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<title>avram - a virtual machine code interpreter: D.8.2 harminv output</title>

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<a name="harminv-output"></a>
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<a name="harminv-output-1"></a>
<h3 class="subsection">D.8.2 <code>harminv</code> output</h3>

<p>The result returned by a call to
</p>
<table><tr><td>&nbsp;</td><td><pre class="example">library('harminv','hsolve')
</pre></td></tr></table>

<p>with valid input (<a href="harminv-input-parameters.html#harminv-input-parameters"><code>harminv</code> input parameters</a>) is a list of similar tuples of the form
</p>
<table><tr><td>&nbsp;</td><td><pre class="example">&lt;(amplitude,frequency,decay,quality,error)...&gt;
</pre></td></tr></table>

<p>with all members being real valued except for the amplitudes, which are
complex. Each tuple describes a function of the form
</p>
<table><tr><td>&nbsp;</td><td><pre class="example">f(t) = A * sin (frequency * t + P) * exp (-decay * t)
</pre></td></tr></table>

<p>such that the summation of these functions approximates the original
given signal (<a href="harminv-input-parameters.html#harminv-input-parameters"><code>harminv</code> input parameters</a>). The real amplitude
<code>A</code> and phase <code>P</code> are given by the modulus and argument of
the complex amplitude returned in the result,
</p>
<table><tr><td>&nbsp;</td><td><pre class="example">A = library('complex','cabs') amplitude
P = library('complex','carg') amplitude
</pre></td></tr></table>

<p>in terms of the complex library functions (<a href="complex.html#complex"><code>complex</code></a>).
The error values are measures of the goodness of fit, and the quality
factors are defined as
</p>
<table><tr><td>&nbsp;</td><td><pre class="example">quality = (pi * |frequency| / decay)
</pre></td></tr></table>

<p>It may be useful in some applications to ignore components with
quality factors outside of a certain range.
</p>
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