Instant Audio Processing with Web Audio

Building an equalizer using BiquadFilterNode (Advanced)

One of the big advantages of using Web Audio is its built-in supporting for constructing sophisticated audio effects in real time. In this recipe, we'll use Web Audio's BiquadFilterNode functionality to build a 5-band equalizer. The implementation includes a real-time equalizer frequency response chart display so that we can visualize the equalizer's impact on the sound output.

Getting ready

This time, we're building our recipe from an audio mixer template so that we can focus specifically on the equalizer implementation (you'll find the template source code in the code bundle at tools/ AudioMixerTemplate). I recommend familiarizing yourself with its implementation—the implementation uses the Web Audio techniques and features we've covered so far.

The complete source code for this recipe is available in the code bundle at recipes/Recipe6_1.

How to do it...

Start with a clean copy of the audio mixer template. The template bundle is located at tools/AudioMixerTemplate in the code bundle.
Open index.html in a text editor.

We'll add our equalizer controls to the HTML section:

<div id="appwindow">
<h2>Audio Mixer</h2>
<form>
    <div class="audiopanel" style="text-align: center;">
        <h3>Equalizer</h3>
        <canvas id="eqcanvas" width="400" height="250">
        </canvas><br>
        <div style="display: inline-block; margin: 0 20px;">
            <span id="eq_label_0"></span><br>
            <div style="display: inline-block;">
                <span id="eq_gain_0" style="display: inline-block; height: 100px; margin: 10px;"></span><br>
                <span>Gain</span>
            </div>
        </div>
        <div style="display: inline-block; margin: 0 20px;">
            <span id="eq_label_1"></span><br>
            <div style="display: inline-block;">
                <span id="eq_gain_1" style="display: inline-block; height: 100px; margin: 10px;"></span><br>
                <span>Gain</span>
            </div>
            <div style="display: inline-block;">
                <span id="eq_q_1" style="display: inline-block; height: 100px; margin: 10px;"></span><br>
                <span>Q</span>
            </div>
        </div>
        <div style="display: inline-block; margin: 0 20px;">
            <span id="eq_label_2"></span><br>
            <div style="display: inline-block;">
                <span id="eq_gain_2" style="display: inline-block; height: 100px; margin: 10px;"></span><br>
                <span>Gain</span>
            </div>
            <div style="display: inline-block;">
                <span id="eq_q_2" style="display: inline-block; height: 100px; margin: 10px;"></span><br>
                <span>Q</span>
            </div>
        </div>
        <div style="display: inline-block; margin: 0 20px;">
            <span id="eq_label_3"></span><br>
            <div style="display: inline-block;">
                <span id="eq_gain_3" style="display: inline-block; height: 100px; margin: 10px;"></span><br>
                <span>Gain</span>
            </div>
            <div style="display: inline-block;">
                <span id="eq_q_3" style="display: inline-block; height: 100px; margin: 10px;"></span><br>
                <span>Q</span>
            </div>
        </div>
        <div style="display: inline-block; margin: 0 20px;">
            <span id="eq_label_4"></span><br>
            <div style="display: inline-block;">
                <span id="eq_gain_4" style="display: inline-block; height: 100px; margin: 10px;"></span><br>
                <span>Gain</span>
            </div>
        </div>
    </div>

    ...

</form>
</div>

We'll add the equalizer functionality to AudioLayer. In its class constructor, we integrate the equalizer node instances into the audio layer node graph:

function AudioLayer( audioContext ) {
    this.audioContext = audioContext;

    // Create the volume GainNode
    this.volNode = audioContext.createGain();

    // Expose the gain control
    this.gain = this.volNode.gain;

    // Calculate the frequency metrics
    var EQ_FREQ_MARGIN = 1000;  // margin for equalizer range
    var NODES_NUM = 5;          // number of equalizer nodes

    var tempFilter = audioContext.createBiquadFilter();
    var freqMin = tempFilter.frequency.minValue 
                  + EQ_FREQ_MARGIN;
    var freqMax = tempFilter.frequency.maxValue 
                  - EQ_FREQ_MARGIN;
    var freqStep = (freqMax - freqMin) / (NODES_NUM - 1);

