect or compression it was invented for.
i.e. a'[ i ] = a[ i ] * d^i
originally found at line 116 here: https://github.com/xiph/vorbis/blob/master/lib/lpc.c
My observation is that LPC filters will generate curves that go above unit amplitude, when excited by an impulse. Their magnitude is the gain of the filter which is the theoretical numerator in the TF, something like
G
------------------
1-sum(a[k]*z^k)
The LPC texts also talk about 'reflection coefficients' which are supposed to be immune to exploding. I can't vouch for this because my matrix solver doesn't do it, and most LPC references I find hard to interpret due to optimisation and/or terminology.
'Pre-emphasis' i.e. difference/highpass before analysis is supposed to prevent the system from coding large swings
The way linear prediction can split a signal into auto-regressive and residual (whitened) components is amazing, experimenting with it beyond just the talkbox effect or compression it was invented for.
