[SciPy-dev] Is this a bugfix for scipy.hilbert?

josef.pktd@gmai... josef.pktd@gmai...
Thu Jan 14 22:27:34 CST 2010


On Thu, Jan 14, 2010 at 11:02 PM,  <josef.pktd@gmail.com> wrote:
> On Thu, Jan 14, 2010 at 10:54 PM,  <josef.pktd@gmail.com> wrote:
>> On Thu, Jan 14, 2010 at 10:24 PM, Ariel Rokem <arokem@berkeley.edu> wrote:
>>> Hi everyone,
>>>
>>> I have been trying to use scipy.signal.hilbert and I got the following
>>> puzzling result:
>>>
>>> In [22]: import scipy
>>>
>>> In [23]: scipy.__version__ #I have r6182
>>> Out[23]: '0.8.0.dev'
>>>
>>> In [24]: import scipy.signal as signal
>>>
>>> In [25]: a = np.random.rand(100,100)
>>>
>>> In [26]: np.abs(signal.hilbert(a[-1]))
>>> Out[26]:
>>> array([ 0.57567681,  0.25918624,  0.50207097,  0.51834052,  0.24293389,
>>>         0.5779464 ,  0.6515758 ,  0.89973173,  1.00275444,  0.37352935,
>>>         0.62332717,  0.93599749,  0.40651376,  0.65088756,  0.8332281 ,
>>>         0.5770101 ,  0.9288512 ,  0.46671906,  0.41536055,  0.71418068,
>>>         0.81250913,  0.07652627,  0.72939072,  0.26755626,  0.36396146,
>>>         0.59725999,  1.02264694,  0.41227986,  0.98122853,  0.71906675,
>>>         0.58582611,  0.77288117,  0.3217015 ,  0.65261394,  0.11947618,
>>>         0.75632703,  0.43432935,  0.52182485,  1.0277177 ,  1.01104986,
>>>         0.3023265 ,  0.6024772 ,  0.69257548,  0.55418735,  0.46259052,
>>>         0.25832231,  0.38278355,  0.45508532,  0.26215872,  0.34207947,
>>>         0.80704729,  0.80755477,  0.95317178,  0.97458885,  0.58762294,
>>>         0.82540618,  0.62005585,  0.82494646,  1.04221293,  0.14983027,
>>>         1.01571579,  0.99381328,  0.24158714,  0.84256569,  0.53418924,
>>>         0.24067628,  0.90489883,  1.02217747,  0.34988034,  0.5310065 ,
>>>         0.48135002,  1.03020269,  0.6013679 ,  0.46062485,  0.3918485 ,
>>>         0.21554545,  0.31704519,  0.04868385,  0.1787766 ,  0.37361852,
>>>         0.21977912,  0.7649772 ,  0.77867281,  0.37684278,  0.64432638,
>>>         0.77494951,  0.87106309,  0.77611484,  0.52666801,  0.88683667,
>>>         0.69164967,  0.98618191,  0.84811375,  0.35934198,  0.32650478,
>>>         0.1752677 ,  0.60574454,  0.5109132 ,  0.52332287,  0.99777805])
>>>
>>> In [27]: np.abs(signal.hilbert(a))[-1]
>>> Out[27]:
>>> array([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
>>>         0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
>>>         0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
>>>         0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
>>>         0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
>>>         0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
>>>         0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
>>>         0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.])
>>>
>>>
>>> ----------------------------------------------------------------------
>>>
>>> I was expecting both of these to have the same values - am I missing
>>> something?
>>>
>>> I think that the following solves this issue, but now I am not that sure
>>> whether it does what it is supposed to do and I couldn't find a test for
>>> this in test_signaltools.py. Does anyone know of a good test-case for the
>>> analytic signal, that I could create for this?
>>>
>>> Index: scipy/signal/signaltools.py
>>> ===================================================================
>>> --- scipy/signal/signaltools.py    (revision 6182)
>>> +++ scipy/signal/signaltools.py    (working copy)
>>> @@ -1062,13 +1062,13 @@
>>>      """
>>>      x = asarray(x)
>>>      if N is None:
>>> -        N = len(x)
>>> +        N = x.shape[-1]
>>>      if N <=0:
>>>          raise ValueError, "N must be positive."
>>>      if iscomplexobj(x):
>>>          print "Warning: imaginary part of x ignored."
>>>          x = real(x)
>>> -    Xf = fft(x,N,axis=0)
>>> +    Xf = fft(x,N,axis=-1)
>>>      h = zeros(N)
>>>      if N % 2 == 0:
>>>          h[0] = h[N/2] = 1
>>> @@ -1078,7 +1078,7 @@
>>>          h[1:(N+1)/2] = 2
>>>
>>>      if len(x.shape) > 1:
>>> -        h = h[:, newaxis]
>>> +        h = h[newaxis,:]
>>>      x = ifft(Xf*h)
>>>      return x
>>
>> I think your change would break the currently advertised behavior,
>> axis=0 (The transformation is done along the first axis)
>>
>> but fft and ifft have default axis=-1
>>
>> fft in hilbert uses axis=0 as in docstring
>> but ifft uses default axis=-1
>>
>> so, I would think the fix should be  x = ifft(Xf*h, axis=0)
>>
>> But as it currently looks like the axis argument doesn't work anyway,
>> there wouldn't be much breakage if the axis would be included as an
>> argument and default to -1.
>> However, I don't know what the "standard" for scipy.signal is for default axis.
>>
>> Josef
>
> after adding axis to ifft:
>>>> print hilbert(aa).real
> [[ 0.82584851  0.15215031  0.14767381]
>  [ 0.95021675  0.16803995  0.43562964]
>  [ 0.13033881  0.06198952  0.70729614]
>  [ 0.69409563  0.06962778  0.72552601]
>  [ 0.34297612  0.50579001  0.86463304]
>  [ 0.28355261  0.21626889  0.85165102]
>  [ 0.49481491  0.21290645  0.71416814]
>  [ 0.2645843   0.95783096  0.77514016]
>  [ 0.38735994  0.14274852  0.56344808]
>  [ 0.88084015  0.39879649  0.64949951]]
>>>> print hilbert(aa[:,:1]).real
> [[ 0.82584851]
>  [ 0.95021675]
>  [ 0.13033881]
>  [ 0.69409563]
>  [ 0.34297612]
>  [ 0.28355261]
>  [ 0.49481491]
>  [ 0.2645843 ]
>  [ 0.38735994]
>  [ 0.88084015]]
>
> but it treats a 1d array as row vector and transforms along zero axis
> of length 1, and not along the length of the array.
> so another fix to handle 1d arrays correctly should be done
>
>>>> print hilbert(aa[:,1]).real
> [ 0.15215031  0.16803995  0.06198952  0.06962778  0.50579001  0.21626889
>  0.21290645  0.95783096  0.14274852  0.39879649]
>>>> aa[:,1]
> array([ 0.15215031,  0.16803995,  0.06198952,  0.06962778,  0.50579001,
>        0.21626889,  0.21290645,  0.95783096,  0.14274852,  0.39879649])
>>>>