    // Create the equalizer nodes to cover the
    // frequency spectrum evenly
    var headNode = audioContext.destination;
    this.eqNodes = [];
    this.eqParms = [];
    for( var nodeIndex = 0;
         nodeIndex < NODES_NUM;
         nodeIndex++ ) {
        // Set up the filter
        var eqNode = audioContext.createBiquadFilter();

        eqNode.frequency.value =
                Math.round(freqMin + (nodeIndex * freqStep));

        if( nodeIndex == 0 ) {
            // Use a low shelf filter for the lowest filter
            eqNode.type = "lowshelf";
        } else if( nodeIndex == NODES_NUM - 1 ) {
            // Use a high shelf filter for the lowest filter
            eqNode.type = "highshelf";
        } else {
            eqNode.type = "peaking";
        }

        // Connect to the previous node
        eqNode.connect( headNode );

        // Keep track of the node
        this.eqNodes.push( eqNode );

        // Add the tweakable audio parameters to the
        // equalizer parameter array
        this.eqParms.push({
            frequency:  eqNode.frequency,
            Q:          eqNode.Q,
            gain:       eqNode.gain
        } );

        // Keep track of the head node
        headNode = eqNode;
    }

    // Connect the volume control to the last head node
    this.volNode.connect( headNode );
}

We'll add the function AudioLayer.getEqResponse() to return the equalizer's frequency response graph:

AudioLayer.prototype.getEqResponse = function( freqs ) {
    var magCombined = new Float32Array( freqs.length );

    // Get the frequency response from all the eq nodes
    var eqNodes = this.eqNodes;
    var magCurr = new Float32Array( freqs.length );
    var phaseCurr = new Float32Array( freqs.length );
    for(var eqIndex=0; eqIndex<eqNodes.length; eqIndex++ ) {
        eqNodes[ eqIndex ].getFrequencyResponse(
                freqs,
                magCurr,
                phaseCurr );

        // Combine the node magnitudes
        for( var freqIndex = 0; 
             freqIndex < freqs.length; 
             freqIndex++ ) {
            var magDb = Math.log(magCurr[ freqIndex ]) * 20;
            magCombined[ freqIndex ] += magDb;
        }
    }

    return magCombined;
};

In WebAudioApp, we add the member function updateEqGraphic() for rendering the equalizer's response graph:

WebAudioApp.prototype.updateEqGraphic = function() {
    var FREQ_MIN  = 10;           // Hz
    var FREQ_MAX  = Math.round(
            this.audioContext.sampleRate * 0.5 );

    var MAG_MIN = -80;
    var MAG_MAX = 80;

    // Build the frequency response sampler list
    if( this.eqFreqs == null ) {
        var FREQS_NUM = 100;
        var FREQ_STEP = (FREQ_MAX - FREQ_MIN) 
                           / (FREQS_NUM - 1);

        this.eqFreqs = new Float32Array( FREQS_NUM );
        for( var freqIndex = 0; 
                 freqIndex < FREQS_NUM; 
                freqIndex++ ) {
            this.eqFreqs[freqIndex] = Math.round( 
                FREQ_MIN + (freqIndex * FREQ_STEP) );
         }
    }

    // If we have an update scheduled, don't do anything
    if( this.eqUpdateHandle != null )
        return;

    // Schedule the graphic update
    this.eqUpdateHandle = later( 0, function(){
        this.eqUpdateHandle = null;

        var canvasCtx       = $("#eqcanvas")[0]
                              .getContext( "2d" );
        var canvasWidth     = canvasCtx.canvas.width;
        var canvasHeight    = canvasCtx.canvas.height;

        // Calculate the draw steps
        var stepX = canvasWidth / (FREQ_MAX - FREQ_MIN);
        var stepY = canvasHeight / (MAG_MAX - MAG_MIN );

        // Clear the canvas
        canvasCtx.fillStyle = "#f0f0f0";
        canvasCtx.fillRect( 0, 0, canvasWidth, canvasHeight );

        // Draw the frequency response
        var eqFreqs = this.eqFreqs;
        var eqMag   = this.musicLayer.getEqResponse(eqFreqs);
        var firstPt = true;
        canvasCtx.beginPath();
        for(var index = 0; index < eqFreqs.length; index++ ) {
            var x = Math.round( 
                        (eqFreqs[index] - FREQ_MIN) * stepX );
            var y = canvasHeight - Math.round( 
                        (eqMag[index] - MAG_MIN) * stepY );

            if( firstPt ) {
                firstPt = false;
                canvasCtx.moveTo( x, y );
            } else {
                canvasCtx.lineTo( x, y );
            }
        }

        canvasCtx.strokeStyle = "#ff0000";  // red line
        canvasCtx.stroke();

