octaveFilter

Octave-band and fractional octave-band filter

Description

The octaveFilter System object™ performs octave-band or fractional octave-band filtering independently across each input channel. An octave-band is a frequency band where the highest frequency is twice the lowest frequency. Octave-band and fractional octave-band filters are commonly used to mimic how humans perceive loudness. Octave filters are best understood when viewed on a logarithmic scale, which models how the human ear weights the spectrum.

To perform octave-band or fractional octave-band filtering on your input:

1. Create the octaveFilter object and set its properties.

2. Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

Creation

Syntax

octFilt = octaveFilter

octFilt = octaveFilter(centerFreq)

octFilt = octaveFilter(centerFreq,bw)

octFilt = octaveFilter(___,Name,Value)

Description

octFilt = octaveFilter creates a System object, octFilt, that performs octave-band filtering independently across each input channel.

octFilt = octaveFilter(centerFreq) sets the CenterFrequency property to centerFreq.

octFilt = octaveFilter(centerFreq,bw) sets the Bandwidth property to bw.

octFilt = octaveFilter(___,Name,Value) sets each property Name to the specified Value. Unspecified properties have default values.

Example: octFilt = octaveFilter(1000,'1/3 octave','SampleRate',96000) creates a System object, octFilt, with a center frequency of 1000 Hz, a 1/3 octave filter bandwidth, and a sample rate of 96,000 Hz.

Properties

Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

FilterOrder — Order of octave filter

6 (default) | even integer

Order of the octave filter, specified as an even integer.

Tunable: No

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

CenterFrequency — Center frequency of octave filter (Hz)

1000 (default) | positive scalar

Center frequency of the octave filter in Hz, specified as a positive scalar.

When using the parameterTuner, the center frequency must be in the range [0.2, SampleRate/2] Hz.

Tunable: Yes

Data Types: single | double

Bandwidth — Filter bandwidth (octaves)

'1 octave' (default) | '2/3 octave' | '1/2 octave' | '1/3 octave' | '1/6 octave' | '1/12 octave' | '1/24 octave' | '1/48 octave'

Filter bandwidth in octaves, specified as '1 octave', '2/3 octave', '1/2 octave', '1/3 octave', '1/6 octave', '1/12 octave', '1/24 octave', or '1/48 octave'.

Tunable: Yes

Data Types: char | string

Oversample — Oversample toggle

false (default) | true

Oversample toggle, specified as false or true.

• false –– The octave filter runs at the input sample rate.

• true –– The octave filter runs at two times the input sample rate. Oversampling minimizes the frequency warping effects introduced by the bilinear transformation. An FIR halfband interpolator implements oversampling before octave filtering. A halfband decimator reduces the sample rate back to the input sampling rate after octave filtering.

Tunable: No

Data Types: logical

SampleRate — Input sample rate (Hz)

44100 (default) | positive scalar

Input sample rate in Hz, specified as a positive scalar.

Tunable: Yes

Data Types: single | double

Usage

Syntax

audioOut = octFilt(audioIn)

Description

audioOut = octFilt(audioIn) applies octave-band filtering to the input signal, audioIn, and returns the filtered signal, audioOut. The type of filtering is specified by the algorithm and properties of the octaveFilter System object, octFilt.

Input Arguments

audioIn — Audio input to octave filter

matrix

Audio input to the octave filter, specified as a matrix. The columns of the matrix are treated as independent audio channels.

Data Types: single | double

Output Arguments

audioOut — Audio output from octave filter

matrix

Audio output from the octave filter, returned as a matrix the same size as audioIn.

Data Types: single | double

Object Functions

To use an object function, specify the System object as the first input argument. For example, to release system resources of a System object named obj, use this syntax:

release(obj)

Specific to octaveFilter

createAudioPluginClass	Create audio plugin class that implements functionality of System object
visualize	Visualize and validate filter response
isStandardCompliant	Verify octave filter design is ANSI S1.11-2004 compliant
getFilter	Return filter object with design parameters set
getANSICenterFrequencies	Get the list of valid ANSI S1.11-2004 center frequencies
parameterTuner	Tune object parameters while streaming

MIDI

configureMIDI	Configure MIDI connections between audio object and MIDI controller
disconnectMIDI	Disconnect MIDI controls from audio object
getMIDIConnections	Get MIDI connections of audio object

Common to All System Objects

clone	Create duplicate System object
isLocked	Determine if System object is in use
release	Release resources and allow changes to System object property values and input characteristics
reset	Reset internal states of System object
step	Run System object algorithm

Note

octaveFilter supports additional filter analysis functions. See Analyze Octave Filter Design for details.

