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<h1 id="noiseslib">noises.lib</h1>
<p>Faust Noise Generator Library. Its official prefix is <code>no</code>.</p>
<h4 id="references">References</h4>
<ul>
<li><a href="https://github.com/grame-cncm/faustlibraries/blob/master/noises.lib">https://github.com/grame-cncm/faustlibraries/blob/master/noises.lib</a></li>
</ul>
<h2 id="functions-reference">Functions Reference</h2>
<hr />
<h3 id="nonoise"><code>(no.)noise</code></h3>
<p>White noise generator (outputs random number between -1 and 1).
<code>noise</code> is a standard Faust function.</p>
<h4 id="usage">Usage</h4>
<pre><code>noise : _
</code></pre>
<hr />
<h3 id="nomultirandom"><code>(no.)multirandom</code></h3>
<p>Generates multiple decorrelated random numbers in parallel.</p>
<h4 id="usage_1">Usage</h4>
<pre><code>multirandom(N) : si.bus(N)
</code></pre>
<p>Where:</p>
<ul>
<li><code>N</code>: the number of decorrelated random numbers in parallel, a constant numerical expression</li>
</ul>
<hr />
<h3 id="nomultinoise"><code>(no.)multinoise</code></h3>
<p>Generates multiple decorrelated noises in parallel.</p>
<h4 id="usage_2">Usage</h4>
<pre><code>multinoise(N) : si.bus(N)
</code></pre>
<p>Where:</p>
<ul>
<li><code>N</code>: the number of decorrelated random numbers in parallel, a constant numerical expression</li>
</ul>
<hr />
<h3 id="nonoises"><code>(no.)noises</code></h3>
<p>A convenient wrapper around multinoise.</p>
<h4 id="usage_3">Usage</h4>
<pre><code>noises(N,i) : _
</code></pre>
<p>Where:</p>
<ul>
<li><code>N</code>: the number of decorrelated random numbers in parallel, a constant numerical expression</li>
<li><code>i</code>: the selected random number (i in [0..N[)</li>
</ul>
<hr />
<h3 id="norandomseed"><code>(no.)randomseed</code></h3>
<p>A random seed based on the foreign function <code>arc4random</code>
(see man arc4random). Used in <code>rnoise</code>, <code>rmultirandom</code>, etc. to 
avoid having the same pseudo random sequence at each run.</p>
<p>WARNING: using the foreign function <code>arc4random</code>, so only available in C/C++ and LLVM backends.</p>
<h4 id="usage_4">Usage</h4>
<pre><code>randomseed : _
</code></pre>
<hr />
<h3 id="nornoise"><code>(no.)rnoise</code></h3>
<p>A randomized white noise generator (outputs random number between -1 and 1).</p>
<p>WARNING: using the foreign function <code>arc4random</code>, so only available in C/C++ and LLVM backends.</p>
<h4 id="usage_5">Usage</h4>
<pre><code>rnoise : _
</code></pre>
<hr />
<h3 id="normultirandom"><code>(no.)rmultirandom</code></h3>
<p>Generates multiple decorrelated random numbers in parallel.</p>
<p>WARNING: using the foreign function <code>arc4random</code>, so only available in C/C++ and LLVM backends.</p>
<h4 id="usage_6">Usage</h4>
<pre><code>rmultirandom(N) : _
</code></pre>
<p>Where:</p>
<ul>
<li><code>N</code>: the number of decorrelated random numbers in parallel, a constant numerical expression</li>
</ul>
<hr />
<h3 id="normultinoise"><code>(no.)rmultinoise</code></h3>
<p>Generates multiple decorrelated noises in parallel.</p>
<p>WARNING: using the foreign function <code>arc4random</code>, so only available in C/C++ and LLVM backends.</p>
<h4 id="usage_7">Usage</h4>
<pre><code>rmultinoise(N) : _
</code></pre>
<p>Where:</p>
<ul>
<li><code>N</code>: the number of decorrelated random numbers in parallel, a constant numerical expression</li>
</ul>
<hr />
<h3 id="nornoises"><code>(no.)rnoises</code></h3>
<p>A convenient wrapper around rmultinoise.</p>
<p>WARNING: using the foreign function <code>arc4random</code>, so only available in C/C++ and LLVM backends.</p>
<h4 id="usage_8">Usage</h4>
<pre><code>rnoises(N,i) : _
</code></pre>
<p>Where:</p>
<ul>
<li><code>N</code>: the number of decorrelated random numbers in parallel</li>
<li><code>i</code>: the selected random number (i in [0..N[)</li>
</ul>
<hr />
<h3 id="nopink_noise"><code>(no.)pink_noise</code></h3>
<p>Pink noise (1/f noise) generator (third-order approximation covering the audio band well).
