This section contains the following pages:

General Information

The Audio Weaver Filters folder lists over 60 filters. They have been broken down according to user needs, with the folder labels Adaptive, Calculated Coeffs, Controllable, High Precision, Raw Coeffs, and list the most commonly used filters. The Adaptive folder contains the LMS module, an adaptive filter with tracking capabilities. For those users less experienced with designing filters, the Calculated Coeffs filters take in frequency information, Q, Gain, and type, similar to tuning a filter in a DAW. Users with more DSP background can use the Raw Coeffs filters to tune filters with mathematical information. The most frequently used filters are the ButterworthFilter (highpass, lowpass, allpass), SecondOrderFilterSmoothed, with 20 different filter types, and the SecondOrderFilterSmoothedCascade: multiple 2nd order filters in series.

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A very common use of the SOFControl module is within a perceptual volume control. As the volume of the system is reduced, overall spectral balance should be maintained. Due to the sensitivity of the human auditory system, low frequencies and high frequencies appear to drop off more quickly than mid frequencies. Thus, to maintain the overall spectral balance, boost low and high frequencies as the volume level decreases. The VolumeControl module accomplishes this with a fixed boost table. For finer control over the boost, use a TableInterp module together with a SOFControl filter as shown below. The control signal “Volume” specifies the listening level and ranges from 0 (loud) to -80 (soft). The lookup tables convert the Volume setting into low frequency and high frequency boosts which are applied using the SOFControl module. The low frequency SOFControl module implements a peaking filter at 40 Hz and the gain is taken from the control pin. The high frequency SOFControl module implements a high shelf in which the gain is taken from the control pin.

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Filters with Raw Coefficients

Audio Weaver contains several filter types which operate on raw coefficients. These filters are for expert users who understand DSP and know how to calculate the filter coefficients[1]. .

There are two types of filters – Finite Impulse Response (FIR) and Infinite Impulse Response (IIR). Although Audio Weaver supports both types of filters, the majority of the filters used in audio applications are IIR due to their computational efficiency.

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There are 5 coefficients that the user must set: b₀, b₁, b₂, a₁, and a₂ (a₀ is always assumed to be 1). Audio Weaver does not check for stability and care must be used when computing the filter coefficients. There are several variants of Biquad filters. The simples – Biquad – has a single stage and implements the different equation shown above. BiquadCascade implements N stages of filtering with each channel using the same coefficients. BiquadNCascade implements N stages with each channel have its own set of coefficients. Finally, BiquadSmoothed implements a single Biquad stage with coefficient smoothing on a block-by-block basis.

Image RemovedImage Removed    

Image Added	FIR	Time domain FIR filter Specify filter length in module properties
Image Removed		Image Added	Biquad	Second order IIR filter. 5 filter coefficients are specified. No smoothing.
Image Added	BiquadCascade	Multiple Biquad filters in series. The number of filters is specified in module properties. The same coefficients are used per channel.
Image Added					BiquadSmoothed	Second order IIR filter. 5 filter coefficients are specified. Smoothed on a block-by-block basis
Image Added					BiquadNCascade	Multiple Biquad filters in series. The number of filters is specified in module properties. Different coefficients are used per channel.
Image Added			FIR Sparse	Sparse FIR filter in which most values are zero. Less convolution cycles than normal FIR
Image Added					FIR Sparse Reader	Sparse FIR that connects to a delay state writer. Convolution is based on a pointer rather than a separate FIR buffer.
Image Added	FIR Sparse Reader Fract16	Like FIR Sparse Reader except half the memory. Data is converted to fract16 for computations and has a conversion for the output if necessary.

High Precision Filters

Audio Weaver contains a variety of Biquad filters for equalizing audio. Some filters require raw coefficients (such as Biquad or BiquadCascade) while others contain built-in design equals (such as the SecondOrderFilter or ButterworthFilter). These filters are implemented using a Direct Form 2 (DF2) structure:

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All Biquad filters including the DF2 have 5 coefficients. The advantage of the DF2 structure is that it requires only 2 state variables per filter as compared to 4 state variables for the DF1 structure.

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The High Precision modules are designed to be drop in replacements for the non-high precision filters. That way, numerical problems can be resolved by replacing the offending filter with its high precision version.

Image Added	BiqudSmoothedHP	Smoothly varying Biquad
Image Added	ButterworthFilterHP	Butterworth lowpass, highpass, and allpass filters
	Image Added	BiquadCascadeHP	Cascade of N Biquad stages
Image Added	GraphicEQBandHP	Single band of a graphic equalizer
	Image Added	SOFControlHP	Controllable second order filter with design equations
	Image Added	SOFCascadeHP	Cascade of second order filters each with design equations
	Image Added	SecondOrderFilterHP	Single second order filter with design equations
	Image Added	VolumeControlHP	Fletcher Munson volume control with loudness compensation

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The crossover filter module (XoverNway) is actually a subsystem consisting of multiple individual modules. The module properties give the option to construct the crossover using standard Biquads or high precision Biquads:

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The graphic equalizer gives the option of using standard precision or high precision filters.

Here is an example of the benefits of the high precision filter. The system in the example has a peaking filter at 20 Hz with a gain of 6 dB and a Q of 2 and operates at a 48 kHz sample rate. The total harmonic distortion and noise (THD+N) for different input frequencies is plotted below. First for standard Biquad filters

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And now with a high precision filter, notice that the noise floor is reduced significantly – by up to 90 dB at low frequencies.