Examples

Perform Fractional Octave-Band Filtering

Use octaveFilter to design a 1/3 octave-band filter centered at 1000 Hz. Process an audio signal using your octave filter design.

Create a dsp.AudioFileReader object.

samplesPerFrame = 1024;
reader = dsp.AudioFileReader("RockGuitar-16-44p1-stereo-72secs.wav",SamplesPerFrame=samplesPerFrame);

Create an octaveFilter object. Use the sample rate of the reader as the sample rate of the octave filter.

centerFreq = 1000;
bw = "1/3 octave";
Fs = reader.SampleRate;

octFilt = octaveFilter(centerFreq,bw,SampleRate=Fs);

Visualize the filter response and verify that it fits within the class 0 mask of the ANSI S1.11-2004 standard.

visualize(octFilt,"class 0")

Create a spectrum analyzer to visualize the original audio signal and the audio signal after octave-band filtering.

scope = spectrumAnalyzer( ...
    SampleRate=Fs, ...
    PlotAsTwoSidedSpectrum=false, ...
    FrequencyScale="log", ...
    Title="Octave-Band Filtering", ...
    ShowLegend=true, ...
    ChannelNames=["Original signal","Filtered signal"]);

Process the audio signal in an audio stream loop. Visualize the filtered audio and the original audio. As a best practice, release the System objects when complete.

while ~isDone(reader)
    x = reader();
    y = octFilt(x);
    scope([x(:,1),y(:,1)])
end

release(octFilt)
release(reader)
release(scope)

Analyze Octave Filter Design

Create an octave filter. Visualize the filter response and validate that it is class 2 compliant.

octFilt = octaveFilter(CenterFrequency=1000);
visualize(octFilt,"class 2")

Visualize and analyze the filter.

filterAnalyzer(octFilt,SampleRates=octFilt.SampleRate)

The octaveFilter object supports several filter analysis methods. For more information, use help at the command line:

help octaveFilter.helpFilterAnalysis

    The following analysis methods are available for discrete-time filter System objects:
 
    filterAnalyzer -  Filter Analyzer app
 
    info         -  Filter information
    freqz        -  Frequency response
    phasez       -  Phase response
    zerophase    -  Zero-phase response
    grpdelay     -  Group delay response
    phasedelay   -  Phase delay response
    impz         -  Impulse response
    impzlength   -  Length of impulse response
    stepz        -  Step response
    zplane       -  Pole/zero plot
    cost         -  Cost estimate for implementation of the filter System object
    measure      -  Measure characteristics of the frequency response
 
    outputDelay  -  Output delay value
    order        -  Filter order
    coeffs       -  Filter coefficients in a structure
    firtype      -  Determine the type (1-4) of a linear phase FIR filter System object
    tf           -  Convert to transfer function
    zpk          -  Convert to zero-pole-gain
    ss           -  Convert to state space representation
 
    isallpass    -  Verify if filter System object is allpass
    isfir        -  Verify if filter System object is FIR
    islinphase   -  Verify if filter System object is linear phase
    ismaxphase   -  Verify if filter System object is maximum phase
    isminphase   -  Verify if filter System object is minimum phase
    isreal       -  Verify if filter System object is minimum real
    issos        -  Verify if filter System object is in second-order sections form
    isstable     -  Verify if filter System object is stable
 
    realizemdl   -  Filter realization (Simulink diagram)
 
    specifyall   -  Fully specify fixed-point filter System object settings
 
    cascade      -  Create a dsp.FilterCascade System object
    parallel     -  Create a dsp.ParallelFilter System object
 
    Second-order sections:
 
    scale        -  Scale second-order sections of BiquadFilter System object
    scalecheck   -  Check scaling of BiquadFilter System object
    reorder      -  Reorder second-order sections of BiquadFilter System object
    cumsec       -  Cumulative second-order section of BiquadFilter System object
    scaleopts    -  Create an options object for second-order section scaling
    sos          -  Convert to second-order-sections (for IIRFilter System objects only)
 
