Int. J. Data Analysis Techniques and Strategies, Vol. 5, No. 3, 2013 291
Copyright © 2013 Inderscience Enterprises Ltd.
An equivalence between typical spectrographic data
analysis and the formulations for time series analysis
Leonardo Bennun
Departamento de Física,
Laboratorio de Física Aplicada,
Facultad de Ciencias Físicas y Matemáticas,
Universidad de Concepcion – Concepcion (41), Chile
Fax: 56-41-2224520
E-mail: bennun@yahoo.com
Abstract: We have demonstrated the equivalence of two formulations
for data processing, which usually are studied separately and independently.
Habitually, for time series analysis, like signals processed in communications,
electronics, control sciences, etc., mathematical tools based on autocorrelations,
cross-correlations or convolutions, etc., are applied. Another sort of
formulations is applied for analysis in spectrographic techniques, where the
data is usually processed with statistical procedures based on the least square
method. The equivalence demonstrated between both methodologies opens new
possibilities in time series analysis, in order to find predetermined structures in
the acquired data. Also, all of the mathematical criteria often used in
spectroscopic analysis (like the limit of detection, or the determination limit),
could be applied in methods for analysis of data depending on time.
Keywords: data analysis; maximum likelihood principle; processing methods.
Reference to this paper should be made as follows: Bennun, L. (2013)
‘An equivalence between typical spectrographic data analysis and the
formulations for time series analysis’, Int. J. Data Analysis Techniques and
Strategies, Vol. 5, No. 3, pp.291–302.
Biographical notes: Leonardo Bennun graduated from the Balseiro Institute,
Argentina where he obtained his PhD (2005) and MS (1993) in Nuclear
Engineering. He joined the Applied Physics Group at Concepción University,
Chile in 2006 as a Research Scientist. His research interests include the
development of nuclear methods applied to exploration and exploitation of
energetic and mineral resources; metrology, data treatment and the study of
stochastic processes.
1 Introduction
In the following, we show that two mathematical formulations of analysis, usually
considered independent, the first applied to spectroscopic data and the second applied to
time series, are absolutely equivalent from a mathematical point of view.
There are standard procedures commonly used for the analysis of a time series, which
are widely applied to signal processing in communication, mathematical finance, control
sciences, etc. These formulations have application areas much more diverse, as many