expander

Dynamic range expander

Description

The expander System object™ performs dynamic range expansion independently across each input channel. Dynamic range expansion attenuates the volume of quiet sounds below a given threshold. It uses specified attack, release, and hold times to achieve a smooth applied gain curve. Properties of the expander System object specify the type of dynamic range expansion.

To perform dynamic range expansion:

Create the expander object and set its properties.
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

dRE = expander

dRE = expander(thresholdValue)

dRE = expander(thresholdValue,ratioValue)

dRE = expander(___,Name,Value)

Description

dRE = expander creates a System object, dRE, that performs dynamic range expansion independently across each input channel.

dRE = expander(thresholdValue) sets the Threshold property to thresholdValue.

dRE = expander(thresholdValue,ratioValue) sets the Ratio property to ratioValue.

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

Example: dRE = expander('AttackTime',0.01,'SampleRate',16000) creates a System object, dRE, with a 0.01 second attack time and a 16 kHz sample rate.

Properties

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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.

`Threshold` — Operation threshold (dB)
`–10` (default) | real scalar

Operation threshold in dB, specified as a real scalar.

Operation threshold is the level below which gain is applied to the input signal.

Tunable: Yes

Data Types: single | double

`Ratio` — Expansion ratio
`5` (default) | real scalar

Expansion ratio, specified as a real scalar greater than or equal to 1.

Expansion ratio is the input/output ratio for signals that undershoot the operation threshold.

Assuming a hard knee characteristic and a steady-state input such that x[n] dB < thresholdValue, the expansion ratio is defined as $R = \frac{(y [n] - T)}{(x [n] - T)}$ .

R is the expansion ratio.
y[n] is the output signal in dB.
x[n] is the input signal in dB.
T is the threshold in dB.

Tunable: Yes

Data Types: single | double

`KneeWidth` — Knee width (dB)
`0` (default) | real scalar

Knee width in dB, specified as a real scalar greater than or equal to 0.

Knee width is the transition area in the expansion characteristic.

For soft knee characteristics, the transition area is defined by the relation

$y = x + \frac{(1 - R) \times {(x - T - \frac{W}{2})}^{2}}{(2 \times W)}$

for the range $(2 \times | x - T |) \leq W$ .

y is the output level in dB.
x is the input level in dB.
R is the expansion ratio.
T is the threshold in dB.
W is the knee width in dB.

Tunable: Yes

Data Types: single | double

`AttackTime` — Attack time (s)
`0.05` (default) | real scalar

Attack time in seconds, specified as a real scalar greater than or equal to 0.

Attack time is the time it takes the expander gain to rise from 10% to 90% of its final value when the input goes below the threshold.

Tunable: Yes

Data Types: single | double

`ReleaseTime` — Release time (s)
`0.2` (default) | real scalar

Release time in seconds, specified as a real scalar greater than or equal to 0.

Release time is the time it takes the expander gain to drop from 90% to 10% of its final value when the input goes above the threshold.

Tunable: Yes

Data Types: single | double

`HoldTime` — Hold time (s)
`0.05` (default) | real scalar

Hold time in seconds, specified as a real scalar greater than or equal to 0.

Hold time is the period in which the applied gain is held constant before it starts moving toward its steady-state value. Hold time begins when the input level crosses the operation threshold.

Tunable: Yes

Data Types: single | double

`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 = dRE(audioIn)

[audioOut,gain] = dRE(audioIn)

Description

example

audioOut = dRE(audioIn) performs dynamic range expansion on the input signal, audioIn, and returns the expanded signal, audioOut. The type of dynamic range expansion is specified by the algorithm and properties of the expander System object, dRE.

[audioOut,gain] = dRE(audioIn) also returns the applied gain, in dB, at each input sample.

