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*To*: AUDITORY@xxxxxxxxxxxxxxx*Subject*: Re: Fourier decomposition*From*: "Richard F. Lyon" <DickLyon@xxxxxxx>*Date*: Sat, 17 Sep 2005 14:06:47 -0700*Comments*: To: Mark Every <mre104@york.ac.uk>*Delivery-date*: Sat Sep 17 17:15:50 2005*In-reply-to*: <001a01c5bb65$09ba1c10$ee882090@jespc01>*References*: <432B5321.3050805@alum.mit.edu> <p06230901bf514a440abc@[192.168.1.102]> <001a01c5bb65$09ba1c10$ee882090@jespc01>*Reply-to*: "Richard F. Lyon" <DickLyon@xxxxxxx>*Sender*: AUDITORY Research in Auditory Perception <AUDITORY@xxxxxxxxxxxxxxx>

Although the STFT coefficients do not directly give an accurate estimation of the sinusoidal/harmonic parameters(frequency, amplitude and phase), unless the sinusoid happens to fit an exact integer number of times into the analysis window, it is possible to improve the estimation of these parameters over the values computed from the STFT maximum frequency bin corresponding to each harmonic.

I think Fred's point, which I claim is self-evident, is that all such methods have inherent accuracy limits. I would go further and argue that Fourier techniques make the problem harder, not easier, than a direct time-domain or autocorrelation technique.

So, knowing the period of the signal is not a prerequisite to accurately finding the parameters of the harmonics of that signal. ...

And my point is that "knowing the period" is not a prequisite, but that finding the period is equivalent to solving the stated problem. That is, the period is found if the harmonics are found, and the harmonics are trivial to find if the period is found. So the problem can be reduced to the problem of identifying the period of a signal that is known to be periodic but of unknown period.

Dick

**References**:**Fourier decomposition***From:*Fred Herzfeld

**Re: Fourier decomposition***From:*Richard F. Lyon

**Re: Fourier decomposition***From:*Mark Every

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