Path: utzoo!attcan!uunet!lll-winken!lll-tis!ames!husc6!linus!mbunix!eachus
From: eachus@mitre-bedford.ARPA (Robert Eachus)
Newsgroups: comp.sys.amiga.tech
Subject: Re: 2 More Questions
Summary: Yes, it is doable
Keywords: fft, regression, time-series analysis
Message-ID: <39616@linus.UUCP>
Date: 8 Sep 88 18:28:59 GMT
References: <8809071942.AA05026@cory.Berkeley.EDU>
Sender: news@linus.UUCP
Reply-To: eachus@mitre-bedford.arpa (Robert I. Eachus)
Organization: The MITRE Corporation, Bedford, Mass.
Lines: 33

In article <8809071942.AA05026@cory.Berkeley.EDU> dillon@CORY.BERKELEY.EDU (Matt Dillon) writes:
>>>    QUESTION#2)  Is it possible with software and hardware capabilities
>>>                 to digitize a song and have the computer convert the
>>>                 wavelengths into notes/sheetmusic and then print it
>>>                 out?
>
>	This is strictly a (read: major math) processing thing and is not 
>dependant on the particular graphics or sound capabilities for any computer.

>	Maybe on a mainframe, if it's possible at all!

>			-Matt

     This would certainly be doable on  an Amiga (not  in real-time of
course),  and it would be  a lot of fun  (and a lot   of work).  First
digitize the signal, then do a sequential  FFT with  a  sliding window
128  samples long.  Use this to  decide when new   notes begin.  (Look
every  16   samples  or   so to see   if succesive  power  spectra are
proportional (same note increasing or decreasing) or not.

     Now   transform each sample  interval   determined  above using a
larger number of samples.  Determine the lowest fundamental frequency,
and any notes within an octave above it.  Use templates (transforms of
samples of a single  instrument playing a  single note) to do a linear
regression best fit to  match  notes being  played to  the instruments
playing  them.  Analyze the  residues   for notes in  the next highest
octave and refit if necessary.

     Do any ADSR (attack, delay,  sustain, release) analysis necessary
to determine  when each  particular note  ends, and you  have  all the
information necessary  to  print the music  (and to reconstruct it and
subtract the power spectra) to make sure you got it right.

					Robert I. Eachus