chebwin improvement: use the Chebyshev polynomial

[akumar]

Hi!

I noticed that the Dolph Chebyshev I wrote earlier was not working due to some issues with the hyperbolic functions. For example:

In [2]: signal.chebwin(20, 50)
Out[2]: 
array([ NaN,  NaN,  NaN,  NaN,  NaN,  NaN,  NaN,  NaN,  NaN,  NaN,  NaN,
        NaN,  NaN,  NaN,  NaN,  NaN,  NaN,  NaN,  NaN,  NaN])

In [3]: signal.chebwin(10, 50)
Out[3]: array([ NaN,  NaN,  NaN,  NaN,  NaN,  NaN,  NaN,  NaN,  NaN,  NaN])

I prodded it a bit, and found that the issue lies with the way I am calculating the Chebyshev polynomial. After two hours, I gave up and tried using the special.chebyt function, only to find that it works perfectly.

All values are matching the Matlab generated ones (from my test). I am attaching diff of signaltools.py, which applies against the HEAD of SVN. Please consider adding it.

Thanks.

Kumar Appaiah

[akumar]

chebwin fix: patch applies to SVN HEAD

[akumar]

Fixed chebwin function

[akumar]

Referring to http://projects.scipy.org/pipermail/scipy-user/2008-February/015574.html gives a solution to this bug. Is there any chance of this making it into SciPy??

Thanks.

Kumar

[rmay]

Patch against SVN head that makes chebwin work for high orders

[rmay]

Ok, the attached patch makes chebwin work for me, on at least 52nd and 53rd order windows. I'm willing to submit test case(s) if someone can give me guidance on how I'm supposed to test something like this. Do I just accept the current output of my code as working and use that as truth? Anyhow, can we get this in for 0.7?

[rmay]

I guess I should clarify, for those who didn't read the mailing list post. The built in chebyt uses an expansion, which becomes less accurate as you increase the order. Since the chebyshev window uses an (n-1)th order polynomial for a window with n points, this becomes a problem. I was able to hit a problem with just 53 points, which really isn't *that* many for a window function. This patch changes chebwin to go back to using the analytical definition of the Chebyshev (Tn) polynomial, and it corrects the previous implementation to work for all of the domain of Tn.

[rmay]

Test cases for chebwin. These values are sensible in both the time and frequency domains.

[stefan]

Thanks, Kumar and Ryan, for supplying patches and tests. Fixed in r4662.