Análise do gráfico de controle CUSUM para a filtragem de sinais utilizando coeficientes wavelet

Abstract

The Fourier transform has long been one of the few available signal processing options. However, in the last decades different types of transform have become efficient alternatives for filtering, compression and other types of signal analysis. In this work, the Daubechies wavelet transform will be one of the tools for filtering signals with different noise levels. In a signal corrupted by additive noise, the high frequency components are the most compromised, and they require a more rigorous treatment for a more faithful reconstruction of the ideal signal. The present work investigates the feasibility of using cumulative sum control chart (CUSUM) as a technique to determine the cut-off thresholds for the truncation process of the wavelet coefficients, resulting from the wavelet transform. The proposed methodology will be validated through numerical simulations for different signals and different associated noise levels, called scenarios. In the end, was finded a configuration that adapts in the major of this scenarios, showing the competivity of CUSUM chart for signal filtering, using wavelet coefficients, to analise and compare your efficiency with classic algorithms for signal statistical filtering.