Subject: Fourier decomposition From: David Havelock <david.havelock(at)nrc.ca> Date: Mon, 19 Sep 2005 09:17:40 -0400A fairly detailed discussion of the problem, and a solution, can be found in "Accurate analysis of multitone signals using a DFT" John C. Burgess J. Acoust. Soc. Am. 116, 389 (2004) The optimized estimation of phase and magnitude take into account the effects of windowing, using an optimized window design. The paper addresses details of discrete signal analysis that are often glossed over. David I. Havelock Acoustics and Signal Processing Group Institute for Microstructural Sciences (M36) National Research Council Canada ----------- Date: Sun, 18 Sep 2005 20:15:31 -0500 From: beaucham <beaucham(at)MANFRED.MUSIC.UIUC.EDU> Subject: Re: Fourier decomposition What is meant by "accurately"?. I.e., how do you test and how close do the results have to be before you'd say the analysis method is accurate? The method described at http://ccrma.stanford.edu/~jos/parshl/parshl.html does a pretty darn good job. We have an implementation similar to this in our SNDAN package which performs very well on harmonic and inharmonic sounds. See http://ems.music.uiuc.edu/beaucham/software/sndan/ Regards, Jim Beauchamp Univ. of Illinois at Urbana-Champaign On Sat, 17 Sep 2005, Bob Masta wrote: > On 16 Sep 2005 at 19:20, Fred Herzfeld wrote: > > > Hello List: > > > > I am now about to make public some work on signal decomposition. As > > part > > of the disclosure I will make the statement: > > ------------------ > > It is not possible to accurately recover the coefficients (amplitude and > > phase of the individual harmonics) of a function consisting of harmonic > > sinusoidal components, when the Period of the not necessarily present > > fundamental is not known, by using the normal computational procedure of > > either the Fourier Series or the Short term Fourier Transform. > > ----------------------- > > > > I would appreciate any and all comments. > > > > Interesting question. Pre-multiplication by ordinary windowing > functions seems to do a pretty good job when recovering the > magnitudes, but I've never looked into what this does to the phase. I > gather from your statement that it screws it up, and that there is no > analogous window function for obtaining phase? > > Thanks for your insights... > > Bob Masta >