الگوریتم های پردازش سیگنال تطبیقی
Abstract
I. Introduction
II. Algorithm EMD
III. Algorithm ITD
IV. Synthesis of Adaptive Filter Banks Using EMD and ITD
V. Spectral Analysis of Signals Using EMD, ITD and Hilbert Transform
Authors
Figures
References
Abstract
In the last two decades, both Empirical Mode Decomposition (EMD) and Intrinsic Time-Scale Decomposition (ITD) algorithms deserved a variety of applications in various fields of science and engineering due to their obvious advantages compared to conventional (e.g. correlation- or spectral-based analysis) approaches like the ability of their direct application to non-stationary signal analysis. However, high computational complexity remains a common drawback of these otherwise universal and powerful algorithms. Here we compare similarly designed signal analysis algorithms utilizing either EMD or ITD as their core functions. Based on extensive computer simulations, we show explicitly that the replacement of EMD by ITD in several otherwise similar signal analysis scenarios leads to the increased noise robustness with simultaneous considerable reduction of the processing time. We also demonstrate that the proposed algorithms modifications could be successfully utilized in a series of emerging applications for processing of non-stationary signals.
Introduction
Majority of the observational signals considered in various fields of knowledge are non-stationary indicated by the variability of their statistical characteristics over time. In most practical scenarios, the stationarity assumption is validated for the first- and second-order moments only indicated by the time independence of both average and variance as well as the autocorrelation function having only a single time scale argument. Existing approaches to the non-stationary signal analysis and processing have several significant drawbacks. For example, the widely used classical Fourier analysis, due to its relative calculation simplicity and fast computational algorithms availability, immediately began to overwhelm all other signal analysis methods. Despite the fact that the Fourier transform is performed under very general assumptions such as the Dirichlet boundary conditions and absolute integrability, there are several significant limitations on the signals for which it is calculated [1]. Fourier analysis has been originally suggested for strictly periodic functions that could be directly expanded in a Fourier series, i.e. represented by a superposition of multiple harmonic functions. Otherwise, the frequency domain based analysis may lead to incorrect results interpretation. It is also necessary that signals exhibiting the stationarity property for their certain characteristics such as average values and instant frequencies [1].