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<h4 class="subsection">D.8.2 <code>harminv</code> output</h4>

<p>The result returned by a call to

<pre class="example">     library('harminv','hsolve')
</pre>
   <p class="noindent">with valid input (<a href="harminv-input-parameters.html#harminv-input-parameters">harminv input parameters</a>) is a list of similar tuples of the form

<pre class="example">     &lt;(amplitude,frequency,decay,quality,error)...&gt;
</pre>
   <p class="noindent">with all members being real valued except for the amplitudes, which are
complex. Each tuple describes a function of the form

<pre class="example">     f(t) = A * sin (frequency * t + P) * exp (-decay * t)
</pre>
   <p class="noindent">such that the summation of these functions approximates the original
given signal (<a href="harminv-input-parameters.html#harminv-input-parameters">harminv 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,

<pre class="example">     A = library('complex','cabs') amplitude
     P = library('complex','carg') amplitude
</pre>
   <p class="noindent">in terms of the complex library functions (<a href="complex.html#complex">complex</a>). 
The error values are measures of the goodness of fit, and the quality
factors are defined as

<pre class="example">     quality = (pi * |frequency| / decay)
</pre>
   <p class="noindent">It may be useful in some applications to ignore components with
quality factors outside of a certain range.

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