    Fixed-Point (Fixed-Point Designer Required):
 
    freqrespest  -  Frequency response estimate via filtering
    freqrespopts -  Create an options object for frequency response estimate
    noisepsd     -  Power spectral density of filter output due to roundoff noise
    noisepsdopts -  Create an options object for output noise PSD computation
 
    Multirate Analysis:
 
    freqzmr                  - DTFT of the impulse response
    polyphase                - Polyphase decomposition of multirate filter System object
    gain (CIC decimator)     - Gain of CIC decimator filter System object
    gain (CIC interpolator)  - Gain of CIC interpolator filter System object
 
    For decimator, interpolator, or rate change filter System objects
    the analysis tools perform computations relative to the rate at
    which the filter is running. If a sampling frequency is specified,
    it is assumed that the filter is running at that rate.

Help for octaveFilter.helpFilterAnalysis is inherited from superclass dsp.internal.FilterAnalysis

Effect of Center Frequency on Octave-Band Filtering

Process a speech signal using different octave bands from an octave-band filter bank.

Design a 1/2 octave filter with an estimated center frequency of 800 Hz. Use isStandardCompliant to find the nearest compliant center frequency.

octFilt = octaveFilter(800,"1/2 octave");
[complianceStatus,suggestedCenterFrequency] = isStandardCompliant(octFilt,"class 0")

complianceStatus =

  logical

   0


suggestedCenterFrequency =

  841.3951

Change the center frequency of the octFilt object to the suggested center frequency returned by isStandardCompliant. Get a list of valid ANSI S1.11-2004 center frequencies, given your specified octFilt center frequency.

octFilt.CenterFrequency = suggestedCenterFrequency;
Fo = getANSICenterFrequencies(octFilt);

Create an audio file reader and audio device writer.

fileReader = dsp.AudioFileReader("Counting-16-44p1-mono-15secs.wav");
deviceWriter = audioDeviceWriter(SampleRate=fileReader.SampleRate);

Create a scope to visualize the filtered and unfiltered signals.

scope = spectrumAnalyzer(...
    PlotAsTwoSidedSpectrum=false,...
    FrequencyScale="log",...
    Title="Octave-Band Filtering",...
    ShowLegend=true,...
    ChannelNames=["Original signal","Filtered signal"]);

In an audio stream loop, process the audio signal using your octave-band filter. Vary the center frequency to hear the effect. As a best practice, release your objects after processing.

index = 12;
octFilt.CenterFrequency = Fo(index);
count = 1;
while ~isDone(fileReader)
    x = fileReader();
    y = octFilt(x);
    scope([x,y])
    deviceWriter(y);

    if mod(count,100)==0
        octFilt.CenterFrequency = Fo(index);
        index = index+1;
    end
    count = count+1;
end

release(scope)
release(deviceWriter)
release(fileReader)

Remove Noise from Tone Scale

Remove additive noise from an audio tone scale using an octaveFilter.

Create audioOscillator and audioDeviceWriter objects with default properties. Create an octaveFilter object with the center frequency set to 100 Hz.

osc = audioOscillator;
deviceWriter = audioDeviceWriter;
octFilt = octaveFilter(100);

In an audio stream loop, listen to a tone created by your audio oscillator. The tone contains additive Gaussian noise.

for i = 1:400
    x = osc();
    x1 = x + 0.1*randn(512,1);
    deviceWriter(x1);
    if rem(i,100)==0
        osc.Frequency = osc.Frequency*2;
    end
end

Create a spectrum analyzer to view your filtered and unfiltered signals.

scope = spectrumAnalyzer( ...
    PlotAsTwoSidedSpectrum=false, ...
    FrequencyScale="log", ...
    Title="Octave-Band Filtering", ...
    ShowLegend=true, ...
    ChannelNames=["Original signal","Filtered signal"]);

Reset the frequency of your audio oscillator to its default, 100 Hz.

osc.Frequency = 100;

In an audio stream loop, filter the corrupted tone using your octave-band filter. When the tone changes frequency in the loop, change the center frequency of your octave filter to match. As a best practice, release your audio device once done.

for i = 1:400
    x = osc();
    x1 = x + 0.1*randn(512,1);
    x2 = octFilt(x1);
    deviceWriter(x2);
    if rem(i,100)==0
        osc.Frequency = osc.Frequency*2;
        octFilt.CenterFrequency = octFilt.CenterFrequency*2;
    end
    scope([x1,x2])
end

release(deviceWriter)
release(scope)