<code>pink_noise</code> is a standard Faust function.</p>
<h4 id="usage_9">Usage</h4>
<pre><code>pink_noise : _
</code></pre>
<h4 id="reference">Reference</h4>
<ul>
<li><a href="https://ccrma.stanford.edu/~jos/sasp/Example_Synthesis_1_F_Noise.html">https://ccrma.stanford.edu/~jos/sasp/Example_Synthesis_1_F_Noise.html</a></li>
</ul>
<h4 id="alternatives">Alternatives</h4>
<p>Higher-order approximations covering any frequency band can be obtained using</p>
<pre><code>no.noise : fi.spectral_tilt(order,lowerBandLimit,Bandwidth,p)
</code></pre>
<p>where <code>p=-0.5</code> means filter rolloff <code>f^(-1/2)</code> which gives 1/f rolloff in the
power spectral density, and can be changed to other real values.</p>
<h4 id="example">Example</h4>
<p>// pink_noise_compare.dsp - compare three pinking filters</p>
<pre><code>process = pink_noises with {
    f0 = 35; // Lower bandlimit in Hz
    bw3 = 0.7 * ma.SR/2.0 - f0; // Bandwidth in Hz, 3rd order case
    bw9 = 0.8 * ma.SR/2.0 - f0; // Bandwidth in Hz, 9th order case
    pink_tilt_3 = fi.spectral_tilt(3,f0,bw3,-0.5);
    pink_tilt_9 = fi.spectral_tilt(9,f0,bw9,-0.5);
    pink_noises = 1-1' &lt;:
      no.pink_filter, // original designed by invfreqz in Octave
      pink_tilt_3,    // newer method using the same filter order
      pink_tilt_9;    // newer method using a higher filter order
};
</code></pre>
<h4 id="output-of-example">Output of Example</h4>
<pre><code>faust2octave pink_noise_compare.dsp
Octave:1&gt; semilogx(20*log10(abs(fft(faustout,8192))(1:4096,:)));
...