        // Draw the neutral response line
        var neutralY = canvasHeight -
                Math.round( (0 - MAG_MIN) * stepY );

        canvasCtx.beginPath();
        canvasCtx.moveTo( 0, neutralY );
        canvasCtx.lineTo( canvasWidth, neutralY );

        canvasCtx.strokeStyle = "#3030ff";  // blue line
        canvasCtx.stroke();
    }, this );
};

Finally, we link the equalizer's HTML control widgets to its corresponding equalizer node and set up the equalizer response graph rendering in WebAudioApp.start():

WebAudioApp.prototype.start = function() {

    ..

    // Initialize the volume slider
    this.initSlider(
            "#musicvol",
            this.musicLayer.gain,
            0.01,
            "music volume" );

    // Initialize the equalizer sliders
    var eqParms = this.musicLayer.eqParms;
    for( var nodeIndex = 0; 
         nodeIndex < eqParms.length; 
         nodeIndex++ ) {

        var parms = eqParms[ nodeIndex ];
        var freqValue = String( parms.frequency.value );
        this.initSlider(
            "#eq_gain_" + nodeIndex,
            parms.gain,
            0.01,
            "Gain " + freqValue + " Hz",
            {
                orientation: "vertical"
            } );
        this.initSlider(
            "#eq_q_" + nodeIndex,
            parms.Q,
            0.01,
            "Q " + freqValue + " Hz",
            {
                orientation: "vertical",
                min: 0.25,
                max: 2.5
            } );

        // Set up the label
        $("#eq_label_" + nodeIndex).text( freqValue + " Hz" );
    }

    // Set up equalizer graphics update on slider change
    var me = this;
    $( "[id^=eq_]" ).on( "slide", function() {
        me.updateEqGraphic();
    } );

    // Refresh the equalizer graphics
    this.updateEqGraphic();
};

Launch the application test URL in a web browser (http://localhost/myaudiomixer) to see the end result. Have fun playing with the mixer!

How it works...

Web Audio offers a variety of built-in audio processing nodes which can be combined to build sophisticated audio effects. One of these audio processor node types is BiquadFilterNode.

BiquadFilterNode is actually a collection of common low order filters. These low order filters form the building blocks for tonal control and more advanced filters. The following is its class definition:

The type attribute indicates the filter type represented by the instance as shown in the following code. Filter types support low-pass, high-pass, low-shelf, high-shelf, and notch filters. We'll discuss this in detail later:
```
interface BiquadFilterNode : AudioNode {

    var type:String;
```
The frequency, detune, Q, and gain audio parameters affect how the filter processes its input signal. The units for frequency, detune, and gain are Hz, cents (1/100th of a semitone), and dB (decibels—a logarithmic scale for measuring gain), respectively. The units for Q vary depending on the type of filter. In fact, the audio parameters are interpreted differently depending on the type of filter:
```
    var frequency:AudioParam;       // in Hz
    var detune:AudioParam;          // in Cents
    var Q:AudioParam;               // Quality factor
    var gain:AudioParam             // in dB
```
Note
The filter's applied frequency is the combined result of the frequency and detune audio parameters.
The getFrequencyResponse() method returns the frequency response for a list of frequencies as shown in the following code. Applications specify the list of frequencies (in Hz) to sample through the frequency parameter. The function then returns the magnitude and phase values associated with the frequencies through the array parameters magResponse and phaseResponse. Therefore, it is important that the frequency, magResponse, and phaseResponse arrays are of the same size:
```
    function getFrequencyResponse(
                 frequency:Float32Array,        // in
                 magResponse:Float32Array,      // out
                 phaseResponse:Float32Array );  // out
};
```
The magnitude values are returned as a gain multiplier while the phase values are returned in radians.
Tip
Make sure that the getFrequencyResponse() parameters are the Float32Array objects instead of Array objects! When the function parameters are not the Float32Array objects, the function seems to operate normally, except that the method will exit without filling magResponse and phaseResponse with the desired information.

