Example 3. Creating a Butterworth Filter

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<?xml version="1.0" encoding="utf-8"?>
<Function xmlns:xsd="http://www.w3.org/2001/XMLSchema"
      xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
      Application="FlexDCA" MinimumSoftwareVersion="5.00.328">
   <Name>Butterworth</Name>
   <Abbreviation>Butter</Abbreviation>
   <Comments>Implements a Butterworth filter.</Comments>
   <Script>Butterworth.py</Script>
   <Icon></Icon>
   <FunctionType>1 Source</FunctionType>
   <Variable Name = "FType" Value = "low"/>
   <Control Name = "N">
      <Integer>
         <Min>1</Min>
         <!--Python Butterworth implementation has problems above 4th order.-->
         <Max>4</Max>
         <Units>None</Units>
         <Default>2</Default>
      </Integer>
   </Control>
   <Control Name = "Fc">
      <Double>
         <Min>10e6</Min>
         <Max>1000e9</Max>
         <Resolution>1000</Resolution>
         <Units>Hertz</Units>
         <Default>7.5e9</Default>
      </Double>
   </Control>
</Function>

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""" Python 3.9 FlexDCA Butterworth User Operator. 
"""

import math
import numpy as np
from scipy.fftpack import fft, ifft
from scipy.signal import butter, freqz, lfilter

# Expects a dictionary mapping from variable name to value.
def algorithm(inputVars):

    # Initialize
    FiltData = []
    XOrg = 0.0
    XInc = 0.0
    Gain = 1.0
    FilterWidth = 0.0
    FilterDelay = 0.0
    XUnits = 'Same'
    YUnits = 'Same'
    ErrorMsg = ''

    # N, Fc, and FType are additional variables specified in the XML config file
    # for this filter.
    if ('N' not in inputVars) or ('Fc' not in inputVars) or ('FType' not in inputVars):
        return { 'ErrorMsg' : 'Please configure the operator by loading the XML configuration file ' \
                              'rather than loading the Python script directly.' }

    # Gather custom controls
    N = inputVars['N']
    Fc = inputVars['Fc']
    FType = inputVars['FType']

    # Gather system info
    SrcData = inputVars['SrcData']
    XOrg = inputVars['XOrg']
    XInc = inputVars['XInc']
    IsPeriodic = inputVars['IsPeriodic']

    FilterDelay = N * 0.112 / Fc
    FilterWidth = N / Fc

    num_points = len(SrcData)
    if num_points > 0:
        # Create the filter
        Wn = 2 * XInc * Fc
        b, a = butter(N, Wn, FType)

        if IsPeriodic:
            # Perform filtering circularly using FFTs
            fft_src_data = fft(SrcData)
            _unused, H = freqz(b, a, num_points, True)
            FiltData = ifft(fft_src_data * H).real

            # Rotate to remove FilterDelay.
            shift = int(round(FilterDelay / XInc))
            FiltData = np.roll(FiltData, -shift)
        else:
            start_index = int(math.ceil(FilterWidth / XInc))
            if start_index >= num_points:
                ErrorMsg = 'Too few points. Pipeline eats up entire waveform.'
            else:
                # Perform filtering
                FiltData = lfilter(b, a, SrcData)

                # Remove filter delay and pipeline
                FiltData = FiltData[start_index:]
                leading_pipeline = FilterWidth - FilterDelay
                XOrg = XOrg + leading_pipeline

    # Return output variables as dictionary.
    return { 'FiltData' : FiltData,
             'XOrg' : XOrg,
             'XInc' : XInc,
             'Gain' : Gain,
             'FilterWidth' : FilterWidth,
             'FilterDelay' : FilterDelay,
             'XUnits' : XUnits,
             'YUnits' : YUnits,
             'ErrorMsg' : ErrorMsg
           }