Re: STFT vs Power Spectral in Musical recognition system ?

["Richard F. Lyon" <DickLyon@xxxxxxx>]

Edwin,

A power spectral density is only defined for stationary signals, not 
music.  The STFT generalizes it to short segments, if you use the 
squared magnitude.

The difference between the absolute value, square, log, etc. are just 
point nonlinearities that do not change the information content, but 
do change the metric structure of the space a bit.  Log is too 
compressed, leading to too much emphasis on near-silent segments, 
while the square (the power you ask about) is too expanded, leading 
to too much emphasis on the louder parts.  A good compromise is 
around a square root or cube root of magnitude (roughly matching 
perceptual magnitude via Stevens's law), but the magnitude itself is 
also sometimes acceptable, depending on what you're doing.

Dick

At 7:12 AM -0700 8/25/06, Edwin Sianturi wrote:
> Content-Type: text/html
> X-MIME-Autoconverted: from 8bit to quoted-printable by 
> torrent.cc.mcgill.ca id k7PED6jh031610
>
> Hello,
>
> I am just a master student, doing my internship. Right now, I am 
> building a musical instrument recognition system. I have read 
> several papers on it, and I am just curious:
>
> All the papers/journals that I have read use the STFT, a.k.a the 
> |X(t,f)| of a signal x(t), in order to extract several (spectral) 
> features to be used as the input to the recognition system.
>
> What are the reasons behind using the |X(t,f)| instead of using the 
> "power spectral" |X(t,f)|^2 ?
> (technically speaking, a power spectral density is the expectation 
> of |X(f)|^2, i.e. E(|X(f)|^2) )
>
> Thanks in advance,
>
> Edwin SIANTURI