</code></pre>
<p><img alt="pink_noise_demo figure" src="https://ccrma.stanford.edu/wiki/Images/8/86/Tpinkd.jpg" width="600" /></p>
<hr />
<h3 id="nopink_noise_vm"><code>(no.)pink_noise_vm</code></h3>
<p>Multi pink noise generator.</p>
<h4 id="usage_10">Usage</h4>
<pre><code>pink_noise_vm(N) : _
</code></pre>
<p>Where:</p>
<ul>
<li><code>N</code>: number of latched white-noise processes to sum,
    not to exceed sizeof(int) in C++ (typically 32).</li>
</ul>
<h4 id="references_1">References</h4>
<ul>
<li><a href="http://www.dsprelated.com/showarticle/908.php">http://www.dsprelated.com/showarticle/908.php</a></li>
<li><a href="http://www.firstpr.com.au/dsp/pink-noise/#Voss-McCartney">http://www.firstpr.com.au/dsp/pink-noise/#Voss-McCartney</a></li>
</ul>
<hr />
<h3 id="nolfnoise-nolfnoise0-and-nolfnoisen"><code>(no.)lfnoise</code>, <code>(no.)lfnoise0</code> and <code>(no.)lfnoiseN</code></h3>
<p>Low-frequency noise generators (Butterworth-filtered downsampled white noise).</p>
<h4 id="usage_11">Usage</h4>
<pre><code>lfnoise0(rate) : _   // new random number every int(ma.SR/rate) samples or so
lfnoiseN(N,rate) : _ // same as &quot;lfnoise0(rate) : fi.lowpass(N,rate)&quot; [see filters.lib]
lfnoise(rate) : _    // same as &quot;lfnoise0(rate) : seq(i,5,fi.lowpass(N,rate))&quot; (no overshoot)
</code></pre>
<h4 id="example_1">Example</h4>
<p>(view waveforms in faust2octave):</p>
<pre><code>rate = ma.SR/100.0; // new random value every 100 samples (ma.SR from maths.lib)
process = lfnoise0(rate),   // sampled/held noise (piecewise constant)
          lfnoiseN(3,rate), // lfnoise0 smoothed by 3rd order Butterworth LPF
          lfnoise(rate);    // lfnoise0 smoothed with no overshoot
</code></pre>
<hr />
<h3 id="nosparse_noise"><code>(no.)sparse_noise</code></h3>
<p>Sparse noise generator.</p>
<h4 id="usage_12">Usage</h4>
<pre><code>sparse_noise(f0) : _
</code></pre>
<p>Where:</p>
<ul>
<li><code>f0</code>: average frequency of noise impulses per second</li>
</ul>
<p>Random impulses in the amplitude range -1 to 1 are generated
at an average rate of f0 impulses per second.</p>
<h4 id="reference_1">Reference</h4>
<ul>
<li>See velvet_noise</li>
</ul>
<hr />
<h3 id="novelvet_noise_vm"><code>(no.)velvet_noise_vm</code></h3>
<p>Velvet noise generator.</p>
<h4 id="usage_13">Usage</h4>
<pre><code>velvet_noise(amp, f0) : _
</code></pre>
<p>Where:</p>
<ul>
<li><code>amp</code>: amplitude of noise impulses (positive and negative)</li>
<li><code>f0</code>: average frequency of noise impulses per second</li>
</ul>
<h4 id="reference_2">Reference</h4>
<ul>
<li>Matti Karjalainen and Hanna Jarvelainen,
  "Reverberation Modeling Using Velvet Noise",
  in Proc. 30th Int. Conf. Intelligent Audio Environments (AES07),
  March 2007.</li>
</ul>
<hr />
<h3 id="nognoise"><code>(no.)gnoise</code></h3>
<p>Approximate zero-mean, unit-variance Gaussian white noise generator.</p>
<h4 id="usage_14">Usage</h4>
<pre><code>gnoise(N) : _
</code></pre>
<p>Where:</p>
<ul>
<li><code>N</code>: number of uniform random numbers added to approximate Gaussian white noise</li>
</ul>
<h4 id="reference_3">Reference</h4>
<ul>
<li>See Central Limit Theorem</li>
</ul>
<hr />
<h3 id="nocolored_noise"><code>(no.)colored_noise</code></h3>
<p>Generates a colored noise signal with an arbitrary spectral
roll-off factor (alpha) over the entire audible frequency range
(20-20000 Hz). The output is normalized so that an equal RMS
level is maintained for different values of alpha.</p>
<h4 id="usage_15">Usage</h4>
<pre><code>colored_noise(N,alpha) : _
</code></pre>
<p>Where:</p>
<ul>
<li><code>N</code>: desired integer filter order (constant numerical expression)</li>
<li><code>alpha</code>: slope of roll-off, between -1 and 1. -1 corresponds to 
brown/red noise, -1/2 pink noise, 0 white noise, 1/2 blue noise,
and 1 violet/azure noise.</li>
</ul>
<h4 id="examples">Examples</h4>
<p>See <code>dm.colored_noise_demo</code>.</p></div>
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