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:

1. Create the limiter 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

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

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

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

for the range $$\left(2\times \left|x-T\right|\right)\le W$$.

• 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

EnableSidechain — Enable sidechain input

false (default) | true

Enable sidechain input, specified as true or false. This property determines the number of available inputs on the limiter object.

• false –– Sidechain input is disabled and the limiter object accepts one input: the audioIn data to be limited.

• true –– Sidechain input is enabled and the limiter object accepts two inputs: the audioIn data to be limited and the sidechain input used to compute the limiter gain.

The sidechain datatype and (frame) length must be the same as audioIn.

The number of channels of the sidechain input must be equal to the number of channels of audioIn or be equal to one. When the number of sidechain channels is one, the gain computed based on this channel is applied to all channels of audioIn. When the number of sidechain channels is equal to the number of channels in audioIn, the gain computed for each sidechain channel is applied to the corresponding channel of audioIn.

Tunable: No

Usage

Syntax

audioOut = dRL(audioIn)

[audioOut,gain] = dRL(audioIn)

Description

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.

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

Input Arguments

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

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)

Specific to limiter

visualize	Visualize static characteristic of dynamic range controller
staticCharacteristic	Return 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

Limit Audio Signal

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

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

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:

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

2. Apply dynamic range limiting.

3. 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)

Sidechain Ducking with Limiter

Use the EnableSidechain input of a limiter object to limit the amplitude level of a separate audio signal. The sidechain signal controls the dynamic range limiting of the input audio signal. When the sidechain signal exceeds the limiter Threshold, the limiter activates and limits the amplitude of the input signal. When the sidechain signal level falls below the threshold, the audio input returns to its original amplitude. For a detailed comparison of compression and dynamic range limiting, see Compare Dynamic Range Limiter and Compressor.

Prepare Audio Files

In this section, you resample and zero-pad a speech file to use as input to the EnableSidechain property of your limiter object.

Read in an audio signal. Resample it to match the sample rate of the input audio signal (44.1 kHz).

targetFs = 44100;
[originalSpeech,originalFs] = audioread('Rainbow-16-8-mono-114secs.wav');
resampledSpeech = resample(originalSpeech,targetFs,originalFs);

Pad the beginning of the resampled signal with 10 seconds worth of zeros. This allows the input audio signal to be clearly heard before any limiting is applied.

resampledSpeech = [zeros(10*targetFs,1);resampledSpeech];

Normalize the amplitude to avoid potential clipping.

resampledSpeech = resampledSpeech ./ max(resampledSpeech);

Write the resampled, zero-padded, and normalized sidechain signal to a file.

audiowrite('resampledSpeech.wav',resampledSpeech,targetFs);

Construct Audio Objects

Construct a dsp.AudioFileReader object for the input and sidechain signals. Using the ReadRange property of the AudioFileReader, select the second verse of the input signal and the first 26.5 seconds of the sidechain signal for playback. To allow the script to run indefinitely, change the playbackCount variable from 1 to Inf.

inputAudio = 'SoftGuitar-44p1_mono-10mins.ogg';
sidechainAudio  = 'resampledSpeech.wav';
playbackCount = 1;
inputAudioAFR = dsp.AudioFileReader(inputAudio,'PlayCount',playbackCount,'ReadRange',...
    [115*targetFs round(145.4*targetFs)]);
sidechainAudioAFR = dsp.AudioFileReader(sidechainAudio,'PlayCount',playbackCount,...
    'ReadRange',[1 round(26.5*targetFs)]);

Construct a limiter object. Use a fast AttackTime, and a moderately slow ReleaseTime. These settings are ideal for voice-over work. The fast attack time ensures that the input audio is limited almost immediately after the sidechain signal surpasses the limiter threshold. The slow release time ensures the limiting on the input audio lasts through any potential short silent regions in the sidechain signal.

iAmYourLimiter = limiter('EnableSidechain',true,...
               'SampleRate',targetFs,...
               'Threshold',-48,...
               'AttackTime',0.01,...
               'ReleaseTime',1.75);

Construct an audioDeviceWriter object to play the sidechain and input signals.

afw = audioDeviceWriter;