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For the interested reader, this measurement is performed by passing sine waves of different frequencies through the filter. Apply a notch filter at the output which removes the sine wave and then measure the RMS energy in the residual. This residual energy equals the THD+N. The measurement is repeated for many different frequencies and the plot reflects the measured THD+N at each input frequency. 

Common Filter Modules

The following filters are found as modules with no folder in the Filters directory. This is because they are the most common types of filters, which cover most general cases of filtering needs.

ButterworthFilter

This module implements lowpass, highpass, or allpass filters using a Butterworth design. The filters have a gain of 0 dB in the passband and are then monotonically decreasing in the stopband. The filter order is specified under module properties and ranges from 1^st order (6dB/octave) to 10^th order (60dB/octave). The filter order can only be changed in Design mode. Specify the filter type on the inspector (lowpass, highpass, or allpass) as well as the cutoff frequency, in Hz. Since these parameters are on the inspector, the filter type and cutoff frequency can be changed at run-time. Unfortunately, the ButterworthFilter does not have coefficient smoothing and there may be discontinuities when coefficients are updated.

Figure 3 - Butterworth lowpass filter frequency response as a function of filter order. The filter order goes from 1^st order (least steep line) to 10^th order (steepest line). The cutoff frequency is 100 Hz and the sample rate is 48 kHz

Figure 4 - Butterworth high filter frequency response as a function of filter order. The filter order goes from 1^st order (least steep line) to 10^th order (steepest line). The cutoff frequency is 100 Hz and the sample rate is 48 kHz

SecondOrderFilterSmoothed

This module is the most frequently used filter among all of the Audio Weaver modules. It implements a 2^nd order Biquad filter and includes design equations for 20 different filter types. The filter type and high-level design parameters (frequency, gain, and Q) can be changed at run-time using the inspector:

Depending on the filter type, some parameters are not used. See the table below for the filter types available and which control parameters are applicable.

Pass Through

filterType = 0

Applicable parameters: none.

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SecondOrderFilterSmoothed

This module is the most frequently used filter among all of the Audio Weaver modules. It implements a 2^nd order Biquad filter and includes design equations for 20 different filter types. The filter type and high-level design parameters (frequency, gain, and Q) can be changed at run-time using the inspector:

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Depending on the filter type, some parameters are not used. See the table below for the filter types available and which control parameters are applicable.

Pass Through filterType = 0   Applicable parameters: none.   Biquad coefficients are set to b0=1, b1=0, b2=0, a1=0, and a2=0. The filter runs and consumes processing but the output equals the input.	Image Added
Gain filterType = 1   Applicable parameters: gain   A simple gain with coefficients set to b0=undb20(gain), b1=0, b2=0, a1=0, and a2=0. The filter runs and consumes processing but the output equals the input.     Gain	Image Added
1st order Butterworth lowpass filter filterType = 12   Applicable parameters: gainfreq   A simple gain with coefficients set to b0=undb20(gain), b1=0, b2=0, a1=0, and a2=0 1st	Image Added
2nd order Butterworth lowpass filter filterType = 23   Applicable parameters: freq	Image Added
2nd 1st order Butterworth lowpass filterType = 3   Applicable parameters: freq 1st order Butterworth highpass filterType = 4   Applicable parameters: freq	Image Added
2nd order Butterworth highpass filterType = 5   Applicable parameters: freq	Image Added
1st order allpass filterType = 6   Applicable parameters: freq	Image Added
2nd order allpass filterType = 7   Applicable parameters: freq and Q	Image Added
2nd order low shelf filterType = 8   Applicable parameters: freq and gain    Use as a low frequency tone control	Image Added
2nd order low shelf with Q filterType = 9   Applicable parameters: freq, gain, and Q	Image Added
2nd order high shelf filterType = 10   Applicable parameters: freq and gain   Use as a high frequency tone control	Image Added
2nd order high shelf with Q filterType = 11   Applicable parameters: freq, gain, and Q	Image Added
2nd order peaking / parametric filterType = 12   Applicable parameters: freq, gain, and Q   Commonly used for generic equalization since it has controllable frequency, gain, and Q settings.	Image Added
2nd order notch filterType = 13   Applicable parameters: freq and Q	Image Added
2nd order bandpass filter filterType = 14   Applicable parameters: freq and Q	Image Added
1st order Bessel lowpass filter filterType = 15   Applicable parameters: freq	Image Added
1st order Bessel highpass filter filterType = 16   Applicable parameters: freq	Image Added
1st order asymmetrical low shelf filterType = 17   Applicable parameters: freq and gain	Image Added
1st order asymmetrical high shelf filterType = 18   Applicable parameters: freq and gain	Image Added
1st order symmetrical low shelf filterType = 19   Applicable parameters: freq and gain	Image Added
1st order symmetrical high shelf filterType = 20   Applicable parameters: freq and gain	Image Added

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Low/high shelf filter and low/high shelf filter Q are identical if Q is set to 0.707 (  ).

Second Order Filter Smoothed Cascade

This module contains several SecondOrderFilterSmoothed modules in series. This can be used to implement a more complicated EQ with only a single module. Under module properties, specify the number of stages of filtering. If the number of stages is set to 1, then this module is equivalent to the SecondOrderFilterSmoothed module. When there are multiple stages, the inspector expands as shown right:

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Second Order Filter Smoothed Cascade

This module contains several SecondOrderFilterSmoothed modules in series. This can be used to implement a more complicated EQ with only a single module. Under module properties, specify the number of stages of filtering. If the number of stages is set to 1, then this module is equivalent to the SecondOrderFilterSmoothed module. When there are multiple stages, the inspector expands as shown right:

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Table of Filter Modules