[SciPy-User] convolve/deconvolve

[josef.pktd at gmail.com]

On Fri, Feb 1, 2013 at 9:23 AM, François Boulogne <fboulogne at sciunto.org> wrote:
> Hi,
>
> I need to deconvolve a signal with a filter. I had a look in the
> documentation. The function exists but the docstring is missing and I'm
> not satisfied of the result I got from a "simple" example.
>
> filter = np.array([0,1,1,1,1,0])
> step = np.array([0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
> 1, 1, 1, 1])
> # I convolve both
> res = convolve(step, filter, 'valid')
> # and it returns a slope as expected
> array([0, 0, 1, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4])
>
> Now, I want to deconvolve.
> deconvolve(res, filter)
> # oops, it raises an exception
> ValueError: BUG: filter coefficient a[0] == 0 not supported yet
>
> # well, let's try this
> deconvolve(res, filter+1e-9)
> (array([  0.00000000e+00,   0.00000000e+00,   1.00000000e+09,
>         -9.99999999e+17,   9.99999999e+26,  -9.99999999e+35,
>          9.99999999e+44,  -9.99999999e+53,   9.99999999e+62,
>         -9.99999999e+71,   9.99999999e+80,  -9.99999999e+89]),
>  array([  0.00000000e+00,   0.00000000e+00,   1.11022302e-16,
>         -8.27130862e-08,  -4.42500000e+01,   5.46901335e+10,
>          8.27266814e+19,   7.56858250e+28,  -8.74285726e+37,
>          9.99419626e+46,   8.27205507e+55,  -8.26933326e+64,
>          9.99999999e+89,   9.99999999e+89,   9.99999999e+89,
>          1.00000000e+90,   9.99999999e+80]))
>
> It's better but I do not recognize my signal :)
> 1/ Am I misunderstanding or missing something?
> 2/ How can I do it correctly?

AFAICS:

not supported, maybe using the numpy polynomial might work for the deconvolution

from the docstring of lfilter, which is used by deconvolve:

   a : array_like
        The denominator coefficient vector in a 1-D sequence.  If ``a[0]``
        is not 1, then both `a` and `b` are normalized by ``a[0]``.

with the normalization your 1e-9 blows up the calculations.

(it's been a long time since I tried to figure out deconvolve, and I
always had 1 in the first position)

Josef


>
> I also noted that no test exists for deconvolve() :(
>
> Cheers,
> François.
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