Hodgkinson, Matthieu
(2011)
ExponentialPlusConstant Fitting based on Fourier Analysis.
Proceedings of the 17èmes Journées d'Informatique Musicale SaintEtienne, France, 2011.
Abstract
A closed form method for Exponential Plus Constant (EPC)
curve fitting is introduced. The method, referred to as Fourierbased
Exponential Plus Constant Fitting (FEPCF), returns
estimates of the EPC coefficients for userinput sets of
equidistant time values and corresponding data points. An
analytical expression for the exponent’s coefficient is found
through algebraic manipulation of the Fourier series of the
EPC, taken over a finite time interval. The unknown is therefore
approximated through the Discrete Fourier Transform
(DFT) of the input sequence, itself used as an approximation
of Fourier series. The discrepancy between
Fourier series and DFT, byproduct of aliasing, is reduced
with sine windowing. This is the essential contribution
of the paper – the exponent coefficient found, what remains
of the problem can be approached with standard linear
least squares. FEPCF was motivated by the need for a
measuring tool for the timemodeling of fundamental frequency
and inharmonicity coefficient of tensionmodulated
strings. Care is however taken in the mathematical formulation
of the method to facilitate its transportation to other
fields of science. MATLAB function implementation and
a demonstration of FEPCF can be downloaded from the
address http://www.cs.nuim.ie/~matthewh/.
Item Type: 
Article

Keywords: 
Fourier Analysis; 
Academic Unit: 
Faculty of Science and Engineering > Computer Science 
Item ID: 
3963 
Depositing User: 
Matthieu Hodgkinson

Date Deposited: 
01 Nov 2012 15:08 
Journal or Publication Title: 
Proceedings of the 17èmes Journées d'Informatique Musicale SaintEtienne, France, 2011 
Publisher: 
Universite Jean Monnet, SaintEtienne, France, 
Refereed: 
Yes 
URI: 

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