Input Arguments

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`audioIn` — Audio input to expander
matrix

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

Data Types: single | double

Output Arguments

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`audioOut` — Audio output from expander
matrix

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

Data Types: single | double

`gain` — Gain applied by expander (dB)
matrix

Gain applied by expander, 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)

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Specific to expander

`visualize`	Visualize static characteristic of dynamic range controller
`createAudioPluginClass`	Create audio plugin class that implements functionality of System object
`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

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

Property	Range	Mapping	Unit
`Threshold`	[–140, 0]	linear	dB
`Ratio`	[1, 50]	linear	none
`KneeWidth`	[0, 20]	linear	dB
`AttackTime`	[0, 4]	linear	seconds
`ReleaseTime`	[0, 4]	linear	seconds
`HoldTime`	[0, 4]	linear	seconds

Examples

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Expand Audio Signal

Open Live Script

Use dynamic range expansion to attenuate background noise from an audio signal.

Set up the dsp.AudioFileReader and audioDeviceWriter System objects.

frameLength = 1024;
fileReader = dsp.AudioFileReader( ...
    'Filename','Counting-16-44p1-mono-15secs.wav', ...
    'SamplesPerFrame',frameLength);
deviceWriter = audioDeviceWriter( ...
    'SampleRate',fileReader.SampleRate);

Corrupt the audio signal with Gaussian noise. Play the audio.

while ~isDone(fileReader)
    x = fileReader();
    xCorrupted = x + (1e-2/4)*randn(frameLength,1);
    deviceWriter(xCorrupted);
end

release(fileReader)

Set up the expander with a threshold of -40 dB, a ratio of 10, an attack time of 0.01 seconds, a release time of 0.02 seconds, and a hold time of 0 seconds. Use the sample rate of your audio file reader.

dRE = expander(-40,10, ...
    'AttackTime',0.01, ...
    'ReleaseTime',0.02, ...
    'HoldTime',0, ...
    'SampleRate',fileReader.SampleRate);

Set up the scope to visualize the signal before and after dynamic range expansion.

scope = timescope( ...
    'SampleRate',fileReader.SampleRate, ...
    'TimeSpanOverrunAction','Scroll', ...
    'TimeSpanSource','property','TimeSpan',16, ...
    'BufferLength',1.5e6, ...
    'YLimits',[-1 1], ...
    'ShowGrid',true, ...
    'ShowLegend',true, ...
    'Title','Corrupted vs. Expanded Audio');

Play the processed audio and visualize it on the scope.

while ~isDone(fileReader)
    x = fileReader();
    xCorrupted = x + (1e-2/4)*randn(frameLength,1);
    y = dRE(xCorrupted);
    deviceWriter(y);
    scope([xCorrupted,y])
end

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

Apply Split-Band De-Essing

Open Live Script

De-essing is the process of diminishing sibilant sounds in an audio signal. Sibilance refers to the s, z, and sh sounds in speech, which can be disproportionately emphasized during recording. es sounds fall under the category of unvoiced speech with all consonants and have a higher frequency than voiced speech. In this example, you apply split-band de-essing to a speech signal by separating the signal into high and low frequencies, applying an expander to diminish the sibilant frequencies, and then remixing the channels.

Create a dsp.AudioFileReader object and an audioDeviceWriter object to read from a sound file and write to an audio device. Listen to the unprocessed signal. Then release the file reader and device writer.

fileReader = dsp.AudioFileReader( ...
    'Sibilance.wav');
deviceWriter = audioDeviceWriter;

while ~isDone(fileReader)
    audioIn = fileReader();
    deviceWriter(audioIn);
end

release(deviceWriter)
release(fileReader)

Create an expander System object to de-ess the audio signal. Set the sample rate of the expander to the sample rate of the audio file. Create a two-band crossover filter with a crossover of 3000 Hz. Sibilance is usually found in this range. Set the crossover slope to 12. Plot the frequency response of the crossover filter to confirm your design visually.

dRExpander = expander( ...
    'Threshold',-50, ...
    'AttackTime', 0.05, ...
    'ReleaseTime',0.05, ...
    'HoldTime',0.005, ...
    'SampleRate',fileReader.SampleRate);

crossFilt = crossoverFilter( ...
    'NumCrossovers',1, ...
    'CrossoverFrequencies',3000, ...
    'CrossoverSlopes',12);
visualize(crossFilt)

Create a timescope object to visualize the original and processed audio signals.

