Overview

Cascade of second order filters. High precision implementation

Discussion

This module implements a general purpose second order cascade filter that is capable of realizing many different filter types. The module performs internal smoothing allowing the filters to be updated without introducing clicks. In all cases, the module implements an underlying cascade second order filters. First order filters are realized by setting some of the second order coefficients to zero.

The behavior of the cascade filters are controlled by the filterType arrary. The variable, filterType is an integer in the range from 0 to 14 inclusive.

After specifying filterType, adjust the filter parameters by setting the fields, gain, freq, and Q. Some filter parameters are not applicable to all filter types. The variable, freq controls the center frequency of the filter, gain determines the boost or cut in dB, and Q determines how sharp the filter is. Low Q values lead to broad filters and high Q values lead to narrow filters.

The following list discusses the various filter types and which variables are active in each case.

filterType=0, Simple pass through with unity gain.

filterType=1, Linear gain. [gain].

filterType=2, 1st order Butterworth low pass filter. [freq].

filterType=3, 2nd order Butterworth low pass filter. [freq].

filterType=4, 1st order Butterworth high pass filter. [freq].

filterType=5, 2nd order Butterworth high pass filter. [freq].

filterType=6, 1st order allpass filter. [freq].

filterType=7, 2nd order allpass filter. [freq, Q].

filterType=8, 2nd order low shelf. It allows you to vary the gain of the low frequencies. The high frequencies have a gain of 1.0. [freq, gain].

filterType=9, 2nd order low shelf with Q. It allows you to vary the gain of the low frequencies. The high frequencies have a gain of 1.0. [freq, gain, Q].

filterType=10, 2nd order high shelf. It allows you to vary the gain of the high frequencies. The low frequencies have a gain of 1.0. [freq, gain].

filterType=11, 2nd order high shelf with Q. It allows you to vary the gain of the high frequencies. The low frequencies have a gain of 1.0. [freq, gain, Q].

filterType=12, 2nd order peaking filter. It has unity gain except around the specified frequency. By varying gain, you can get a peak or a notch in the frequency band. [freq, gain, Q].

filterType=13, 2nd order notch filter. It has unity gain except around the specified frequency. At the specified frequency, the filter has a true notch with -inf dB gain. [freq, Q].

filterType=14, 2nd order bandpass filter. It has unity gain at the specified frequency and falls off in both directions. The bandwidth of the filter is determined by Q. [freq, Q].

filterType=15, 1st order Bessel low pass filter. [freq].

filterType=16, 1st order Bessel low pass filter. [freq].

filterType=17, 1st order asymmetrical low shelf. [freq, gain].

filterType=18, 1st order asymmetrical high shelf. [freq, gain].

filterType=19, 1st order symmetrical low shelf. [freq, gain].

filterType=20, 1st order symmetrical high shelf. [freq, gain].

filterType=21, 2nd order Butterworth low pass filter with variable Q. [freq, Q].

filterType=22, 2nd order Butterworth high pass filter with variable Q. [freq, Q].

Type Definition

typedef struct _ModuleSOFCascadeHP
{
    ModuleInstanceDescriptor instance;            // Common Audio Weaver module instance structure
    INT32 numStages;                              // Number of cascaded stages of the second order filter.
    FLOAT32 smoothingTime;                        // Time constant of the smoothing process.
    INT32 updateActive;                           // Specifies whether the filter coefficients are updating (=1) or fixed (=0).
    FLOAT32 smoothingCoeff;                       // Smoothing coefficient. This is computed based on the smoothingTime, sample rate, and block size of the module.
    INT32* filterType;                            // Selects the type of filter that is implemented by the module: Bypass=0, Gain=1, Butter1stLPF=2, Butter2ndLPF=3, Butter1stHPF=4, Butter2ndHPF=5, Allpass1st=6, Allpass2nd=7, Shelf2ndLow=8, Shelf2ndLowQ=9, Shelf2ndHigh=10, Shelf2ndHighQ=11, PeakEQ=12, Notch=13, Bandpass=14, Bessel1stLPF=15, Bessel1stHPF=16, AsymShelf1stLow=17, AsymShelf1stHigh=18, SymShelf1stLow=19, SymShelf1stHigh=20, VariableQLPF=21, VariableQHPF=22.
    FLOAT32* freq;                                // Cutoff frequency of the filter, in Hz.
    FLOAT32* gain;                                // Amount of boost or cut to apply, in dB if applicable.
    FLOAT32* Q;                                   // Specifies the Q of the filter, if applicable.
    FLOAT32* targetCoeffs;                        // Matrix of filter target coefficients. The size of the matrix is 5 x numStages. Each column contains the variables for a biquad arranged as [Fb; Gaa; Gab; K; Fa].
    FLOAT32* currentCoeffs;                       // Matrix of filter current coefficients. The size of the matrix is 5 x numStages. Each column contains the variables for a biquad.
    FLOAT32* state;                               // State variables. 2*numChannels per section.
} ModuleSOFCascadeHPClass;

Variables

Properties

Name	Type	Usage	isHidden	Default value	Range	Units
numStages	int	const	0	1	Unrestricted
smoothingTime	float	parameter	0	10	0:1:1000	msec
updateActive	int	parameter	1	1	0:1
smoothingCoeff	float	derived	1	0.06449	Unrestricted
filterType	int*	parameter	0	[1 x 1]	0:22
freq	float*	parameter	0	[1 x 1]	9.6:0.1:23760	Hz
gain	float*	parameter	0	[1 x 1]	-24:0.1:24	dB
Q	float*	parameter	0	[1 x 1]	0:0.1:20
targetCoeffs	float*	derived	0	[5 x 1]	Unrestricted
currentCoeffs	float*	state	0	[5 x 1]	Unrestricted
state	float*	state	1	[2 x 1]	Unrestricted

Pins

Input Pins

Name: in

Description: audio input

Data type: float

Channel range: Unrestricted

Block size range: Unrestricted

Sample rate range: Unrestricted

Complex support: Real

Output Pins

Name: out

Description: audio output

Data type: float

MATLAB Usage

File Name: second_order_filter_cascadeHP_module.m

 M=second_order_filter_cascadeHP_module(NAME, ISSMOOTH, NUMSTAGES)
 Creates a general purpose second order cascade filter that implements a
 number of standard filter types. The filter operates on multiple
 interleaved channels, with all channels being processed by the same set
 of coefficients.  This version uses high precision implementation 
 Arguments:
    NAME - name of the module.
    ISSMOOTH - optional argument which specifies whether the filter
         is smoothly updating. By default, ISSMOOTH=1.
    NUMSTAGES - number of second order filter stages.