The following table summarizes the BiquadFilterNode filters and how their audio parameters are interpreted:

Description	`type`	Interpretation
Description	`type`	`Frequency`	`gain`	`Q`
Low-pass filter	`lowpass`	The cutoff frequency	Unused	The frequency drop-off steepness at the cutoff frequency
High-pass filter	`highpass`	The cutoff frequency	Unused	The frequency drop-off steepness at the cutoff frequency
Band-pass filter	`bandpass`	Center of the frequency band	Unused	The width of the frequency band
Notch filter	`notch`	Center of the frequency band	Unused	The width of the frequency band
Low-shelf filter	`lowshelf`	The upper limit of the frequencies boosted/attenuated	The boost or attenuation level	Unused
High-shelf filter	`highshelf`	The lower limit of the frequencies boosted/attenuated	The boost or attenuation level	Unused
Peaking filter	`peaking`	Center of the frequency band which is boosted/attenuated	The boost or attenuation level	The width of the frequency band
All-pass filter	`allpass`	Center frequency where the phase transition occurs	Unused	The transition steepness

The following is the graphical representation of the filter types:

In our recipe, we build a 5-band equalizer by:

Inserting five BiquadFilterNode instances into the node graph—one for each equalizer band. These instances must be inserted in a series so that the output signal is a product of all the BiquadFilterNode instances.
Exposing each BiquadFilterNode instance's gain and Q audio parameters so that users can tune the equalizer behavior.

The following is the resulting node graph:

Let's take a look at the equalizer set up code in the AudioLayer class constructor:

First, we'll need to determine the default frequencies for all the equalizer bands. In order to determine this, we'll need to know the supported frequency range. We create a temporary BiquadFilterNode instance and sample its frequency audio parameter to get the frequency range. This range is reduced by EQ_FREQ_MARGIN at both ends yielding the cutoff frequencies for the lowest and highest equalizer bands, freqMin and freqMax. It's important that the equalizer frequency range has margins on both ends to ensure that the band filters at the ends have enough frequency range to operate properly. Finally, we calculate the default frequency step size between bands and store it in freqStep:
```
function AudioLayer( audioContext ) {

    ...
    // Calculate the frequency metrics
    var EQ_FREQ_MARGIN = 1000;  // margin for equalizer range
    var NODES_NUM = 5;          // number of equalizer nodes

    var tempFilter = audioContext.createBiquadFilter();
    var freqMin = tempFilter.frequency.minValue 
                  + EQ_FREQ_MARGIN;
    var freqMax = tempFilter.frequency.maxValue 
                  - EQ_FREQ_MARGIN;
    var freqStep = (freqMax - freqMin) / (NODES_NUM - 1);
```

We instantiate BiquadFilterNode for each equalizer band and set its frequency audio parameter to its default band frequency:

    // Create the equalizer nodes to cover the
    // frequency spectrum evenly
    var headNode = audioContext.destination;
    this.eqNodes = [];
    this.eqParms = [];

    for( var nodeIndex = 0;
         nodeIndex < NODES_NUM;
         nodeIndex++ ) {
        // Set up the filter
        var eqNode = audioContext.createBiquadFilter();
        eqNode.frequency.value =
            Math.round( freqMin + (nodeIndex * freqStep) );

We use a combination of peaking filters, low-shelf filters, and high-shelf filters to model the equalizer's frequency response as shown in the following code. We use a low-shelf filter and a high-shelf filter for the lowest frequency and the highest frequency equalization bands, respectively. We use peaking filters for all the other bands:
```
        if( nodeIndex == 0 ) {
            // Use a low shelf filter for the lowest filter
            eqNode.type = "lowshelf";
        } else if( nodeIndex == NODES_NUM - 1 ) {
            // Use a high shelf filter for the lowest filter
            eqNode.type = "highshelf";
        } else {
            eqNode.type = "peaking";
        }
```
Tip
Low-shelf/high-shelf versus peaking filters
It's good practice to use low-shelf/high-shelf filters over peaking filters when dealing with filtering at the frequency extremes. In theory, peaking filters should behave like low-shelf/high-shelf filters when used at the frequency extremes. In practice, the peaking filter frequency response deteriorates rapidly as it approaches the extremes. On the other hand, the low-shelf/high-shelf frequency response remains consistent.

