Some assorted links of examples, tutorials and reflections regarding sound visualizers in Flash:
1. Tutorials
http://livedocs.adobe.com/flash/9.0/main/00000296.html
http://www.ultrashock.com/tutorials/flash8/spectrum.php
http://www.thetechlabs.com/sound/create-a-as3-flash-9-mp3-player-with-spectrum-display/
http://www.thetechlabs.com/3d/create-a-as3-mp3-player-with-papervision3d-spectrum-display/
http://www.communitymx.com/content/article.cfm?cid=8E9A0
2. Examples with source code
http://www.terrypaton.com/as3-sound-spectrum/
http://www.anttikupila.com/flash/revolt-actionscript-3-based-spectrum-analyzer-source-released/
http://labs.blitzagency.com/?p=118
http://clockmaker.jp/blog-en/2008/11/pv3d_visualizer/
3. Links to visualizers
http://www.gskinner.com/blog/archives/2006/10/as3_music_visua.html
http://theflashblog.com/?p=197
4. Discussion
http://www.ultrashock.com/forums/actionscript/as3-soundmixer-computespectrum-82605.html
http://www.actionscript.org/forums/showthread.php3?t=176574
There is also an older post related to this: