Second Order Section Filtering

Module name: sosfiltering

This module contains second order section filtering routines implemented in c, cffi and numpy.

A bilinear transform converting sos analog weights to sos digital weights is provided by bilinear_sos().

There are different implementations of sos filtering routines:

The c-implementations are for real valued signals only.

With the function freqz() you can check the frequency response of your second order section filters.

For the cffi you need pycparser being installed.

Compiling the c source

Firstly i implemented a prototype-function in python for easy debugging “sosfilter_cprototype_py()”. After that i translated this prototype into a c-function. By compiling a shared library from it with the listed steps below, one can use the python cffi to access this shared library in python.

$ gcc -c -std=c99 -O3 sosfilter.c
$ gcc -shared -o sosfilter.so sosfilter.o
$ or the last line for windows users:
$ gcc -shared -o sosfilter.dll sosfilter.o

Functions

sosfiltering.bilinear_sos(d, c)[source]

Bilinear transformation of analog weights to digital weights. >>>>>>> 8d01abb1e1f252834c0666d50c645dd3d35a1f52

Bilinear transformation of analog weights to digital weights. Weights of IIR digital filter in cascade form with 2-pole sections; H(z)=H(z,1)H(z,2)...H(z,L/2) where L is the number of poles and each section is a ratio of quadratics.

Parameters:

d : ndarray

Numerator weights of analog filter in 1-pole sections. d is dimensioned (L/2 x 2).

c : ndarray

Denominator weights, dimensioned same as d.
Returns:

b : ndarray

Digital numerator weights, dimensioned (L/2 x 3).

a : ndarray

Digital denominator weights, dimensioned the same.
sosfiltering.freqz(sosmat, nsamples=44100, sample_rate=44100, plot=True)[source]

Plots Frequency response of sosmat.

sosfiltering.sosfilter_c(signal, sos, states=None)[source]

Second order section filter function using cffi

signal_out, states = sosfilter_c(signal_in, sos, states=None)

Parameters:

signal : ndarray

Input array of shape (N x 0).

sos : ndarray

Second order section coefficients array of shape (K*6 x 0). One biquad -> 6 coefficients: [b00, b01, b02, a00, a01, a02, ..., bK1, ..., aK2]

states : ndarray

Array with filter states. Initial value can be None.
Returns:

signal : ndarray

Filtered signal of shape (N x 0).

states : ndarray

Array with filter states.
sosfiltering.sosfilter_cprototype_py(signal, sos, states)[source]

Prototype for second order section filtering c function. Implements a IIR DF-II biquad filter strucure.

sosfiltering.sosfilter_double_c(signal, sos, states=None)[source]

Second order section filter function using cffi, double precision.

signal_out, states = sosfilter_c(signal_in, sos, states=None)

Parameters:

signal : ndarray

Signal array of shape (N x 0).

sos : ndarray

Second order section coefficients array of shape (K*6 x 0). One biquad -> 6 coefficients: [b00, b01, b02, a00, a01, a02, ..., b10, bK1 ... , aK2]

states : ndarray

Filter states, initial value can be None.
Returns:

signal :

Filtered signal array of shape (N x 0).

states : ndarray

Filter states, initial value can be None.
sosfiltering.sosfilter_double_mimo_c(signal, sos, states=None)[source]

Second order section filter function for multi channel input using cffi, double precision

signal_out, states = sosfilter_c(signal_in, sos, states=None)

Parameters:

signal : ndarray

Signal array of shape (N x C).

sos : ndarray

Second order section filter coefficients (K*6 x B x C) np-array.

states : ndarray

Filter states, initial can be None. Otherwise shape is (K*2 x B x C)
Returns:

signal : ndarray

Filtered signal of shape (N x B x C). Where N is the number of samples, B is th number of filter bands and C is the number of signal channels.

states : ndarray

Filter states of shape (K*2 x B x C).
sosfiltering.sosfilter_mimo_cprototype_py(signal_in, sos_in, states_in=None)[source]

Prototype for the mimo c-filter function. Implements a IIR DF-II biquad filter strucure. But with multiple input und multiple bands.

sosfiltering.sosfilter_py(x, sos, states=None)[source]

Second order section filter routing with scipy lfilter.

Parameters:

x : ndarray

Input signal array.

sos : ndarray

Second order section coefficients array.

states : ndarray or None

Filter states, initial value can be None.
Returns:

signal : ndarray

Filtered signal.

states : ndarray

Array with filter states.

butterworth

The butterworth module provides functions to design butterwort filters.

butterworth.butter_analog_sos(band, L, w1, w2=0)[source]

Returns analog filter coeffitients for Butterworth filters. compute analog weights of a butterworth filter

Parameters:

band : {‘lowpass’, ‘highpass, ‘bandpass’, ‘bandstop’}

L : int

Order of lowpass / highpass filter.

w1 : scalar

Critical frequency one.

w2 : scalar

Critical frequency two. (for ‘bandpass’ or ‘bandstop’).
Returns:

d, c : Analog weights of the filter

Notes

implements SOS H(s) butterwort if you need H(z) apply a bilinear transform

butterworth.butter_sos(band, L, v1, v2=0.0)[source]

Compute weights of a digital Butterworth filter in cascade form.

Parameters:

band : {‘lowpass’, ‘highpass’, ‘bandpass’, ‘bandstop’}

L : int

Number of lowpass poles. L is doubled for ‘bandpass’ and ‘bandstop’. L must be even.

v1 : scalar

First critical frequency (Hz-s); 0.0 <v1 < 0.5.

v2 : scalar

Second critical frequency; v1 < v2 < 0.5. v2 is used only if ‘bandpass’ or ‘bandstop’.
Returns:

sosmat : ndarray

Contains the numerator and denominator coeffs for each cascade in one row.

Notes

Adapted from: Samuel D. Stearns, “Digital Signal Processing with Examples in MATLAB”