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:

1. Create the expander 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

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

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

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

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.

• 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 for which the (negative) gain is held before starting to decrease towards its steady state value when the input level drops below the 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

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 expander object.

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

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

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

The number of channels of the sidechain 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 = dRE(audioIn)

[audioOut,gain] = dRE(audioIn)

Description

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

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

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)

Specific to expander

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 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

Expand Audio Signal

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

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:

1. Read in a frame of the audio file.

2. Split the audio signal into two bands.

3. Apply dynamic range expansion to the upper band.

4. Remix the channels.

5. Write the processed audio signal to your audio device for listening.

6. 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

Create a dsp.AudioFileReader to read in audio frame-by-frame. Create an audioDeviceWriter to write audio to your sound card. Create an 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:

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

2. Apply dynamic range expansion.

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

4. 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 when done.

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

Sidechain Dynamic Range Expansion

Use the EnableSidechain input of an expander object to emulate an electronic drum controller, also known as a multipad. This technique is common in recording studio production and creates interesting changes to the timbre of an instrument. The sidechain signal controls the expansion on the input signal. Sidechain expansion decreases the amplitude of the input signal when the sidechain signal falls below the Threshold of the expander.

Prepare Audio Files

Convert the sidechain signal from stereo to mono.

[expanderSideChainStereo,Fs] = audioread('FunkyDrums-44p1-stereo-25secs.mp3');
expanderSideChainMono = (expanderSideChainStereo(:,1) + expanderSideChainStereo(:,2)) / 2;

Write the converted sidechain signal to a file.

audiowrite('convertedSidechainSig.wav',expanderSideChainMono,Fs);

Construct Audio Objects

Construct a dsp.AudioFileReader object for the input and sidechain signals. To allow the script to run indefinitely, change the playbackCount variable from 1 to Inf.

inputAudio = 'SoftGuitar-44p1_mono-10mins.ogg';
sidechainAudio  = 'convertedSidechainSig.wav';
playbackCount = 1;
inputAudioAFR = dsp.AudioFileReader(inputAudio,'PlayCount',playbackCount);
sidechainAudioAFR = dsp.AudioFileReader(sidechainAudio,'PlayCount',playbackCount);

Construct and visualize an expander object. Use a high Ratio, a soft KneeWidth, a fast AttackTime and ReleaseTime, and a short HoldTime.

dRE = expander('EnableSidechain',true,'Threshold',-20,'Ratio',6.5,...
    'KneeWidth',20,'AttackTime',0.84,'ReleaseTime',0.001,'HoldTime',0.0001);
visualize(dRE)

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

afw = audioDeviceWriter;

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

scope = timescope('NumInputPorts',3,...
                      'SampleRate',Fs,...
                      'TimeSpanSource','property',...
                      'TimeSpan',5,...
                       'TimeDisplayOffset',0,...
                      'LayoutDimensions',[3 1],...
                      'BufferLength',Fs*15,...
                      'TimeSpanOverrunAction','Scroll',...
                      'YLimits',[-1 1],...
                      'ShowGrid',true,...
                      'Title','Input Audio - Classical Guitar');
scope.ActiveDisplay = 2;
scope.YLimits = [-1 1];
scope.Title = 'Sidechain Audio - Drums';
scope.ShowGrid = true;
scope.ActiveDisplay = 3;
scope.YLimits = [-1 1];
scope.ShowGrid = true;
scope.Title = 'Expanded Input Audio - Classical Guitar';

Call parameterTuner to open a UI to tune parameters of the expander while streaming. Adjust the property values and listen to the effect in real time.

parameterTuner(dRE)

Create Audio Streaming Loop

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

The top panel of your timescope displays the input audio signal and the middle panel displays the sidechain audio signal. The bottom panel displays the expanded input audio signal.

Substitute different audio files for your inputAudio variable to create different textures and timbres in your drum mix.

while ~isDone(sidechainAudioAFR)
   inputAudioFrame = inputAudioAFR();
   sideChainAudioFrame = sidechainAudioAFR();
   expanderOutput  = dRE(inputAudioFrame,sideChainAudioFrame);
   afw(sideChainAudioFrame+expanderOutput); 
   scope(inputAudioFrame,sideChainAudioFrame,expanderOutput);
   drawnow limitrate;   % required to update parameter settings from UI
end

Release your objects.

release(inputAudioAFR)
release(sidechainAudioAFR)
release(dRE)
release(afw)
release(scope)

Algorithms

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:

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

Gain Computer

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

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

$$x_{\text{sc}}(x_{\text{dB}})=\{\begin{array}{cc}T+\left(x_{\text{dB}}-T\right)\times R& x_{\text{dB}}<\left(T-\frac{W}{2}\right)\\ x_{\text{dB}}+\frac{\left(1-R\right){\left(x_{\text{dB}}-T-\frac{W}{2}\right)}^2}{2W}& \left(T-\frac{W}{2}\right)\le x_{\text{dB}}\le \left(T+\frac{W}{2}\right)\\ x_{\text{dB}}& x_{\text{dB}}>\left(T+\frac{W}{2}\right)\end{array},$$

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:

$$x_{\text{sc}}(x_{\text{dB}})=\{\begin{array}{cc}T+\left(x_{\text{dB}}-T\right)\times R& x_{\text{dB}}<T\\ x_{\text{dB}}& x_{\text{dB}}\ge T\end{array}$$

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, release, and hold time properties:

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

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.

C_A is the hold counter for attack. 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:

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

The output of the dynamic range expander 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