Re: Fourier decomposition

[beaucham <beaucham@xxxxxxxxxxxxxxxxxxxxxx>]

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
> 
> audioATdaqartaDOTcom
>