Design Compliant High-Frequency Filters

Design a sixth-order 1/3 octave filter with a sample rate of 96 kHz.

octFilt = octaveFilter('FilterOrder',6, ...
    'Bandwidth','1/3 octave', ...
    'SampleRate',96e3);

Get the center frequencies defined by the ANSI S1.11-2004 standard. The center frequencies defined by the standard depend on the Bandwidth and SampleRate properties.

centerFrequencies = getANSICenterFrequencies(octFilt)

centerFrequencies = 1×53
104 ×

    0.0000    0.0000    0.0000    0.0001    0.0001    0.0001    0.0001    0.0001    0.0002    0.0002    0.0003    0.0003    0.0004    0.0005    0.0006    0.0008    0.0010    0.0013    0.0016    0.0020    0.0025    0.0032    0.0040    0.0050    0.0063    0.0079    0.0100    0.0126    0.0158    0.0200    0.0251    0.0316    0.0398    0.0501    0.0631    0.0794    0.1000    0.1259    0.1585    0.1995    0.2512    0.3162    0.3981    0.5012    0.6310    0.7943    1.0000    1.2589    1.5849    1.9953

Set the center frequency of the octave filter to 19.953 kHz and visualize the response with a 'class 0' compliance mask.

octFilt.CenterFrequency = centerFrequencies(38);
visualize(octFilt,'class 0')

The red mask on the plot defines the bounds for the magnitude response of the filter. The magnitude response of this filter goes above the upper bound of the compliance mask around 6.6 kHz. One way to counter this is to increase the filter order so that the filter's rolloff is steeper.

To bring the octave filter design into compliance, set the octave filter order to 8.

octFilt.FilterOrder = 8;

Another option to bring the octave filter design into compliance is to set the Oversample property to true. This designs and runs the filter at twice the specified SampleRate to reduce the effects of the bilinear transformation during the design stage.

octFilt.FilterOrder = 6;
octFilt.Oversample = true;

Design Compliant Low-Frequency Filters

Design a sixth-order 2/3 octave filter with a 96 kHz sample rate.

octFilt = octaveFilter('FilterOrder',6, ...
    'Bandwidth','2/3 octave', ...
    'SampleRate',96e3);

Get the center frequencies defined by the ANSI S1.11-2004 standard. The center frequencies defined by the standard depend on the Bandwidth and SampleRate properties.

centerFrequencies = getANSICenterFrequencies(octFilt)

centerFrequencies = 1×25
104 ×

    0.0000    0.0001    0.0001    0.0002    0.0003    0.0004    0.0006    0.0010    0.0016    0.0025    0.0040    0.0063    0.0100    0.0158    0.0251    0.0398    0.0631    0.1000    0.1585    0.2512    0.3981    0.6310    1.0000    1.5849    2.5119

Set the center frequency of the octave filter to ~6 Hz and visualize the response with a 'class 0' compliance mask.

octFilt.CenterFrequency = centerFrequencies(2);
visualize(octFilt,'class 0')

The red mask on the plot defines the bounds for the magnitude response of the filter. The magnitude response of this filter goes below the lower bound of the compliance mask between 5.5 and 7.5 Hz.

Low-frequency filters in an octave filter bank have very low normalized center frequencies, and the filters designed for them have poles that are almost on the unit circle. To make this filter ANSI compliant, it has to be designed and operated at a lower sample rate.

To bring the octave filter design into compliance, set the sample rate to 48 kHz.

octFilt.SampleRate = 48e3;

Tune Octave Filter Parameters

Create a dsp.AudioFileReader to read in audio frame-by-frame. Create a audioDeviceWriter to write audio to your sound card. Create an octaveFilter to process the audio data. Call visualize to plot the frequency response of the octave filter.

frameLength = 1024;
fileReader = dsp.AudioFileReader('RockDrums-44p1-stereo-11secs.mp3', ...
    'SamplesPerFrame',frameLength);
deviceWriter = audioDeviceWriter('SampleRate',fileReader.SampleRate);

octFilt = octaveFilter('SampleRate',fileReader.SampleRate);
visualize(octFilt)

