Smoothing and background filters¶
This module provides background extraction functions and smoothing functions. These functions are extracted from PyMca module SpecFitFuns.
Index of background extraction functions:¶
strip()
snip1d()
snip2d()
snip3d()
Smoothing functions:¶
savitsky_golay()
smooth1d()
smooth2d()
smooth3d()
References:¶
- Morhac97(1,2,3)
Miroslav Morháč et al. Background elimination methods for multidimensional coincidence γ-ray spectra. Nucl. Instruments and Methods in Physics Research A401 (1997) 113-132. https://doi.org/10.1016/S0168-9002(97)01023-1
- Ryan88
C.G. Ryan et al. SNIP, a statistics-sensitive background treatment for the quantitative analysis of PIXE spectra in geoscience applications. Nucl. Instruments and Methods in Physics Research B34 (1988) 396-402*. https://doi.org/10.1016/0168-583X(88)90063-8
API documentation:¶
- smooth1d(data)¶
Simple smoothing for 1D data.
For a data array \(y\) of length \(n\), the smoothed array \(ys\) is calculated as a weighted average of neighboring samples:
\(ys_0 = 0.75 y_0 + 0.25 y_1\)
\(ys_i = 0.25 (y_{i-1} + 2 y_i + y_{i+1})\) for \(0 < i < n-1\)
\(ys_{n-1} = 0.25 y_{n-2} + 0.75 y_{n-1}\)
- Parameters
data (numpy.ndarray) – 1D data array
- Returns
Smoothed data
- Return type
numpy.ndarray(dtype=numpy.float64)
- smooth2d(data)¶
Simple smoothing for 2D data:
smooth1d()
is applied succesively along both axis- Parameters
data (numpy.ndarray) – 2D data array
- Returns
Smoothed data
- Return type
numpy.ndarray(dtype=numpy.float64)
- smooth3d(data)¶
Simple smoothing for 3D data:
smooth2d()
is applied on each 2D slice of the data volume along all 3 axis- Parameters
data (numpy.ndarray) – 2D data array
- Returns
Smoothed data
- Return type
numpy.ndarray(dtype=numpy.float64)
- savitsky_golay(data, npoints=5)¶
Smooth a curve using a Savitsky-Golay filter.
- Parameters
data (1D numpy array) – Input data
npoints – Size of the smoothing operator in number of samples Must be between 3 and 100.
- Returns
Smoothed data
- snip1d(data, snip_width)¶
Estimate the baseline (background) of a 1D data vector by clipping peaks.
Implementation of the algorithm SNIP in 1D is described in [Morhac97]. The original idea for 1D and the low-statistics-digital-filter (lsdf) comes from [Ryan88].
- Parameters
data (numpy.ndarray) – Data array, preferably 1D and of type numpy.float64. Else, the data array will be flattened and converted to dtype=numpy.float64 prior to applying the snip filter.
snip_width – Width of the snip operator, in number of samples. A sample will be iteratively compared to it’s neighbors up to a distance of
snip_width
samples. This parameters has a direct influence on the speed of the algorithm.
- Returns
Baseline of the input array, as an array of the same shape.
- Return type
numpy.ndarray
- snip2d(data, snip_width)¶
Estimate the baseline (background) of a 2D data signal by clipping peaks.
Implementation of the algorithm SNIP in 2D described in [Morhac97].
- Parameters
data (numpy.ndarray) – 2D array
width (int) – Width of the snip operator, in number of samples. A wider snip operator will result in a smoother result (lower frequency peaks will be clipped), and a longer computation time.
- Returns
Baseline of the input array, as an array of the same shape.
- Return type
numpy.ndarray
- snip3d(data, snip_width)¶
Estimate the baseline (background) of a 3D data signal by clipping peaks.
Implementation of the algorithm SNIP in 3D described in [Morhac97].
- Parameters
data (numpy.ndarray) – 3D array
width (int) – Width of the snip operator, in number of samples. A wider snip operator will result in a smoother result (lower frequency peaks will be clipped), and a longer computation time.
- Returns
Baseline of the input array, as an array of the same shape.
- Return type
numpy.ndarray
- strip(data, w=1, niterations=1000, factor=1.0, anchors=None)¶
Extract background from data using the strip algorithm, as explained at http://pymca.sourceforge.net/stripbackground.html.
In its simplest implementation it is just as an iterative procedure depending on two parameters. These parameters are the strip background width
w
, and the number of iterations. At each iteration, if the contents of channeli
,y(i)
, is above the average of the contents of the channels atw
channels of distance,y(i-w)
andy(i+w)
,y(i)
is replaced by the average. At the end of the process we are left with something that resembles a spectrum in which the peaks have been stripped.- Parameters
data (numpy.ndarray) – Data array
w – Strip width
niterations – number of iterations
factor – scaling factor applied to the average of
y(i-w)
andy(i+w)
before comparing toy(i)
anchors – Array of anchors, indices of points that will not be modified during the stripping procedure.
- Returns
Data with peaks stripped away