Some Remarks about Entropy of Digital Filtered Signals

Abstract

The finite numerical resolution of digital number representation has an impact on the properties of filters. Much effort has been done to develop efficient digital filters investigating the effects in the frequency response. However, it seems that there is less attention to the influence in the entropy by digital filtered signals due to the finite precision. To contribute in such a direction, this manuscript presents some remarks about the entropy of filtered signals. Three types of filters are investigated: Butterworth, Chebyshev, and elliptic. Using a boundary technique, the parameters of the filters are evaluated according to the word length of 16 or 32 bits. It has been shown that filtered signals have their entropy increased even if the filters are linear. A significant positive correlation (p < 0.05) was observed between order and Shannon entropy of the filtered signal using the elliptic filter. Comparing to signal-to-noise ratio, entropy seems more efficient at detecting the increasing of noise in a filtered signal. Such knowledge can be used as an additional condition for designing digital filters.

Nonlinear Neural Patterns Are Revealed In High Frequency fNIRS Analysis

“…SampEn contained significant areas of difference between fast and slow wave fNIRS for detectors in all 4 quadrants of the sensor space covering cortex, and generally had a higher Friedman score across the cortex compared to mean analysis. It is not evident exactly how the filters affect the regularity of state space, however Borges et al show that high pass filtering results in lower mean entropy but higher variance than low-pass filtering [52]. This effect may correspond to the significantly different SampEn representational similarity across subjects seen.…”

Multivariate Pattern Analysis of Entropy estimates in Fast- and Slow-Wave Functional Near Infrared Spectroscopy: A Preliminary Cognitive Stress study

“…Considering the mean estimate is a linear estimate corresponding to the direct current value of the signal, it is not surprising that representational similarity analysis found no significant differences between fast or slow waves, as the band pass highly attenuates the direct current component, thus, the mean value is merely scaled by the filter. Regarding SampEn and fuzzyEn, how the filters affect the regularity of state space is not as easily understood, however Borges et al show that high pass filtering results in lower mean entropy but higher variance than low-pass filtering [24]. This effect may correspond to the significantly different mean representational similarity across subjects seen.…”

O Efeito da Digitalização num Sistema de Comunicação Baseado em Sincronismo Caótico

“…Esse erro de digitalização pode ser visto de uma maneira alternativa se considerarmos os coeficientes dos mapas delimitados por um intervalo [26]. Assim, a digitalização pode ser vista como a adição de uma certa quantidade de incerteza [27]. Quanto menos bits for usado na digitalização; mais ruído é adicionado.…”

“…Com isso, a capacidade de armazenamento, a precisão com que as constantes são armazenadas e os cálculos efetuados podem ser severamente afetados [9]. Dessa forma, as consequências das limitações computacionais são investigadas em diversas áreas, como por exemplo, processamento digital de sinais [10][11][12][13], simulação computacional [14,15] e sistemas dinâmicos [16][17][18].…”