We connect the BiquadFilterNode instances in a series to the audio context's AudioDestinationNode instance. Then, we cache each instance's frequency, Q, and gain audio parameters in AudioLayer.eqParms so that the applications can access the equalizer controllers directly:

        // Connect to the previous node
        eqNode.connect( headNode );

        // Keep track of the node
        this.eqNodes.push( eqNode );

        // Add the tweakable audio parameters to the
        // equalizer parameter array
        this.eqParms.push({
            frequency:  eqNode.frequency,
            Q:          eqNode.Q,
            gain:       eqNode.gain
        } );

        // Keep track of the head node
        headNode = eqNode;

Finally, we connect the layer's volume control, AudioLayer.volNode, to the BiquadFilterNode chain. The volume control is treated as the audio layer's "terminal" AudioNode instance—all source AudioNode instances must be connected to the volume control node in order to be considered as a part of the AudioLayer instance's node graph:
```
    }

    // Connect the volume control to the last head node
    this.volNode.connect( headNode );
}
```

AudioLayer.getEqResponse() implements the logic for calculating the equalizer's frequency response:

Using biquadFilterNode.getFreqResponse(), we retrieve each equalizer band's frequency response for the target frequency list, freqs. The method fills magCurr with the response magnitude information:

AudioLayer.prototype.getEqResponse = function( freqs ) {
    var magCombined = new Float32Array( freqs.length );

    // Get the frequency response from all the eq nodes
    var eqNodes = this.eqNodes;
    var magCurr = new Float32Array( freqs.length );
    var phaseCurr = new Float32Array( freqs.length );
    for( var eqIndex = 0; 
         eqIndex < eqNodes.length; 
         eqIndex++ ) {

        eqNodes[ eqIndex ].getFrequencyResponse(
                freqs,
                magCurr,
                phaseCurr );

We convert each magnitude value from its original gain multiplier value to its dB equivalent:

        // Combine the node magnitudes
        for( var freqIndex = 0; 
             freqIndex < freqs.length; 
             freqIndex++ ) {
            var magDb = Math.log(magCurr[ freqIndex ]) * 20;

The formula for converting a gain multiplier to dB is as follows:

Then, we sum the magnitude on a per frequency basis. The accumulated magnitude is cached in magCombined:
```
            magCombined[ freqIndex ] += magDb;
```
Tip
An alternate method for calculating the combined frequency response is to multiply the gain multiplier for each sample frequency together, and then convert the combined gain multiplier into dB.
We return magCombined once all the biquadFilterNode frequency responses have been summed:
```
        }
    }

    return magCombined;
};
```

Finally, WebAudioApp.updateEqGraphic() renders the equalizer frequency response to an HTML canvas:

FREQ_MIN and FREQ_MAX specify the graph's rendered frequency range as shown in the following code. FREQ_MAX is set to the highest supported frequency so that we get a complete frequency response graph. The highest sample frequency that is supported by an AudioContext instance is its Nyquist frequency:
```
WebAudioApp.prototype.updateEqGraphic = function() {
    var FREQ_MIN  = 10;             // Hz
    var FREQ_MAX  = Math.round(
            this.audioContext.sampleRate * 0.5 );
```
Note
The Nyquist frequency is calculated by dividing the audio context's sample rate in half.
The graph renders the frequency response in dB units between the range of MAG_MIN and MAG_MAX:
```
    var MAG_MIN = -80;
    var MAG_MAX = 80;
```

The first time we try to render the response graph, we generate the sample frequency list and store it in WebAudioApp.eqFreqs as a Float32Array object:

    // Build the frequency response sampler list
    if( this.eqFreqs == null ) {
        var FREQS_NUM = 100;
        var FREQ_STEP = (FREQ_MAX - FREQ_MIN) / (FREQS_NUM - 1);

        this.eqFreqs = new Float32Array( FREQS_NUM );
        for( var freqIndex = 0; freqIndex < FREQS_NUM; freqIndex++ )
            this.eqFreqs[freqIndex] = Math.round( 
                 FREQ_MIN + (freqIndex * FREQ_STEP) );
    }