Construct a timescope object to view the uncompressed input signal, the sidechain signal, as well as the compressed input signal.

scope = timescope('NumInputPorts',3,...
                      'SampleRate',targetFs,...
                      'TimeSpanSource','property',...
                      'TimeSpan',5,...
                       'TimeDisplayOffset',0,...
                      'LayoutDimensions',[3 1],...
                      'BufferLength',targetFs*15,...
                      'TimeSpanOverrunAction','Scroll',...
                      'YLimits',[-1 1],...
                      'ShowGrid',true,...
                      'Title','Original Input Audio - Guitar');
scope.ActiveDisplay = 2;
scope.YLimits = [-1 1];
scope.Title = 'Sidechain Audio - Speech';
scope.ShowGrid = true;
scope.ActiveDisplay = 3;
scope.YLimits = [-1 1];
scope.ShowGrid = true;
scope.Title = 'Dynamic Range Limited Input Audio - Guitar';

Create Audio Streaming Loop

Read in a frame of audio from your input and sidechain signals. Process your input and sidechain signals with your limiter object. Playback your processed audio signals and display the audio data using a timescope object.

The top panel of your timescope displays the unprocessed input audio signal and the middle panel displays the sidechain audio signal. The bottom panel displays the limited input audio signal. Notice the amplitudes of the signals in the top and bottom panels are identical until the sidechain signal begins. Once the sidechain signal activates, the amplitude in the bottom panel decreases. Once the sidechain signal ends, the amplitude of the bottom panel returns to its original level.

while ~isDone(inputAudioAFR)
   inputAudioFrame = inputAudioAFR();
   sideChainAudioFrame = sidechainAudioAFR();
   limiterOutput  = iAmYourLimiter(inputAudioFrame,sideChainAudioFrame);
   afw(sideChainAudioFrame+limiterOutput); 
   scope(inputAudioFrame,sideChainAudioFrame,limiterOutput);
end

Release your objects.

release(inputAudioAFR)
release(sidechainAudioAFR)
release(iAmYourLimiter)
release(afw)
release(scope)

Algorithms

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:

$$x_{\text{dB}}[n]=20\times {\log }_{10}\left|x[n]\right|$$

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:

$$x_{\text{sc}}(x_{\text{dB}})=\{\begin{array}{cc}{x}_{\text{dB}}& x_{\text{dB}}<\left(T-\frac{W}{2}\right)\\ x_{\text{dB}}-\frac{{\left(x_{\text{dB}}-T+\frac{W}{2}\right)}^2}{2W}& \begin{array}{c}\\ \\ \end{array}\left(T-\frac{W}{2}\right)\le x_{\text{dB}}\le \left(T+\frac{W}{2}\right)\\ T& x_{\text{dB}}>\left(T+\frac{W}{2}\right)\end{array},$$

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:

$$x_{\text{sc}}(x_{\text{dB}})=\{\begin{array}{cc}{x}_{\text{dB}}& x_{\text{dB}}<T\\ T& x_{\text{dB}}\ge T\end{array}$$

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

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

Gain Smoothing

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

$$g_{\text{s}}[n]=\{\begin{array}{cc}{\alpha }_{\text{A}}{g}_{\text{s}}[n-1]+(1-{\alpha }_{\text{A}})g_{\text{c}}[n],& g_{\text{c}}[n]\le g_{\text{s}}[n-1]\\ {\alpha }_{\text{R}}{g}_{\text{s}}[n-1]+(1-{\alpha }_{\text{R}})g_{\text{c}}[n],& g_{\text{c}}[n]>g_{\text{s}}[n-1]\end{array}$$

The attack time coefficient, α_A , is calculated as

$${\alpha }_{\text{A}}=\exp \left(\frac{-\log (9)}{Fs\times T_{\text{A}}}\right).$$

The release time coefficient, α_R , is calculated as

$${\alpha }_{\text{R}}=\exp \left(\frac{-\log (9)}{Fs\times T_{\text{R}}}\right).$$

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:

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

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]:

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

Calculate and Apply Linear Gain

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

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

The output of the dynamic range limiter is given as

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

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.

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 R2016a