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diff --git a/demos/distortion.htm b/demos/distortion.htm new file mode 100644 index 0000000..915fa0d --- /dev/null +++ b/demos/distortion.htm @@ -0,0 +1,118 @@ +<!doctype html public "-//w3c//dtd html 4.0 transitional//en"> +<html> +<head> + <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> + <meta name="GENERATOR" content="Mozilla/4.75 [en] (Windows NT 5.0; U) [Netscape]"> + <title>Untitled Document</title> +</head> +<body bgcolor="#FFFFFF"> + +<h1> +Distortion Tutorial</h1> +This page describes how to use the Nyquist <tt>shape</tt> function to achieve distortion. +<h2> +Terminology</h2> +First, some terminology: +<blockquote><i>Clipping</i> means that you limit the amplitude of samples, +e.g. +<p>sample_out = min(sample_in, 1.0),</blockquote> +or, observing that you might want to limit negative excursions as well +as positive ones: +<blockquote>sample_out = max(min(sample_in, 1.0), -1.0).</blockquote> +This type of clipping is called <i>hard clipping</i> because the transition +from an undistorted one to a maximum or minimum value is instantaneous, +as if the signal hit a brick wall and can go no more. +<p>As you might guess, you can also have <i>soft clipping</i> where the +transition is more gradual, and that's what this tutorial is about. +<p>Before discussing soft clipping, let's introduce a few other terms. +Since <i>clipping</i> seems to be a way of <i>limiting</i> the values of +the signal or <i>compressing</i> the range of the signal, you might think +that clipping is a form of compressing or limiting; however, these terms +have special meanings in the audio processing world. +<blockquote><i>Compression</i>, or <i>dynamics compression</i> (not to +be confused with <i>data compression</i>) is a way of reducing the overall +range of soft to loud.</blockquote> +To do dynamics compression, you generally detect the intensity or peak +level of a sound over a time scale of a few milliseconds, and then construct +a relatively smooth amplitude control that you apply to the signal. For +compression, the amplification goes down as the intensity of the input +goes up, so loud passages get (relatively) softer and soft passages get +(relatively) louder. (Dynamics expansion does just the opposite.) <i>Limiters</i> +work like compressors, but are designed to eliminate peaks -- conceptually, +there is no real difference, and products are often sold as "compressor/limiters". +See nyquist/lib/compress.lsp for an implementation. +<p>In some ways, soft clipping is like dynamics compression. Both reduce +the gain at high levels, but dynamics compression operates relatively slowly, +effectively turning the volume knob up and down, whereas clipping operates +on a sample-by-sample basis. The effect of clipping is to distort the input. +<p>In Nyquist, you use the <tt>shape</tt> function to implement clipping. <tt>shape</tt> +applies a function to each sample, where the function is specified by a +sound. The following is a typical function for soft clipping: +<center><img SRC="softclip.jpg" ></center> +Notice how the function is essentially y=x at small amplitudes, so there +is no distortion for small signals, but at large input values, the function +becomes very non-linear. Also, notice that this is similar to the behavior +of real-life amplifiers, where small signals are undistorted, but at some +point, the power limits of the amplifier clip the output signal. +<p>The Nyquist <tt>shape</tt> function is allows you to specify any function you +like using a sound. Therefore you can use any of the Nyquist primitives +to construct the function. Since a sound is a function of time, where time +must be non-negative, how do you specify a shape function over a range +that includes negative values? The trick is that <tt>shape</tt> takes an <i>offset</i> +parameter that shifts the whole function to the left (in the -y direction). +Note also that whereas a Nyquist sound is generally regarded as a function +of time, <tt>shape</tt> treats the sound as just a real-valued function. +<p>The typical way to use shape is to create some increasing signal over +the interval [0,2] that crosses zero at 1.0. Then you give 1.0 as the offset +(3rd parameter). The result will look something like the graph above. +<h2>Implementation</h2> +In the figure above, I used a sine function to generate the smooth curve. Here is an implementation of distortion in Nyquist using the sine curve: +<blockquote> +<pre>(setf distortion + (osc (hz-to-step 0.25) 2.01 *SINE-TABLE* -90.0)) +(defun distort (snd) + (shape snd distortion 1.0)) + +(play (distort (mult 15.0 (ramp 4) (osc c4 4)))) +</pre> +</blockquote> +<p>Even though I am an expert, and I have done this before, it still took +me a few tries to get right. Here's a step-by-step explanation: +<ul> +<li>I used <tt>osc</tt> to generate a sinusoid so I could control the initial phase. +<li>I set the osc duration to 2 because I want the table to go from +0 to 2 (after which we'll shift it back to [-1, +1]), but 2 is not enough because the interval [0,2] is closed, which +means I need one extra sample. I used 2.01 to be conservative. +<li>I specified <tt>*SINE-TABLE*</tt>, the default value, because the table +parameter comes before the phase parameter. +<li>I specified the phase to get the sine curve to go through zero +in the <i>middle</i> of the generated function. +<li>I assigned this to the variable distortion so I could plot it; try: +<pre>(s-plot (force-srate 100 distortion))</pre> +<li>Finally, I put in a tone that ramps up from zero to 15 in amplitude +to cause some serious clipping. The output amplitude is limited to 1. +</ul> +<p>Note that the input to <tt>shape</tt> is pre-clipped to the range +[-1, +1] so you only need to specify the table from [0, 2] if the origin (third parameter to <tt>shape</tt>) is 1.0. If you specify a little extra, as +in this example, it will be ignored. +<h2>The Output</h2> +<p> +Look +at the generated waveform to observe the soft clipping effect. Here we see the beginning of the output, where the input amplitude is low and there is very little distortion: +<p> +<center> +<img src="beginclip.jpg"> +</center> +But when the input amplitude becomes large, the clipping becomes substantial. This plot is at the same scale, but taken from a later portion of the generated output. Remember that the input at this point is a high-amplitude sinusoid:<p> +<center> +<img src="largeclip.jpg"> +</center> +Also notice +that the distortion is symetrical, so it generates even harmonics. If you +put in an asymetric function, you'll get odd harmonics too. Note that at +soft levels, I actually get some gain from this function. +<p><i>Generated by Roger Dannenberg (roger.dannenberg@cs.cmu.edu) Feb, +2004.</i></blockquote> + +</body> +</html> |