there's something wrong with my example, the real part is the same
which confused me

it works correctly with 1d

>>> np.abs(hilbert(aa[:,0]))
array([ 0.83251128,  1.04487091,  0.27702083,  0.69901499,  0.49170197,
        0.31227114,  0.49505637,  0.26461488,  0.61385196,  0.90716272])

>>> np.abs(hilbert(aa[:,:1])).T
array([[ 0.83251128,  1.04487091,  0.27702083,  0.69901499,  0.49170197,
         0.31227114,  0.49505637,  0.26461488,  0.61385196,  0.90716272]])

>>> np.abs(hilbert(aa))[:,0]
array([ 0.83251128,  1.04487091,  0.27702083,  0.69901499,  0.49170197,
        0.31227114,  0.49505637,  0.26461488,  0.61385196,  0.90716272])

besides reading the docstring, I don't know what hilbert is supposed
to be good for.

Josef


> Josef
>
>
>>
>>>
>>>
>>> Cheers,
>>>
>>> Ariel
>>> --
>>> Ariel Rokem
>>> Helen Wills Neuroscience Institute
>>> University of California, Berkeley
>>> http://argentum.ucbso.berkeley.edu/ariel
>>>
>>> _______________________________________________
>>> SciPy-Dev mailing list
>>> SciPy-Dev@scipy.org
>>> http://mail.scipy.org/mailman/listinfo/scipy-dev
>>>
>>>
>>
>


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