Elimination of White Noise from Time Series through the Wavelet Transform

Iván F. Palacios, and Marilyn V. Cepeda

Department of Earth Sciences and Construction, University of the Armed Forces ESPE, Ecuador

Abstract: The time series is an extensive data set in which you have information about a phenomenon of nature, these data contain certain values that correspond to stochastic errors that occur at the time of obtaining the data. These series are non-stationary in nature so it is assumed that they have white noise, which, for geodetic calculations that require a lot of data accuracy, such as velocity field, gravity, geoid undulation, direct and inverse problem, impact on the final results. The random error is known as white noise, which can be eliminated by using functions that work in variable time and frequency, this new series without noise, is the result of the application of a useful tool called Wavelet, within the types of wavelet is the Haar family that analyzes series with abrupt changes. It is this study was performed automatically the elimination of white noise present in three time series of scale values of the SIRGAS-EPEC station by using the Discrete transformed Wavelet type Haar in order to obtain the clean signal of noise, its energy retained and graphs of the resulting series. It was possible to obtain the graphs of the three series with and without noise, in which a percentage of energy retained was 97.792%, 99.811%, 90.852% in series 1, 2 and 3 respectively. The application of wavelets of the Haar type allowed to obtain the three series without noise, in the case of series 1 and 2.

Key words: white noise, Haar, retained energy, random error, SIRGAS