Does Python/Scipy have a firls( ) replacement (i.e. a weighted, least squares, FIR filter design)?

Question

I am porting code from Matlab to Python and am having trouble finding a replacement for the firls( ) routine. It is used for, least-squares linear-phase Finite Impulse Response (FIR) filter design.

I looked at scipy.signal and nothing there looked like it would do the trick. Of course I was able to replace my remez and freqz algorithsm, so that's good.

On one blog I found an algorithm that implemented this filter without weighting, but I need one with weights.

Thanks, David

Answer 1

This post is really in response to

You can try the firwin function with window='boxcar'...

Do don't use boxcar it means no window at all (it is ideal but only works "ideally" with an infinite number of multipliers - sinc in time). The whole perpose of using a window is the reduce the number of multipliers required to get good stop band attenuation. See Window function

When comparing filters please use dB/log scale.

Scipy not having firls (FIR least squares filter) function is a large limitation (as it generates the optimum filter in many situations).

REMEZ has it's place but the flat roll off is a real killer when your trying to get the best results (and not just meeting some managers spec). ( warning scipy remez implementation can give amplification in stop band - see plot at bottom)

If you are using python (or need to use some window) I recommend using the kasiar window which gets very good results and can easily be tweaked for your attenuation vs transition vs multipliers requirement(attenuation (in dB) = 2.285 * (multipliers - 1) * pi * width + 7.95). It performance is not quite as good as firls but it has the benefit of being fast and easy to calculate (great if you don't store the coefficients).

Answer 2

Since version 0.18 in July, 2016 scipy includes an implementation of firls, as scipy.signal.firls.

Answer 3

It seems unlikely that you'll find exactly what you seek already written in Python, but perhaps the Matlab function's help page gives or references a description of the algorithm?

Answer 4

This blog post contains code detailing how to use scipy.signal to implement FIR filters.

Answer 5

The firls equivalent in python now appears to be implemented as part of the signal package: https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.firls.html#scipy.signal.firls

Also I agree with everything that @pev hall stated above especially how firls is optimum in many situations (such as when overall signal to noise is being optimized for a given number of taps), and to not use the boxcar window as he stated, they are not equivalent at all! firls generally outperforms all window and frequency sampling approaches to filter design when designing traditional FIR filters.

To my current understanding, scipy.signal and Octave only support odd length (even order) least squared filters. In this case when I need an even length (Type II or Type IV filter), I resort to using the windowed design approach with a Kaiser Window specifically. I have found the Kaiser window solution to come quite close to the optimum least squares solution.

Answer 6

I found a firls() implementation attached here in SciPy ticket 648

Minor changes to get it working:

1. Swap the following two lines: bands, desired, weight = array(bands), array(desired), array(weight) if weight==None : weight = ones(len(bands)/2)

2. import roots from numpy instead of scipy.signal

Answer 7

Obviously, this post is somewhat dated, but maybe it is still interesting for some:

I think there are two near-equivalents to firls in Python:

• You can try the firwin function with window='boxcar'. This is similar to Matlab where fir1 with a boxcar window delivers the same (? or at least very similar results) as firls.
• You could also try the firwin2 method (frequency sampling method, similar to fir2 in Matlab), again using window='boxcar'

I did try one example from the Matlab firls reference and achieved near-identical results for:

Matlab:

F = [0 0.3  0.4 0.6  0.7 0.9];
A = [0  1   0  0  0.5 0.5];
b = firls(24,F,A,'hilbert');

Python:

F = [0, 0.3,  0.4, 0.6,  0.7, 0.9, 1]
A = [0,  1,   0,  0,  0.5, 0.5, 0]
bb = sig.firwin2( 25, F,A, window='boxcar', antisymmetric=True )

I had to increase the order to N = 25 and I also had to add another data point (F = 1, A = 0) which Python insisted upon; the option antisymmetric = True is only necessary for this special case (Hilbert filter)