XPost: rec.music.gdead, sci.electronics.design   
   From: spam@spam.com   
      
   On Thu, 03 Mar 2011 17:29:10 +0200, upsidedown@downunder.com wrote:   
      
   >On Thu, 03 Mar 2011 08:39:52 -0500, Dick Pierce   
   > wrote:   
   >   
   >>>   
   >>> I would like to hear how one simulates say piano notes by means of just   
   >>> linear mixing of continuous sine waves.   
   >>   
   >>Are you saying that it's not possible? Here, take   
   >>my shovel, dig up Mr. Fourier, tell him it's not   
   >>possible.   
   >>   
   >>Take ANY amplitude-modulated waveform. Take it's   
   >>Fourier transform. The result is some collection of   
   >>continuous sine waves, n'est ce pas?   
   >   
   >I have always had the impression that you needed something similar of   
   >a continuous waveform to get the FFT, trying to take the FFT of a   
   >single pulse does not make a lot sense.   
   >   
   >While the decaying part of the piano waveform could be simulated with   
   >a series of sine waves multiplied with a curve simulating the   
   >inversely exponentially dying out string oscillations, the attack part   
   >of the waveform is far more complicated.   
      
   You are both right and wrong. You are wrong in that the FFT couldn't   
   care less what shape the waveform is. Provided its frequency is   
   contained within half the sampling rate, it will reproduce it.   
      
   You are right - and this is where most people forget what an FFT   
   really does - in that there is an implicit assumption within the FFT   
   that the entire sample is repeated ad infinitum. In fact when you   
   perform an FFT, you effectively join the ends together to make a loop.   
      
   d   
      
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