mvpa2.mappers.filters.filtfilt¶

mvpa2.mappers.filters.
filtfilt
(b, a, x, axis=1, padtype='odd', padlen=None, method='pad', irlen=None)¶ A forwardbackward filter.
This function applies a linear filter twice, once forward and once backwards. The combined filter has linear phase.
The function provides options for handling the edges of the signal.
When
method
is “pad”, the function pads the data along the given axis in one of three ways: odd, even or constant. The odd and even extensions have the corresponding symmetry about the end point of the data. The constant extension extends the data with the values at the end points. On both the forward and backward passes, the initial condition of the filter is found by usinglfilter_zi
and scaling it by the end point of the extended data.When
method
is “gust”, Gustafsson’s method [R66] is used. Initial conditions are chosen for the forward and backward passes so that the forwardbackward filter gives the same result as the backwardforward filter.Parameters: b : (N,) array_like
The numerator coefficient vector of the filter.
a : (N,) array_like
The denominator coefficient vector of the filter. If
a[0]
is not 1, then botha
andb
are normalized bya[0]
.x : array_like
The array of data to be filtered.
axis : int, optional
The axis of
x
to which the filter is applied. Default is 1.padtype : str or None, optional
Must be ‘odd’, ‘even’, ‘constant’, or None. This determines the type of extension to use for the padded signal to which the filter is applied. If
padtype
is None, no padding is used. The default is ‘odd’.padlen : int or None, optional
The number of elements by which to extend
x
at both ends ofaxis
before applying the filter. This value must be less thanx.shape[axis]  1
.padlen=0
implies no padding. The default value is3 * max(len(a), len(b))
.method : str, optional
Determines the method for handling the edges of the signal, either “pad” or “gust”. When
method
is “pad”, the signal is padded; the type of padding is determined bypadtype
andpadlen
, andirlen
is ignored. Whenmethod
is “gust”, Gustafsson’s method is used, andpadtype
andpadlen
are ignored.irlen : int or None, optional
When
method
is “gust”,irlen
specifies the length of the impulse response of the filter. Ifirlen
is None, no part of the impulse response is ignored. For a long signal, specifyingirlen
can significantly improve the performance of the filter.Returns: y : ndarray
The filtered output with the same shape as
x
.See also
sosfiltfilt
,lfilter_zi
,lfilter
,lfiltic
,savgol_filter
,sosfilt
Notes
The option to use Gustaffson’s method was added in scipy version 0.16.0.
References
[R66] (1, 2) F. Gustaffson, “Determining the initial states in forwardbackward filtering”, Transactions on Signal Processing, Vol. 46, pp. 988992, 1996. Examples
The examples will use several functions from
scipy.signal
.>>> from scipy import signal >>> import matplotlib.pyplot as plt
First we create a one second signal that is the sum of two pure sine waves, with frequencies 5 Hz and 250 Hz, sampled at 2000 Hz.
>>> t = np.linspace(0, 1.0, 2001) >>> xlow = np.sin(2 * np.pi * 5 * t) >>> xhigh = np.sin(2 * np.pi * 250 * t) >>> x = xlow + xhigh
Now create a lowpass Butterworth filter with a cutoff of 0.125 times the Nyquist rate, or 125 Hz, and apply it to
x
withfiltfilt
. The result should be approximatelyxlow
, with no phase shift.>>> b, a = signal.butter(8, 0.125) >>> y = signal.filtfilt(b, a, x, padlen=150) >>> np.abs(y  xlow).max() 9.1086182074789912e06
We get a fairly clean result for this artificial example because the odd extension is exact, and with the moderately long padding, the filter’s transients have dissipated by the time the actual data is reached. In general, transient effects at the edges are unavoidable.
The following example demonstrates the option
method="gust"
.First, create a filter.
>>> b, a = signal.ellip(4, 0.01, 120, 0.125) # Filter to be applied. >>> np.random.seed(123456)
sig
is a random input signal to be filtered.>>> n = 60 >>> sig = np.random.randn(n)**3 + 3*np.random.randn(n).cumsum()
Apply
filtfilt
tosig
, once using the Gustafsson method, and once using padding, and plot the results for comparison.>>> fgust = signal.filtfilt(b, a, sig, method="gust") >>> fpad = signal.filtfilt(b, a, sig, padlen=50) >>> plt.plot(sig, 'k', label='input') >>> plt.plot(fgust, 'b', linewidth=4, label='gust') >>> plt.plot(fpad, 'c', linewidth=1.5, label='pad') >>> plt.legend(loc='best') >>> plt.show()
The
irlen
argument can be used to improve the performance of Gustafsson’s method.Estimate the impulse response length of the filter.
>>> z, p, k = signal.tf2zpk(b, a) >>> eps = 1e9 >>> r = np.max(np.abs(p)) >>> approx_impulse_len = int(np.ceil(np.log(eps) / np.log(r))) >>> approx_impulse_len 137
Apply the filter to a longer signal, with and without the
irlen
argument. The difference betweeny1
andy2
is small. For long signals, usingirlen
gives a significant performance improvement.>>> x = np.random.randn(5000) >>> y1 = signal.filtfilt(b, a, x, method='gust') >>> y2 = signal.filtfilt(b, a, x, method='gust', irlen=approx_impulse_len) >>> print(np.max(np.abs(y1  y2))) 1.80056858312e10