[SciPy-dev] reimplementation of lfilter
Ralf Gommers
ralf.gommers@googlemail....
Tue Sep 22 20:40:48 CDT 2009
On Tue, Sep 22, 2009 at 9:01 PM, Sturla Molden <sturla@molden.no> wrote:
> Ralf Gommers skrev:
> > Sure, I know. The docs I linked have improvements over svn. If you
> > merge your changes, there'll be a conflict and those docs will not get
> > merged soon - I was hoping to avoid that.
>
> Oh, the docs, not the code... Would something like this be better?
>
>
See attached for a new version which incorporates your changes, the latest
wiki version, as well as some more edits. It fixes indentation, type
descriptions and rest markup.
I have one (very minor) comment on the options you added, "direction" and
"inplace". I think these should both be bools, because they select between
two options.
The C++ code looks clean, I do not know enough about that language to say
much more about it.
Cheers,
Ralf
> The Cython module doesn't need to have docs in it.
>
>
>
> from linear_filter import lfilter as _lfilter
>
> def lfilter(b, a, x, axis=-1, zi=None, direction=1, inplace=-1):
> """Filter data along one-dimension with an IIR or FIR filter.
>
> Description
>
> Filter a data sequence, x, using a digital filter. This works for many
> fundamental data types (including Object type). The filter is a direct
> form II transposed implementation of the standard difference equation
> (see "Algorithm").
>
> Inputs:
>
> b -- The numerator coefficient vector in a 1-D sequence.
> a -- 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].
> x -- An N-dimensional input array.
> axis -- The axis of the input data array along which to apply the
> linear filter. The filter is applied to each subarray along
> this axis. If axis is -1, the filter is applied to x
> flattened. (*Default* = -1)
> zi -- Initial conditions for the filter delays. It is a vector
> (or array of vectors for an N-dimensional input) of length
> max(len(a),len(b)). If zi=None or is not given then initial
> rest is assumed. If axis is None, zi should be a vector
> of length K = max(M,N), where M=len(b)-1 and N=len(a)-1. If
> an axis is not None, zi should either be a vector of length
> K, or an array with same shape as x, except for zi.shape[axis]
> which should be K. If zi is a vector, the same initial
> conditions are applied to each vector along the specified
> axis. Default: zi=None (initial rest).
> direction -- Filtered in the reverse direction if -1. (*Default* = 1)
> inplace -- If possible, modification to x is done implace.
> (*Default* = -1)
>
> Outputs: (y, {zf})
>
> y -- The output of the digital filter.
> zf -- If zi is None, this is not returned, otherwise, zf holds the
> final filter delay values.
>
> Algorithm:
>
> The filter function is implemented as a direct II transposed structure.
> This means that the filter implements
>
> a[0]*y[n] = b[0]*x[n] + b[1]*x[n-1] + ... + b[nb]*x[n-nb]
> - a[1]*y[n-1] - ... - a[na]*y[n-na]
>
> using the following difference equations:
>
> y[m] = b[0]*x[m] + z[0,m-1]
> z[0,m] = b[1]*x[m] + z[1,m-1] - a[1]*y[m]
> ...
> z[n-3,m] = b[n-2]*x[m] + z[n-2,m-1] - a[n-2]*y[m]
> z[n-2,m] = b[n-1]*x[m] - a[n-1]*y[m]
>
> where m is the output sample number and n=max(len(a),len(b)) is the
> model order.
>
> The rational transfer function describing this filter in the
> z-transform domain is
> -1 -nb
> b[0] + b[1]z + ... + b[nb] z
> Y(z) = ---------------------------------- X(z)
> -1 -na
> a[0] + a[1]z + ... + a[na] z
>
> """
> if isscalar(a):
> a = [a]
>
> if axis < 0: axis = None
> if inplace < 0: inplace = None
>
> return _lfilter(b, a, x, axis=axis, zi=zi,
> inplace=inplace, direction=direction)
>
>
>
> Regards,
> S.M.
>
>
>
>
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>
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