[SciPy-dev] scipy.signal documentation suggestions
Dan Lenski
dlenski@gmail....
Thu Oct 18 22:53:24 CDT 2007
Jarrod Millman <millman <at> berkeley.edu> writes:
> Thanks a lot for the expanded docstring. We are very interested in
> improving the documentation and appreciate any help you can give us.
> I will take a look at the new docstring you submitted.
Sounds good. Thanks for making all this stuff work :-)
> In the meantime, please read over our current coding/documentation guidelines:
> http://projects.scipy.org/scipy/numpy/wiki/CodingStyleGuidelines
Didn't realize that docstrings were supposed to be in reST format, oops. Here's
an attempt at getting it right, includes an example in doctest format I hope
this version is more useful.
Dan
---
bilinear.__doc__ = ''''''Return a digital filter from an analog filter
using the bilinear transform.
The bilinear transform converts a filter in the continuous-time
domain (an analog filter) to a filter in the discrete-time
domain (a digital filter).
*Parameters*:
b : {array-like}
The numerator coefficient vector of the analog transform.
a : {array-like}
The denominator coefficient vector of the analog transform.
If ``a[0]`` is not 1, then both ``a`` and ``b`` are
normalized by ``a[0]``.
fs : {float}
The desired sampling frequency of the digital transform.
(*Default* = 1.0)
*Returns*:
bd : {array}
The numerator coefficient vector of the digital transform.
ad : {array}
The denominator coefficient vector of the digital transform.
Both ``a`` and ``b`` are normalized such that ``a[0]=1``.
*Algorithm*:
Given an analog filter, with rational transfer function in the
s-domain::
-1 -nb
b[0] + b[1]s + ... + b[nb] s
H(z) = ----------------------------------
-1 -na
a[0] + a[1]s + ... + a[na] s
The bilinear transform maps from the s-plane to the z-plane by
substituting ``s = (2*fs)(z-1)/(z+1)``, where ``fs`` is the
sampling frequency of the digital filter. This gives the rational
transfer function in the z-domain::
-1 -nbd
bd[0] + bd[1]z + ... + b[nbd] z
Y(z) = -------------------------------------- X(z)
-1 -nad
ad[0] + ad[1]z + ... + a[nad] z
*Example*:
Consider a simple first-order low-pass analog filter, with
corner frequency ``w``. Its transfer function is::
-1
1 0 + w s b[0] = 0 b[1] = w
H(z) = --------- = ------------- =>
1 + s/w -1 a[0] = 1 a[1] = w
1 + w s
A bilinear transform on this filter will produce a
digital filter which can be used as input to `lfilter`. For example:
>>> from scipy.signal import *
>>> from numpy import *
>>> from pylab import *
>>>
>>> w = 10.0 # corner frequency
>>> fs = 1000.0 # sampling rate
>>>
>>> t = arange(0, 2*pi, 1/fs)
>>> x = sin(1*t) + sin(100*t) # test signal
>>>
>>> b, a = bilinear([0,w], [1,w], fs)
>>> y = lfilter(b, a, x)
>>>
>>> plot(t, x, label="unfiltered") #doctest: +ELLIPSIS
[<matplotlib.lines.Line2D instance at ...>]
>>> plot(t, y, label="low-pass filtered") #doctest: +ELLIPSIS
[<matplotlib.lines.Line2D instance at ...>]
>>> legend() #doctest: +ELLIPSIS
<matplotlib.legend.Legend instance at ...>
>>> show()
>>>
'''
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