limiter

Dynamic range limiter

Description

The limiter System object™ performs brick-wall dynamic range limiting independently across each input channel. Dynamic range limiting suppresses the volume of loud sounds that cross a given threshold. It uses specified attack and release times to achieve a smooth applied gain curve. Properties of the limiter System object specify the type of dynamic range limiting.

To perform dynamic range limiting:

Create the limiter 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

dRL = limiter

dRL = limiter(thresholdValue)

dRL = limiter(___,Name,Value)

Description

dRL = limiter creates a System object, dRL, that performs brick-wall dynamic range limiting independently across each input channel.

dRL = limiter(thresholdValue) sets the Threshold property to thresholdValue.

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

Example: dRL = limiter('AttackTime',0.01,'SampleRate',16000) creates a System object, dRL, with a 10 ms attack time and a sample rate of 16 kHz.

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 above which gain is applied to the input signal.

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 limiter characteristic.

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

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

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

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

Tunable: Yes

Data Types: single | double

`AttackTime` — Attack time (s)
`0` (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 limiter gain to rise from 10% to 90% of its final value when the input goes above 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 limiter gain to drop from 90% to 10% of its final value when the input goes below the threshold.

Tunable: Yes

Data Types: single | double

`MakeUpGainMode` — Make-up gain mode
`'Property'` (default) | `'Auto'`

Make-up gain mode, specified as 'Auto' or 'Property'.

'Auto' –– Make-up gain is applied at the output of the dynamic range limiter such that a steady-state 0 dB input has a 0 dB output.
'Property' –– Make-up gain is set to the value specified in the MakeUpGain property.

Tunable: No

Data Types: char | string

`MakeUpGain` — Make-up gain (dB)
`0` (default) | real scalar

Make-up gain in dB, specified as a real scalar.

Make-up gain compensates for gain lost during limiting. It is applied at the output of the dynamic range limiter.

Tunable: Yes

Dependencies

To enable this property, set MakeUpGainMode to 'Property'.

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 = dRL(audioIn)

[audioOut,gain] = dRL(audioIn)

Description

example

audioOut = dRL(audioIn)performs dynamic range limiting on the input signal, audioIn, and returns the limited signal, audioOut. The type of dynamic range limiting is specified by the algorithm and properties of the limiter System object, dRL.

example

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

Input Arguments

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`audioIn` — Audio input to limiter
matrix

Audio input to the limiter, 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 limiter
matrix

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

Data Types: single | double

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

Gain applied by the limiter, 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 `limiter`

`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 limiter System object to user-facing parameters:

Property	Range	Mapping	Unit
`Threshold`	[–50, 0]	linear	dB
`KneeWidth`	[0, 20]	linear	dB
`AttackTime`	[0, 4]	linear	seconds
`ReleaseTime`	[0, 4]	linear	seconds
`MakeUpGain` (available when you set `MakeUpGainMode` to `'Property'`)	[–10, 24]	linear	dB

Examples

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Limit Audio Signal

Open Live Script

Use dynamic range limiting to suppress the volume of loud sounds.

Set up the dsp.AudioFileReader and audioDeviceWriter System objects™.

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

Set up the limiter to have a threshold of -15 dB, an attack time of 0.005 seconds, and a release time of 0.1 seconds. Set make-up gain to 0 dB (default). To specify this value, set the make-up gain mode to 'Property' but do not specify the MakeUpGain property. Use the sample rate of your audio file reader.

dRL = limiter(-15, ...
    'AttackTime',0.005, ...
    'ReleaseTime',0.1, ...
    'MakeUpGainMode','Property', ...
    'SampleRate',fileReader.SampleRate);

Set up a time scope to visualize the original signal and the limited signal.

scope = timescope( ...
    'SampleRate',fileReader.SampleRate, ...
    'TimeSpanOverrunAction','Scroll', ...
    'TimeSpanSource','property',...
    'TimeSpan',1, ...
    'BufferLength',44100*4, ...
    'YLimits',[-1 1], ...
    'ShowGrid',true, ...
    'LayoutDimensions',[2,1], ...
    'NumInputPorts',2, ...
    'ShowLegend',true, ...
    'Title',['Original vs. Limited Audio (top)' ...
    ' and Limiter Gain in dB (bottom)']);

Play the processed audio and visualize it on the scope.

while ~isDone(fileReader)
    x = fileReader();
    [y,g] = dRL(x);
    deviceWriter(y);
    x1 = x(:,1);
    y1 = y(:,1);
    g1 = g(:,1);
    scope([x1,y1],g1);
end

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

Compare Dynamic Range Limiter and Compressor

Open Live Script

A dynamic range limiter is a special type of dynamic range compressor. In limiters, the level above an operational threshold is hard limited. In the simplest implementation of a limiter, the effect is equivalent to audio clipping. In compressors, the level above an operational threshold is lowered using a specified compression ratio. Using a compression ratio results in a smoother processed signal.

