[SciPy-User] how to use signal.lfiltic?
Wed Nov 24 15:37:22 CST 2010
On Wed, Nov 24, 2010 at 11:09 AM, Skipper Seabold <email@example.com> wrote:
> On Wed, Nov 24, 2010 at 10:39 AM, Skipper Seabold <firstname.lastname@example.org> wrote:
>> This is mainly for my own understanding of going back and forth
>> between signal processing language and time series econometrics.
>> I don't see how to use lfiltic.
>> Say I have a (known) output vector of errors and an input y vector. y
>> follows a mean zero ARMA(p,q) process given by b and a below where p =
>> q = 2. If I want to use lfilter to recreate the errors, forcing the
>> first p outputs (errors) to be zero, then I need to solve the
>> difference equations for the zi that do this which is given by zi
>> below. But if I try to recreate this using lfiltic, it doesn't work.
>> Am I missing the intention of lfiltic? Matlab's documentation, which
>> a lot of the signal stuff seems to be taken from, suggests that y and
>> x in lfiltic need to be reversed, but this also doesn't give the zi I
>> from scipy import signal
>> import numpy as np
>> errors = np.array([ 0., 0., 0.00903417, 0.89064639, 1.51665674])
>> y = np. array([-0.60177354, -1.60410646, -1.16619292, 0.44003132, 2.36214611])
>> b = np.array([ 1. , -0.8622494 , 0.34549996])
>> a = np.array([ 1. , 0.07918344, -0.81594865])
>> # zi I want to produce errors = 0,0,...
>> zi = np.zeros(2)
>> zi = -b * y
>> zi = -b * y - b * y
>> # array([ 0.60177354, 1.08522758])
>> e = signal.lfilter(b, a, y, zi=zi)
>> # array([ 0. , 0. , 0.00903417, 0.89064639, 1.51665674])
>> zi2 = signal.lfiltic(b,a, errors[:2], y[:2])
>> # array([-0.03533984, -0.20791273])
>> e2 = signal.lfilter(b, a, y, zi=zi2)
>> # array([-0.63711338, -1.24269149, -0.41241704, -0.0899541 , 1.25042151])
> Basically, I think this line in signal.lfiltic
> for m in range(M):
> zi[m] = sum(b[m+1:]*x[:M-m],axis=0)
> should be
> for m in range(M):
> zi[m] = sum(-b[:m+1][::-1]*x[:m+1],axis=0)
> I'm not sure about the next loop, since my output are zero, I didn't
> have to solve for it.
> Is this a bug or am I misunderstanding?
Misunderstanding. Matlab gives the same thing, but I still don't
understand why lfiltic doesn't give the same zi that I used to
actually create the output.
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