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Re: Intermediate representation for music analysis


 Could you give me some references to people/articles that make use of this
technique ? In fact, this is exactly the technique I use to improve the
frequency resolution of the constant-Q filterbank.


Quoting Hugh McDERMOTT <hughm@xxxxxxxxxxxxxx>:

> I would add to this that, using an FFT, it is quite easy to measure the
> component frequencies of a complex signal with precision that is finer
> than the bin spacing. One just needs to estimate the rate of change of
> the phase of a component within a bin. This technique, which has been
> described in the context of the so-called phase vocoder algorithm,
> permits the frequency of each signal component resolved by the FFT to be
> estimated more precisely than the limit apparently imposed by the FFT
> bin spacing in the frequency domain.
> Best regards,
> Hugh McDermott, PhD
> Principal Research Fellow
> Department of Otolaryngology
> The University of Melbourne
> 384 - 388 Albert Street,
> East Melbourne.  3002
> Australia.
> Phone: +61 3 9929 8665
> Fax: +61 3 9663 6086
> E-mail: hughm@xxxxxxxxxxxxxx
> Web page: http://www.medoto.unimelb.edu.au/people/mcdermoh/
> -----Original Message-----
> From: AUDITORY Research in Auditory Perception
> [mailto:AUDITORY@xxxxxxxxxxxxxxx] On Behalf Of Bob Masta
> Sent: Monday, 17 July 2006 11:01 PM
> To: AUDITORY@xxxxxxxxxxxxxxx
> Subject: Re: Intermediate representation for music analysis
> Note that no matter what sort of analysis you do, the frequency
> resolution is determined by the reciprocal of the analysis window
> duration.  So if you want fine resolution for the low frequencies, you
> need a long sample set, even if you only need much coarser resolution at
> the high frequencies (due to the log nature of hearing).
> So, why not just take a long FFT?  Even though they have linear
> frequency spacing, FFTs have been heavily optimized for efficient
> computation.  I wonder if it might be better using a conventional FFT
> and lumping some upper bins together to form quasi-log bands, rather
> than using a less-efficient log-spaced filter bank.
> There is one weakness to that approach, however, in that if you set the
> overall FFT length so that the lowest band you want to handle is just
> exactly matched by the lowest FFT spectral line width, then the next
> spectral line will be at *twie* that... there will be no nice
> fractional-octave alignment.  If you really need that,
> a log filter bank may be best.
> However, the way I have seen this handled is to assume (hope?) that
> there will be plenty of upper harmonics in the signal, many of which
> will fall into regions of the FFT where the resolution (considered on an
> octave basis) is much higher.  By looking at a few of these upper
> harmonics, it was possible to figure out what the actual fundamental
> frequency was to similarly-high resolution.
> Best regards,
> Bob Masta
> audioATdaqartaDOTcom
>  +++++++++++++++++++++++++++++++++++++++++++
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