Compare Limiter and Compressor Applied to Sinusoid

Create a limiter System object™ and a compressor System object. Set the AttackTime and ReleaseTime properties of both objects to zero. Create an audioOscillator System object to generate a sinusoid with Frequency set to 5 and Amplitude set to 0.1.

dRL = limiter('AttackTime',0,'ReleaseTime',0);
dRC = compressor('AttackTime',0,'ReleaseTime',0);

osc = audioOscillator('Frequency',5,'Amplitude',0.1);

Create a time scope to visualize the generated sinusoid and the processed sinusoid.

scope = timescope( ...
    'SampleRate',osc.SampleRate, ...
    'TimeSpanSource','Property','TimeSpan',2, ...
    'BufferLength',osc.SampleRate*4, ...
    'TimeSpanOverrunAction','Scroll', ...
    'ShowGrid',true, ...
    'LayoutDimensions',[2 1], ...
    'NumInputPorts',2);
scope.ActiveDisplay = 1;
scope.Title = 'Original Signal vs. Limited Signal';
scope.YLimits = [-1,1]; 
scope.ActiveDisplay = 2;
scope.Title = 'Original Signal vs. Compressed Signal';
scope.YLimits = [-1,1];

In an audio stream loop, visualize the original sinusoid and the sinusoid processed by a limiter and a compressor. Increment the amplitude of the original sinusoid to illustrate the effect.

while osc.Amplitude < 0.75
    x = osc();
    
    xLimited    = dRL(x);
    xCompressed = dRC(x);
    
    scope([x xLimited],[x xCompressed]);
    
    osc.Amplitude = osc.Amplitude + 0.0002;
end
release(scope)

release(dRL)
release(dRC)
release(osc)

Compare Limiter and Compressor Applied to Audio Signal

Compare the effect of dynamic range limiters and compressors on a drum track. Create a dsp.AudioFileReader System object and a audioDeviceWriter System object to read audio from a file and write to your audio output device. To emphasize the effect of dynamic range control, set the operational threshold of the limiter and compressor to -20 dB.

dRL.Threshold = -20;
dRC.Threshold = -20;

fileReader = dsp.AudioFileReader('FunkyDrums-44p1-stereo-25secs.mp3');
deviceWriter = audioDeviceWriter('SampleRate',fileReader.SampleRate);

Read successive frames from an audio file in a loop. Listen to and compare the effect of dynamic range limiting and dynamic range compression on an audio signal.

numFrames = 300;

fprintf('Now playing original signal...\n')

Now playing original signal...

for i = 1:numFrames
    x = fileReader();
    deviceWriter(x);
end
reset(fileReader);

fprintf('Now playing limited signal...\n')

Now playing limited signal...

for i = 1:numFrames
    x = fileReader();
    xLimited = dRL(x);
    deviceWriter(xLimited);
end
reset(fileReader);

fprintf('Now playing compressed signal...\n')

Now playing compressed signal...

for i = 1:numFrames
    x = fileReader();
    xCompressed = dRC(x);
    deviceWriter(xCompressed);
end
    
release(fileReader)
release(deviceWriter)
release(dRC)
release(dRL)

Tune Limiter 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 limiter to process the audio data.

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

dRL = limiter('SampleRate',fileReader.SampleRate);

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

parameterTuner(dRL)

In an audio stream loop:

Read in a frame of audio from the file.
Apply dynamic range limiting.
Write the frame of audio to your audio device for listening.

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

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

As a best practice, release your objects once done.

release(deviceWriter)
release(fileReader)
release(dRL)

Algorithms

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The limiter 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 limiter to brick-wall gain that is above the threshold.

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

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

where T is the threshold and W is the knee width.

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

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

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 and release time:

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

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.

Calculate and Apply Make-up Gain

If MakeUpGainMode is set to the default 'Auto', the make-up gain is calculated as the negative of the computed gain for a 0 dB input:

$M = {- x_{sc} |}_{x_{dB} = 0}$

Given a steady-state input of 0 dB, this configuration achieves a steady-state output of 0 dB. The make-up gain is determined by the Threshold and KneeWidth properties. It does not depend on the input signal.

The make-up gain, M, is added to the smoothed gain, g_s[n]:

$g_{m} [n] = g_{s} [n] + M$

Calculate and Apply Linear Gain

The calculated gain in dB, g_m[n], is translated to a linear domain:

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

The output of the dynamic range limiter 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

limiter

Description

Creation

Syntax

Description

Properties

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

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

AttackTime — Attack time (s) 0 (default) | real scalar

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

MakeUpGainMode — Make-up gain mode 'Property' (default) | 'Auto'

MakeUpGain — Make-up gain (dB) 0 (default) | real scalar

Dependencies

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

Usage

Syntax

Description

Input Arguments

audioIn — Audio input to limiter matrix

Output Arguments

audioOut — Audio output from limiter matrix

gain — Gain applied by limiter (dB) matrix

Object Functions

Specific to limiter

MIDI

Common to All System Objects

Examples

Limit Audio Signal

Compare Dynamic Range Limiter and Compressor

Tune Limiter Parameters

Algorithms

Convert Input Signal to dB

Gain Computer

Gain Smoothing

Calculate and Apply Make-up Gain

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

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

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

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

`MakeUpGainMode` — Make-up gain mode
`'Property'` (default) | `'Auto'`

`MakeUpGain` — Make-up gain (dB)
`0` (default) | real scalar

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

`audioIn` — Audio input to limiter
matrix

`audioOut` — Audio output from limiter
matrix

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

Specific to `limiter`

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