Because the frequency response retrieval and rendering is a fairly expensive operation, we limit the operation to occur once per update. We enforce this limit by queuing the render operation for the next update and monitoring WebAudioApp.eqUpdateHandle to determine when the operation has executed:
```
    // If we have an update scheduled, don't do anything
    if( this.eqUpdateHandle != null )
        return;

    // Schedule the graphic update
    this.eqUpdateHandle = later( 0, function(){
        this.eqUpdateHandle = null;
```

We start the frequency response graph rendering by clearing the canvas:

        var canvasCtx = $("#eqcanvas")[0].getContext( "2d" );
        var canvasWidth  = canvasCtx.canvas.width;
        var canvasHeight = canvasCtx.canvas.height;

        // Calculate the draw steps
        var stepX = canvasWidth / (FREQ_MAX - FREQ_MIN);
        var stepY = canvasHeight / (MAG_MAX - MAG_MIN );

        // Clear the canvas
        canvasCtx.fillStyle = "#f0f0f0";
        canvasCtx.fillRect( 0, 0, canvasWidth, canvasHeight );

We retrieve the equalizer's frequency response by calling AudioLayer.getEqResponse() with the sample frequency list cached in WebAudioApp.eqFreqs:

        // Draw the frequency response
        var eqFreqs = this.eqFreqs;
        var eqMag = this.musicLayer.getEqResponse( eqFreqs );

We render the response graph as a red line strip:

        var firstPt = true;
        canvasCtx.beginPath();
        for(var index = 0; index < eqFreqs.length; index++) {
            var x = Math.round( 
                       (eqFreqs[index] - FREQ_MIN) * stepX );
            var y = canvasHeight - Math.round( 
                       (eqMag[index] - MAG_MIN) * stepY );
            if( firstPt ) {
                firstPt = false;
                canvasCtx.moveTo( x, y );
            } else {
                canvasCtx.lineTo( x, y );
            }
        }

        canvasCtx.strokeStyle = "#ff0000";  // red line
        canvasCtx.stroke();

Finally, we overlay a blue line indicating the 0 dB position.

        // Draw the neutral response line
        var neutralY = canvasHeight -
                Math.round( (0 - MAG_MIN) * stepY );

        canvasCtx.beginPath();
        canvasCtx.moveTo( 0, neutralY );
        canvasCtx.lineTo( canvasWidth, neutralY );

        canvasCtx.strokeStyle = "#3030ff";  // blue line
        canvasCtx.stroke();
    }, this );
};

There's more...

Finally we talk about the two most popularly used audio processors in Web Audio.

Other built-in Web Audio audio processors

The biquadFilterNode and GainNode instances are just two of the many built-in audio processing nodes available in Web Audio (volume manipulation is considered a form of audio processing).

The following table highlights some of the more popular audio processor classes:

Class	Description
`PannerNode`	Spatializes an incoming audio signal in 3D space.
`DynamicsCompressorNode`	Compresses the volume range of an incoming audio signal. It accomplishes this by lowering the volume of loud segments and raising the volume of soft segments.
`DelayNode`	Delays the incoming audio signal by a specified time delay.
`ConvolverNode`	Mixes an incoming audio signal with an impulse response waveform. This audio processor is a fundamental building block for reverberation effects.

The following node graph illustrates a reverberation effect constructed using Web Audio's built-in audio processing nodes:

The example exposes the most common reverberation control parameters, which are:

Reverberation delay
Impulse response
Reverberation high cut-off frequency
Reverberation low cut-off frequency
Dry/wet mix

Unfortunately, a technical implementation of the reverberation audio processor is beyond the scope of this book. Hopefully, the example will serve as an inspiration and jump point to greater and more exciting real-time audio processors on the Web.

This concludes our exploration of the Web Audio API.

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By : Chris Khoo

Instant Audio Processing with Web Audio

By: Chris Khoo

Overview of this book

Building an equalizer using BiquadFilterNode (Advanced)

Getting ready

How to do it...

How it works...

Note

Tip

Tip

Tip

Note

There's more...

Other built-in Web Audio audio processors

Instant Audio Processing with Web Audio

By : Chris Khoo

Instant Audio Processing with Web Audio

By: Chris Khoo

Overview of this book

Building an equalizer using BiquadFilterNode (Advanced)

Getting ready

How to do it...

How it works...

Note

Tip

Tip

Tip

Note

There's more...

Other built-in Web Audio audio processors

Confirmation

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