Links

Googling "FFT" will get you loads of links, many of them bordering on the edge of incomprehensibility and sanity. The FFT is one of the real 'workhorses' of the digital age, and it's applications extend beyond our musical use (although audio DSP is a big area for FFT usage). Below are a few links I've found particularly useful, following up on our class discussion:
• Who is Fourier? -- This is the book I described in class (and Ethan had a copy). It's really goofy, but it's the best explanation of the Fourier transform that I've found. It also teaches you some calculus for fun! Highly recommended if you want to learn this stuff.
• Musical Applications of Microprocessors -- I also mentioned this book. As the book is (apparently) out-of-print, the cost of the book is very high. Louis found an on-line version through scribd, so we've linked it here. I think we also have a copy floating around the CMC. It has the best explanation of the 'butterfly' bit-swap that the FFT uses (not used in the plain ole FT or DFT).
• The Phase Vocoder: A Tutorial -- Mark Dolson's article on the Phase Vocoder (PVOC) implementation of the FFT. Good description of how 'phase-unwrapping' works.
• Graphs of y = a sin x and y = a cos x -- Nice article on the unit circle, with good demos of how the sine and cosine components unroll in time.
  
  
  code:
  
  
• John Gibson's software -- John Gibson's software download page. The [jg.spectdelay~] spectral delay object lives here.
• [jg.resynth~-beta.zip] -- This archive contains the object (not yet completely finished; it might crash occasionally!) that allows you to use SPEAR data in your max patch. The class archive below contains some simple examples of how it can be used.
• "paulstretch" standalone app download -- The "paulstretch" application that allows for very looooooong stretching of soundfiles using a modified FFT. Paul Nasca (the author) does some randomizing of the phase while resynthesizing the sound, preventing the result from sounding too sonically static. The code for the algorithm can be downloaded here.
• vb-objects -- The download portion of Volker Boehm's website. The [vbstretch~] object partway down the listing is a Max/MSP implementation of the "paulstretch" algorithm. Some other interesting objects here, too.
  
  
  music:
  
  Two things I played in class:
  
  
• Bob Dylan stretched
  
  
• Steve Reich stretched

Class Downloads

• week8-classpatches.zip -- The demos of John Gibson's [jg.resynth~] object. I also included the "hey-mono.sdif" analysis file generated from the SPEAR analysis program.