scope = timescope( ...
    'SampleRate',fileReader.SampleRate, ...
    'TimeSpanOverrunAction','Scroll', ...
    'TimeSpanSource','Property','TimeSpan',4, ...
    'BufferLength',fileReader.SampleRate*8, ...
    'YLimits',[-1,1], ...
    'ShowGrid',true, ...
    'ShowLegend',true, ...
    'ChannelNames',{'Original','Processed'});

In an audio stream loop:

Read in a frame of the audio file.
Split the audio signal into two bands.
Apply dynamic range expansion to the upper band.
Remix the channels.
Write the processed audio signal to your audio device for listening.
Visualize the processed and unprocessed signals on a time scope.

As a best practice, release your objects once done.

while ~isDone(fileReader)
    audioIn = fileReader();
    
    [band1,band2] = crossFilt(audioIn);
    
    band2processed = dRExpander(band2);
    
    procAudio  = band1 + band2processed;
    
    deviceWriter(procAudio);
    
    scope([audioIn procAudio]);
end

release(deviceWriter)
release(fileReader)
release(scope)
release(crossFilt)
release(dRExpander)

Tune Expander Parameters

Open Live Script

Create a dsp.AudioFileReader to read in audio frame-by-frame. Create a audioDeviceWriter to write audio to your sound card. Create a expander to process the audio data. Call visualize to plot the static characteristic of the expander.

frameLength = 1024;
fileReader = dsp.AudioFileReader('Counting-16-44p1-mono-15secs.wav', ...
    'SamplesPerFrame',frameLength);
deviceWriter = audioDeviceWriter('SampleRate',fileReader.SampleRate);

dRE = expander(-40,10, ...
    'AttackTime',0.01, ...
    'ReleaseTime',0.02, ...
    'HoldTime',0, ...
    'SampleRate',fileReader.SampleRate);
visualize(dRE)

Create a timescope to visualize the original and processed audio.

scope = timescope( ...
    'SampleRate',fileReader.SampleRate, ...
    'TimeSpanSource','property','TimeSpan',1, ...
    'BufferLength',fileReader.SampleRate*4, ...
    'YLimits',[-1,1], ...
    'TimeSpanOverrunAction','Scroll', ...
    'ShowGrid',true, ...
    'LayoutDimensions',[2,1], ...
    'NumInputPorts',2, ...
    'Title','Original vs. Processed Audio (top) and Applied Gain in dB (bottom)');
scope.ActiveDisplay = 2;
scope.YLimits = [-300,0];
scope.YLabel = 'Gain (dB)';

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

parameterTuner(dRE)

In an audio stream loop:

Read in a frame of audio from the file.
Apply dynamic range expansion.
Write the frame of audio to your audio device for listening.
Visualize the original and processed audio, and the gain applied.

While streaming, tune parameters of the dynamic range expander and listen to the effect.

while ~isDone(fileReader)
    audioIn = fileReader();
    [audioOut,g] = dRE(audioIn);
    deviceWriter(audioOut);
    scope([audioIn(:,1),audioOut(:,1)],g(:,1));
    drawnow limitrate % required to update parameter
end

As a best practice, release your objects once done.

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

Algorithms

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The expander System object processes a signal frame by frame and element by element.

Convert Input Signal to dB

The N-point signal, x[n], is converted to decibels:

$x_{dB} [n] = 20 \times \log_{10} | x [n] |$

Gain Computer

x_dB[n] passes through the gain computer. The gain computer uses the static characteristic properties of the dynamic range expander to attenuate gain that is below the threshold.

If you specified a soft knee, the gain computer has the following static characteristic:

$x_{sc} (x_{dB}) = {\begin{matrix} T + (x_{dB} - T) \times R & x_{dB} < (T - \frac{W}{2}) \\ x_{dB} + \frac{(1 - R) {(x_{dB} - T - \frac{W}{2})}^{2}}{2 W} & (T - \frac{W}{2}) \leq x_{dB} \leq (T + \frac{W}{2}) \\ x_{dB} & x_{dB} > (T + \frac{W}{2}) \end{matrix},$

where T is the threshold, R is the ratio, and W is the knee width.

If you specified a hard knee, the gain computer has the following static characteristic:

$x_{sc} (x_{dB}) = {\begin{matrix} T + (x_{dB} - T) \times R & x_{dB} < T \\ x_{dB} & x_{dB} \geq T \end{matrix}$

The computed gain, g_c[n], is calculated as

$g_{c} [n] = x_{sc} [n] - x_{dB} [n] .$

Gain Smoothing

g_c[n] is smoothed using specified attack, release, and hold time properties:

$g_{s} [n] = {\begin{matrix} α_{A} g_{s} [n - 1] + (1 - α_{A}) g_{c} [n] \\ g_{s} [n - 1] \\ α_{R} g_{s} [n - 1] + (1 - α_{R}) g_{c} [n] \\ g_{s} [n - 1] \end{matrix} \begin{matrix} (C_{A} > T_{H}) & (g_{c} [n] \leq g_{s} [n - 1]) \\ C_{A} \leq T_{H} \\ (C_{R} > T_{H}) & (g_{c} [n] > g_{s} [n - 1]) \\ C_{R} \leq T_{H} \end{matrix}$

The attack time coefficient, α_A , is calculated as

$α_{A} = \exp (\frac{- \log (9)}{F s \times T_{A}}) .$

The release time coefficient, α_R , is calculated as

$α_{R} = \exp (\frac{- \log (9)}{F s \times T_{R}}) .$

T_A is the attack time period, specified by the AttackTime property. T_R is the release time period, specified by the ReleaseTime property. Fs is the input sampling rate, specified by the SampleRate property.

C_A and C_R are hold counters for attack and release, respectively. The limit, T_H , is determined by the HoldTime property.

Calculate and Apply Linear Gain

The smoothed gain in dB, g_s[n], is translated to a linear domain:

$g_{lin} [n] = 10^{(\frac{g_{s} [n]}{20})}$

The output of the dynamic range expander is given as

$y [n] = x [n] \times g_{lin} [n] .$

References

[1] Giannoulis, Dimitrios, Michael Massberg, and Joshua D. Reiss. "Digital Dynamic Range Compressor Design –– A Tutorial and Analysis." Journal of Audio Engineering Society. Vol. 60, Issue 6, 2012, pp. 399–408.

Documentation

expander

Description

Creation

Syntax

Description

Properties

Threshold — Operation threshold (dB) –10 (default) | real scalar

Ratio — Expansion ratio 5 (default) | real scalar

KneeWidth — Knee width (dB) 0 (default) | real scalar

AttackTime — Attack time (s) 0.05 (default) | real scalar

ReleaseTime — Release time (s) 0.2 (default) | real scalar

HoldTime — Hold time (s) 0.05 (default) | real scalar

SampleRate — Input sample rate (Hz) 44100 (default) | positive scalar

Usage

Syntax

Description

Input Arguments

audioIn — Audio input to expander matrix

Output Arguments

audioOut — Audio output from expander matrix

gain — Gain applied by expander (dB) matrix

Object Functions

Specific to expander

MIDI

Common to All System Objects

Examples

Expand Audio Signal

Apply Split-Band De-Essing

Tune Expander Parameters

Algorithms

Convert Input Signal to dB

Gain Computer

Gain Smoothing

Calculate and Apply Linear Gain

References

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™.

See Also

Topics

Audio Toolbox Documentation

Support

`Threshold` — Operation threshold (dB)
`–10` (default) | real scalar

`Ratio` — Expansion ratio
`5` (default) | real scalar

`KneeWidth` — Knee width (dB)
`0` (default) | real scalar

`AttackTime` — Attack time (s)
`0.05` (default) | real scalar

`ReleaseTime` — Release time (s)
`0.2` (default) | real scalar

`HoldTime` — Hold time (s)
`0.05` (default) | real scalar

`SampleRate` — Input sample rate (Hz)
`44100` (default) | positive scalar

`audioIn` — Audio input to expander
matrix

`audioOut` — Audio output from expander
matrix

`gain` — Gain applied by expander (dB)
matrix

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.