# Filter2D — 2-dimensional spectral filtering.¶

This module defines the 2D filter methods.

class admit.util.filter.Filter2D.Filter2D(data, method, **keyval)[source]

This class defines and runs 2D spectral filters. The currently available filters are Gaussian, Hanning, Triangle, Welch, Boxcar, and Savitzky Golay. The output spectrum will be of the same length as the input spectrum, however some edge channels may be zeroed by some methods, depending on the input parameters.

Parameters: spec : numpy array 2D numpy array of the input spectrum (just the amplitudes). method : str The smoothing filter to apply: boxcar, gaussian, welch, hanning, triangle, or savgol. No default. Minimum matching is enabled with a minimum of 3 characters, i.e. box = boxcar. keyval : various Any keyword value pairs for the specific method chosen, see the notes for specific keywords.

Notes

Details of the different filter keywords and defaults:

Filter Keyword Def. Description
“boxcar” “width” 3 Number of channels to average together
“gaussian” “width” 7 Number of channels to span with the gaussian
“hanning” “width” 5 Number of channels to include in the cos
“triangle” “width” 5 Number of channels to span with the triangle
“welch” “width” 5 Number of channels to use in the function
“savgol” “window_size” 7 Number of channels to use in the calculation
“order” 3 Order of the poynomial fit (must be odd)
“deriv” 0 The number of the derivative to compute (0 = just smooth)

Attributes

 spec (numpy array) The spectrum. len (int) The length of the spectrum. methods (list) A list of the available filters. [method]_args (dict) A dictionary for each method giving its keywords and defaults (e.g. boxcar_args). method (str) The method being used.

Methods

 boxcar(width) Method to apply a boxcar filter to a spectrum. checkmethod(method) Method to interpret the input method and determine the full method gaussian(width) Method to apply a Gaussian filter to a spectrum. hanning(width) Method to apply a Hanning filter to a spectrum. radius(x, y, width) Method to calculate the radius of a point in the kernel run() Method to run the selected filter on the data savgol(window_size, order[, deriv]) Method to apply a Savitzky-Golay filter to a 2D image. triangle(width) Method to apply a Triangular filter to a spectrum. welch(width) Method to apply a Welch filter to a spectrum.
boxcar(width)[source]

Method to apply a boxcar filter to a spectrum. The filter for point x[i] is defined as:

$x[i] = \frac{1}{N} \sum_{n=0}^{N} x[i + n - \frac{N - 1}{2}]$

where N is the width of the filter.

Parameters: width : int The width of the box to use in channels, must be odd numpy array The smoothed image, (width - 1)/2 edge channels will be zeroed
checkmethod(method)[source]

Method to interpret the input method and determine the full method name

Parameters: method : str The method to use, minimal matching is possible, with a minimum of 3 characters (e.g. “box” will be interpreted to be “boxcar”) None
gaussian(width)[source]

Method to apply a Gaussian filter to a spectrum. The filter for point x[i] is defined as:

$x[i] = \frac{3}{N} \sum_{n=0}^{N} x[i + n - \frac{N - 1}{2}] e^{-\frac{1}{2}\left(\frac{n-(N-1)/2}{\sigma(N-1)/2}\right)^2}$

where N is the width of the filter.

Parameters: width : int The number of channels to span with the gaussian for each iteration, must be odd numpy array The smoothed image, (width - 1)/2 edge channels will be zeroed
hanning(width)[source]

Method to apply a Hanning filter to a spectrum. The filter for point x[i] is defined as:

$x[i] = \frac{2}{N-1} \sum_{n=0}^{N} x[i + n - \frac{N - 1}{2}] 0.5 \left(1 - \cos\left(\frac{2\pi n}{N-1}\right)\right)$

where N is the width of the filter.

Parameters: width : int The number of channels to span with the function for each iteration, must be odd numpy array The smoothed image, (width - 1)/2 edge channels will be zeroed
radius(x, y, width)[source]

Method to calculate the radius of a point in the kernel

Parameters: x : float The x coordinate y : float The y coordinate width : int The width of the Gaussian being used Float containing the radius to the point
run()[source]

Method to run the selected filter on the data

Parameters: None The smoothed image
savgol(window_size, order, deriv=None)[source]

Method to apply a Savitzky-Golay filter to a 2D image.

Parameters: window_size : int the size of the window. Must be an odd integer number. order : int the order of the polynomial used in the filtering. Must be less then window_size - 1. deriv: int the order of the derivative to compute (default = None means only smoothing) numpy array The smoothed image, (width - 1)/2 edge channels will be zeroed
triangle(width)[source]

Method to apply a Triangular filter to a spectrum. The filter for point x[i] is defined as:

$x[i] = \sum_{n=0}^{N} x[i + n - \frac{N - 1}{2}] \left(1 - \left|\frac{n-\frac{N-1}{2}}{\frac{N}{2}}\right|\right)$

where N is the width of the filter.

Parameters: width : int The number of channels to span with the function for each iteration, must be odd numpy array The smoothed image, (width - 1)/2 edge channels will be zeroed
welch(width)[source]

Method to apply a Welch filter to a spectrum. The filter for point x[i] is defined as:

$x[i] = \frac{3}{2(N-1)} \sum_{n=0}^{N} x[i + n - \frac{N - 1}{2}] \left(1 - \left(\frac{n - \frac{N-1}{2}}{\frac{N-1}{2}}\right)^2\right)$

where N is the width of the filter.

Parameters: width : int The number of channels to span with the function for each iteration, must be odd numpy array The smoothed image, (width - 1)/2 edge channels will be zeroed