[Octave-patch-tracker] [patch #10352] adding islinphase.m

[Leonardo]

Follow-up Comment #4, patch #10352 (project octave):

I guess the problem with this filter is that at ω = 0 we have undefined or
indeterminate angle.

H(0) = (1 - e^(-j * 0)) / (1 - 2e^(-j * 0)) = 0 / (-1)

arg(0) = ?

In another approach, the numerator might be expressed by:
B(ω) = e^(-jω/2)(e^(jω/2) - e^(-jω/2)) = e^(-jω/2)(2j sin(ω/2))
arg(B(ω)) = -ω/2 + angle(2j sin(ω/2))

and the denominator by:
A(ω) = e^(-jω/2)(3jsin(ω/2) - cos(ω/2)) 
ang(A(ω)) = -ω/2 + arctan((3sin(ω/2)) / (-cos(ω/2)))

angle(H(ω)) = angle(2j sin(ω/2)) - arctan((3sin(ω/2)) / (-cos(ω/2)))

for ω > 0
angle(H(ω)) = π/2 - arctan((3sin(ω/2)) / (-cos(ω/2)))

for ω = 0 it is undefined.

That is causing the warning. 

Here is the compared result of grpdelay in GNU Octave and Matlab for that
particular filter:

GNU Octave
octave:1> pkg load signal
octave:2> b = [1 -1]; a = [1 -2];
octave:3> [gd, w] = grpdelay (b, a);
octave:4> [gd(1:10)'; w(1:10)']
ans =

  -1.0000  -1.4999  -1.4995  -1.4990  -1.4982  -1.4972  -1.4959  -1.4945 
-1.4928  -1.4909
        0   0.0061   0.0123   0.0184   0.0245   0.0307   0.0368   0.0430  
0.0491   0.0552


MATLAB
>> b = [1 -1]; a = [1 -2];
>> [gd, w] = grpdelay (b, a);
>> [gd(1:10)'; w(1:10)']

ans =

   -1.5000   -1.4999   -1.4995   -1.4990   -1.4982   -1.4972   -1.4959  
-1.4945   -1.4928   -1.4909
         0    0.0061    0.0123    0.0184    0.0245    0.0307    0.0368   
0.0430    0.0491    0.0552


Maybe we should point this to Paul Kienzle and Julius O. Smith III who have
created the grpdelay.m function in GNU Octave.

To avoid this warning in the tests, we could just remove this one.


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