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I'm having trouble understanding how the transfer function for a WaveShaperNode in the Web Audio API works. As I understand, a transfer function is a waveshaper which takes in a signal input x and produces a new signal y. So,

y = f(x)

I understand that if x equals zero, then so should y. Therefore, 0 = f(0). And that to fit in an appropriate range, y should be between [-1, 1], so this function: y = x / (1 + |x|) limits the output range to [-1, 1]. And that Chebyshev Polynomials are useful for transfer functions used to "distort" musical input signals.

But for a transfer function you need the input signal x in order to manipulate it and create an output y. However, with a WaveShaperNode in the Web Audio API, you don't have access to the original input x (or do you?). Often I see algorithms like:

for(var i = 0; i < sampleRate; i++){
    var x = i * 2 / sampleRate - 1;
    this.curve[i] = (3 + distortionAmount) * x * 20 * (Math.PI / 180) / (Math.PI + distortionAmount * Math.abs(x));
}

Where, in the above code, this.curve is a Float32Array representing the graphing of each sample frame. And I assume x here is supposed to represent the input audio signal. Yet, it doesn't actually represent the exact input audio signal. Is this because it just represents an average sinusoid and the actual input doesn't matter? Does the WaveShaperNode take the original input x and use (multiply?) the general curve we created to calculate the output y?

chRyNaN
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  • The question is confusing as written, but it sounds like maybe you want to be able to just provide a JavaScript function and have every sample get passed through that function. Is that what you're looking for? That would require a ScriptProcessorNode. WaveShaperNode makes you specify the transfer function as an array of numbers, which is more efficient. – aldel Feb 03 '15 at 20:43

2 Answers2

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The WaveShaper node does not enable generic transfer functions, per se - but you can use it to do that. To answer your question - x is the offset into the array, with a little preprocessing.

The curve you give to the waveshaper is like a lookup table for x - spread across the range [-1,1]. Y does not need to be in [-1,1] - but x does. So, to solve f(x) for x in [-1,1], you just get the value at 

curve[ Math.floor( (x+1)/2 * (curve.length-1) ) ];

or something like that.

It's not actually true that if x equals zero, then so must y; but it's likely. You could use the waveshaper to implement a DC offset, for example.

That "sampleRate" bit in your demo code is goofy - you should use maxint, not samplerate, to determine the size of your array. sampleRate is a time-domain thing, and waveshaper only operates in the amplitude vector.

cwilso
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  • any books or articles on waveshaping you would recommend? I would really like to further my knowledge on the subject. – chRyNaN Feb 04 '15 at 19:38
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    There's a pretty detailed section on waveshaping in [Dodge & Jerse](http://amzn.com/0028646827). It was 20 pages in the original 1985 edition; not sure how much changed in the 2nd edition. – aldel Feb 04 '15 at 22:56
  • @cwilso, what do you mean by maxint? Integers in JS can be huge; not a good size for an array. I can sort of intuitively see using the sample rate, since you might want higher transfer function accuracy at higher rates... but really the number of points should depend on how much detail you need in the function. 3 points would let you do an absolute value; a few hundred would probably give you a pretty good f(x)=x*x, and so on. – aldel Feb 04 '15 at 23:03
  • @aldel: yeah, actually, you don't need maxint anymore. At one point it was not interpolated, and it was more important. (But regardless, my point stands - using sampleRate as the size of that array is just weird. sampleRate is in the time domain, not the amplitude domain; they're completely unrelated.) – cwilso Feb 09 '15 at 17:19
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The WaveShaperNode is described as applying a non-linear distortion. As such it would not have a classical linear time-invariant transfer function (which strictly only applies to linear distortions).

hotpaw2
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  • This does not answer any of the questions I asked. A non-linear function can be a polynomial as long as its order N is greater than one. My question deals with how can you obtain the x input in order to manipulate it to create y, or how does the WaveShaperNode apply the curve (result of all calculations for each instance of x) to the original input. The answer you provided should be a comment and not an answer, if anything. Please answer the question directly or elaborate to explain how this does answer the question. Otherwise, -1. – chRyNaN Feb 03 '15 at 19:17