[SciPy-user] firwin for even order NOT linear phase; returns 0 coefficients

[Tom K.]

This filter is not linear phase:
signal.firwin(4,.3)
--> array([ 0.02051616,  0.23560318,  0.50827748,  0.23560318])

These two filters are identical except that the 2nd has zeros at either end,
the 1st has a zero at the beginning - neither filter is actually the length
requested (19 and 19 instead of 20 and 21).
In [46]: signal.firwin(20,.3)
Out[46]: 
array([  9.34176168e-19,   2.92890318e-03,   6.34234732e-03,
         3.78304197e-03,  -1.23878481e-02,  -3.43265728e-02,
        -3.18598611e-02,   2.65312166e-02,   1.37863165e-01,
         2.51347679e-01,   2.99555858e-01,   2.51347679e-01,
         1.37863165e-01,   2.65312166e-02,  -3.18598611e-02,
        -3.43265728e-02,  -1.23878481e-02,   3.78304197e-03,
         6.34234732e-03,   2.92890318e-03])

In [47]: signal.firwin(21,.3)
Out[47]: 
array([  9.34176168e-19,   2.92890318e-03,   6.34234732e-03,
         3.78304197e-03,  -1.23878481e-02,  -3.43265728e-02,
        -3.18598611e-02,   2.65312166e-02,   1.37863165e-01,
         2.51347679e-01,   2.99555858e-01,   2.51347679e-01,
         1.37863165e-01,   2.65312166e-02,  -3.18598611e-02,
        -3.43265728e-02,  -1.23878481e-02,   3.78304197e-03,
         6.34234732e-03,   2.92890318e-03,   9.34176168e-19])

Can anyone explain this behavior?  I don't think either filter should end in
zero.  I suspect something funny about the way the windows are defined -
like, they are designed for spectral analysis, not FIR filter design.


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