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<div class="refentry" title="spectrum">
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<h2>
<span class="refentrytitle">spectrum</span>
</h2>
<p>spectrum —
Generate a constant-Q, exponentially-spaced DFT.
</p>
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<div class="refsect1" title="Description">
<a id="id3231646"></a>
<h2>Description</h2>
<p>
Generate a constant-Q, exponentially-spaced DFT across all octaves of a multiply-downsampled control or audio input signal.
</p>
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<div class="refsect1" title="Syntax">
<a id="id3231567"></a>
<h2>Syntax</h2>
<pre class="synopsis">wsig <span class="command"><strong>spectrum</strong></span> xsig, iprd, iocts, ifrqa [, iq] [, ihann] [, idbout] \
[, idsprd] [, idsinrs]</pre>
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<div class="refsect1" title="Initialization">
<a id="id3231587"></a>
<h2>Initialization</h2>
<p>
<span class="emphasis"><em>ihann</em></span> (optional) -- apply a Hamming or Hanning window to the input. The default is 0 (Hamming window)
</p>
<p>
<span class="emphasis"><em>idbout</em></span> (optional) -- coded conversion of the DFT output:
</p>
<div class="itemizedlist">
<ul class="itemizedlist" type="disc">
<li class="listitem">
<p>0 = magnitude</p>
</li>
<li class="listitem">
<p>1 = dB</p>
</li>
<li class="listitem">
<p>2 = mag squared</p>
</li>
<li class="listitem">
<p>3 = root magnitude</p>
</li>
</ul>
</div>
<p>
The default value is 0 (magnitude).
</p>
<p>
<span class="emphasis"><em>idisprd</em></span> (optional) -- if non-zero, display the composite downsampling buffer every <span class="emphasis"><em>idisprd</em></span> seconds. The default value is 0 (no display).
</p>
<p>
<span class="emphasis"><em>idsines</em></span> (optional) -- if non-zero, display the Hamming or Hanning windowed sinusoids used in DFT filtering. The default value is 0 (no sinusoid display).
</p>
</div>
<div class="refsect1" title="Performance">
<a id="id3232646"></a>
<h2>Performance</h2>
<p>
This unit first puts signal <span class="emphasis"><em>asig</em></span> or <span class="emphasis"><em>ksig</em></span> through <span class="emphasis"><em>iocts</em></span> of successive octave decimation and downsampling, and preserves a buffer of down-sampled values in each octave (optionally displayed as a composite buffer every <span class="emphasis"><em>idisprd</em></span> seconds). Then at every <span class="emphasis"><em>iprd</em></span> seconds, the preserved samples are passed through a filter bank (<span class="emphasis"><em>ifrqs</em></span> parallel filters per octave, exponentially spaced, with frequency/bandwidth Q of <span class="emphasis"><em>iq</em></span>), and the output magnitudes optionally converted (<span class="emphasis"><em>idbout </em></span>) to produce a band-limited spectrum that can be read by other units.
</p>
<p>
The stages in this process are computationally intensive, and computation time varies directly with <span class="emphasis"><em>iocts</em></span>, <span class="emphasis"><em>ifrqs</em></span>, <span class="emphasis"><em>iq</em></span>, and inversely with <span class="emphasis"><em>iprd</em></span>. Settings of <span class="emphasis"><em>ifrqs</em></span> = 12, <span class="emphasis"><em>iq</em></span> = 10, <span class="emphasis"><em>idbout</em></span> = 3, and <span class="emphasis"><em>iprd</em></span> = .02 will normally be adequate, but experimentation is encouraged. <span class="emphasis"><em>ifrqs</em></span> currently has a maximum of 120 divisions per octave. For audio input, the frequency bins are tuned to coincide with A440.
</p>
<p>
This unit produces a self-defining spectral datablock <span class="emphasis"><em>wsig</em></span>, whose characteristics used (<span class="emphasis"><em>iprd</em></span>, <span class="emphasis"><em>iocts</em></span>, <span class="emphasis"><em>ifrqs</em></span>, <span class="emphasis"><em>idbout</em></span>) are passed via the data block itself to all derivative <span class="emphasis"><em>wsigs</em></span>. There can be any number of spectrum units in an instrument or orchestra, but all <span class="emphasis"><em>wsig</em></span> names must be unique.
</p>
</div>
<div class="refsect1" title="Examples">
<a id="id3232766"></a>
<h2>Examples</h2>
<p>
</p>
<div class="informalexample">
<pre class="programlisting">
asig <span class="emphasis"><em>in</em></span> ; get external audio
wsig <span class="emphasis"><em>spectrum</em></span> asig,.02,6,12,33,0,1,1 ; downsample in 6 octs & calc a 72 pt dft (Q 33, dB out) every 20 msecs
</pre>
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