[SciPy-user] filtering without phase shift

[Lance Boyle]

It looks like symiiorder1 does what you did with your filtfilt, but 
limited to a first-order filter applied twice, once forward and once 
backward. You still have two coefficients to supply.

I can't find info on signal.lfiltic (Python/SciPy newbie).

You don't mention what coefficients you are using on the coefficient 
vectors a and b. This can make a difference in the nature of edge 
effects.

If you can "fade in" your data, that is, multiply it by a ramp starting 
from zero or another small number and increasing to 1 after a few 
samples, the edge effect will be reduced. Also, a quarter-cycle of a 
raised cosine works nicely. Of course, this would mean messing with 
your data.

You can discard the part of your data that is uglified by edge effects. 
I guess that's obvious and that you don't have any data to waste.

You might try "making up" some data to put at the beginning and end of 
your actual data. I haven't tried this but if the edge effect 
("ringing") is pretty much shorter than your data length, you could try 
mirror-imaging your data once to the left and once to the right of your 
original data, so that then you have a data record that is three times 
the length of the original data. Then the first third of the extended 
data and the last third are backwards versions of the middle third. 
This is so that there are no edges at the beginning and end of the 
middle third. Filter as you describe (forward-then-backward) and keep 
only the middle third, corresponding to the location of your original 
data. Depending on the relative lengths of the edge effect and your 
data, a full padding might be unnecessary and only a partial padding 
might work, just as long as the edge effects are outside your actual 
data.

Which brings up a third possibility, but I mention this only in 
principle. I see that lfilter has an option to set the initial 
conditions of the filter, zi. In principle, you could come up with a 
set of initial conditions that would reduce the edge effects. As it is, 
unless you specify otherwise, the filter is starting from the 
zero-state and then it is getting hit with the sudden onset of your 
data. Finding a suitable set of initial conditions is hard. The best 
way would be to pad your data and then record the filter state at the 
beginning of the actual data, then start over with the new initial 
conditions and at the edge of your actual data, but that is the same as 
the previous paragraph.

I'm bored so if you have more questions let me know.

Jerry


On Monday, Apr 7, 2003, at 23:00 America/Phoenix, Andrew Straw wrote:

>
> I trying to lowpass filter my data without introducing a phase shift.  
> I'm not a signal analysis whiz, but I know enough to be dangerous.  So 
> far I've come up with the following, which works except that it has 
> some serious edge-effects.
>
>     from scipy.signal import lfilter
>     from scipy import flipud
>
>     def filtfilt(b, a, input_vector):
>         """input_vector has shape (n,1)"""
>         forward = lfilter(b, a, input_vector, axis=0)
>         return flipud(lfilter(b, a, flipud(forward), axis = 0))
>
> Should I attempt to use the signal.lfiltic to minimize edge effects?  
> Or should I maybe use symiirorder1?  Is there any code anywhere that I 
> can look at using these functions?
>
> I think the matlab function filtfilt that does what I want.  Is there 
> a translation of it to scipy anywhere?
>
> Cheers!
> Andrew