ffects its placement relative to the carrier (giving the effect of
a moving formant).  Here we sweep "r" from -1.0 to -20.0, with an index of 3, m/c ratio of .2, and carrier at 1000 Hz:
</p>

<img class="indented" src="pix/asyfm.png" alt="asy spectra">



<div class="greenish">complex FM: sin(sin+sin)</div>

<p>
So far we have been using just a sinusoid for the modulator; what if we make it a more complicated 
signal?  Here again trigonometry can be used to expand
</p>

<!-- LATEX \sin(\omega_{c}t + B_{1}\s