Call parameterTuner to open a UI to tune parameters of the octaveFilter while streaming.

parameterTuner(octFilt)

In an audio stream loop:

1. Read in a frame of audio from the file.

2. Apply octave filtering.

3. Write the frame of audio to your audio device for listening.

While streaming, tune parameters of the octave filter and listen to the effect.

while ~isDone(fileReader)
    audioIn = fileReader();
    audioOut = octFilt(audioIn);
    deviceWriter(audioOut);
    drawnow limitrate % required to update parameter
end

As a best practice, release your objects once done.

release(deviceWriter)
release(fileReader)
release(octFilt)

More About

Band Edge

A band edge frequency refers to the lower or upper edge of the passband of a bandpass filter.

Center Frequency of Octave Filter

The center frequency of an octave filter is the geometric mean of the lower and upper band edge frequencies.

Tips

The createAudioPluginClass and configureMIDI functions map tunable properties of the octaveFilter to user-facing parameters:

Property	Range	Mapping	Units
CenterFrequency	[3, 22000]	log	Hz
Bandwidth	'1 octave', '2/3 octave', '1/2 octave', '1/3 octave', '1/6 octave', '1/12 octave', '1/24 octave', or '1/48 octave'	Your MIDI controller range is discretized into seven levels, corresponding to the seven Bandwidth choices.	––

Algorithms

Octave Bandwidth to Band Edge Conversion

The octaveFilter System object uses the specified center frequency and filter bandwidth in octaves to determine the band edges [2].

The object computes the upper and lower band edge frequencies:

$$f_{\text{pa}}=f_{\text{c}}\times G^{-\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2b$}\right.}$$

$$f_{\text{pb}}=f_{\text{c}}\times G^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2b$}\right.}$$

• f_c is the center frequency specified by the CenterFrequency property.

• b is the octave bandwidth specified by the Bandwidth property. For example, if Bandwidth is specified as '1/3 octave', the value of b is 3.

• G is a conversion constant:

  $$G={10}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$10$}\right.}.$$

Digital Filter Design

The octaveFilter System object implements a higher-order digital bandpass filter design method specified in [1].

In this design method, a desired digital bandpass filter maps to a Butterworth lowpass analog prototype, which is then mapped back to a digital bandpass filter:

1. The analog Butterworth filter is expressed as a cascade of second-order sections:

   $$H(s)=H_1(s)H_2(s)\cdots H_{2N}(s),$$

   where:

   $$H_i(s)=\frac{1}{1-2\frac{s}{{\Omega }_0}\cos {\theta }_i+\frac{s^2}{{\Omega }_0^2}},i=1,2,\mathrm{...},2N$$

   $${\theta }_i=\frac{\pi }{2N}\left(N-1+2i\right),i=1,2,\mathrm{..},2N$$

   N is the filter order specified by the FilterOrder property.

2. The analog Butterworth filter is mapped to a digital filter using a bandpass version of the bilinear transformation:

   $$s=\frac{1-c{z}^{-1}+z^{-2}}{1-z^{-2}},$$

   where

   $$c=\frac{\sin \left({\omega }_{\text{pa}}+{\omega }_{\text{pb}}\right)}{\sin {\omega }_{\text{pa}}+\sin {\omega }_{\text{pb}}}.$$

   This mapping results in the following substitution:

   $${\Omega }_0=\frac{c-\cos {\omega }_{\text{pb}}}{\sin {\omega }_{\text{pb}}}.$$

3. The analog prototype is evaluated:

   $$H_i(z)={\frac{1}{1-2\frac{s}{{\Omega }_0}\cos {\theta }_i+\frac{s^2}{{\Omega }_0^2}}|}_{s=\frac{1-2c{z}^{-1}+z^{-2}}{1-z^{-2}}}$$

   Because s is second-order in z, the bandpass version of the bilinear transformation is fourth-order in z.

References

[1] Orfanidis, Sophocles J. Introduction to Signal Processing. Englewood Cliffs, NJ: Prentice Hall, 2010.

[2] Acoustical Society of America. American National Standard Specification for Octave-Band and Fractional-Octave-Band Analog and Digital Filters. ANSI S1.11-2004. Melville, NY: Acoustical Society of America, 2009.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

System Objects in MATLAB Code Generation (MATLAB Coder)

Version History

Introduced in R2016b