math::filters(3tcl)

NAME
math::filters - Digital filters

SYNOPSIS
package require Tcl 8.6

package require TclOO

package require math::filters ?0.1?

::math::filters::filterButterworth lowpass order samplefreq cutofffreq

::math::filters::filter coeffs data

::math::filters::filterObj new coeffs yinit

$filterObj filter x

$filterObj reset

DESCRIPTION

The math::filters package implements digital filters, notably Butterworth low-pass and high-pass filters. The procedures allow to filter an entire data series as well as filter data one by one.

PROCEDURES
The package defines the following public procedures:

::math::filters::filterButterworth lowpass order samplefreq cutofffreq
    Determine the coefficients for a Butterworth filter of given order. The coefficients are returned as a list of the x-coefficients, the y-coefficients and the scale. The formula is (n is the filter order):

                       n             n
        scale * y_k = sum x_(k-i) + sum y_(k-i)
                      i=0           i=1

    bool lowpass
        Generate a low-pass filter (1) or a high-pass filter (0)

    integer lowpass
        The order of the filter to be generated

    double samplefreq
        Sampling frequency of the data series

    double cutofffreq
        Cut-off frequency for the filter

::math::filters::filter coeffs data
    Filter the entire data series based on the filter coefficients.

    list coeffs
        List of coefficients as generated by filterButterworth (or in fact any similar list of coefficients)

    list data
        Data to be filtered

::math::filters::filterObj new coeffs yinit
    Create a filter object. The initial x data are taken as zero. The initial y data can be prescribed. If they are not given, they are taken as zero as well.

    list coeffs
        List of coefficients as generated by filterButterworth (or in fact any similar list of coefficients)

    list yinit
        (Optional) initial data for the filter result.

$filterObj filter x
    Filter a single value and return the result.

    double x
        The value to be filtered

$filterObj reset
    Reset the filter object (start anew)

KEYWORDS
digital, filtering

CATEGORY
Mathematics

COPYRIGHT
Copyright (c) 2020 by Arjen Markus