Fuzzy entropy based noisy signal processing method and iterative singular spectrum analysis soft threshold de-noising method
AssigneeHwashen Electronics Co., Ltd.
InventorHongbo Xie
Life of this patent
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Abstract
A fuzzy entropy based noisy signal processing method and an iterative singular spectrum analysis (SSA) soft threshold de-noising method are disclosed. The method employs FuzzyEn, which is used to quantify the system complexity in chaos theory, to characterize a noise floor, which provides a more effective path for processing of noisy signal; its fuzzy entropy spectrum based iterative singular spectrum analysis soft threshold (SSA-IST) de-noising method outperforms the conventional truncated singular spectrum, wavelet transform and empirical mode decomposition de-noising approaches in de-noising performance.
Claims2
A fuzzy entropy based noisy signal processing method, comprising:
- considering a noisy signal Xin={x1,x2, . . . ,xN} of N samples, and it is assumed that the additive white noise is uncorrelated with the signal, i.e., Xin=X+n, where X represents the noise-free signal, and n the white noise,
- constructing a series of d-dimensional vectors Xed={xedxe+1d, . . . ,xe+d−1d}, (1≤e≤N−d+1), from the original signals Xin,
- defining the degree of similarity Srd(e) and the fuzzy probability Srd, and
- constructing a (d+1)-dimensional vector Xed+1 as well as its corresponding degree of similarity Srd+1(e) and fuzzy probability Srd+1,
- wherein the FuzzyEn is defined by:
- FuzzyEn(d,r,N)=−ln(Srd−1/Srd), where d and r are set to 2 and 0.2 respectively, N is the length of the signal to be de-noised, thereby defining the singular spectrum distribution of all components obtained from any signal decomposition approach as a FuzzyEn spectrum.
An iterative singular spectrum analysis soft threshold de-noising method based on a FuzzyEn spectrum, comprising:
- (1) SSA decomposition:
- the noisy signal Xin={x1,x2, . . . ,xN} is embedded into a m×d Hankel matrix, and SVD is employed to decompose the Hankel matrix into the sum of d rank-1 matrices and then reconstruct d signal components Xc={x1c,x2c, . . . ,xNc} (c=1, . . . d);
- (2) fuzzyEn spectrum calculation:
- the FuzzyEn spectrum of SSA components and the FuzzyEn value of original noisy signal are calculated, wherein the FuzzyEn is defined by:
- FuzzyEn(d,r,N)=−ln(Srd−1/Srd) where d and r are set to 2 and 0.2 respectively, N is the length of the signal to be de-noised, thereby defining the singular spectrum distribution of all components obtained from any signal decomposition approach as a FuzzyEn spectrum;
- (3) soft threshold setting:
- no threshold de-noising is made to the first component X1, for components from X2 to Xk whose FuzzyEn value is lower than that of the noisy signal, a smaller threshold is set as τc=σc√{square root over (2log10 N)}/√{square root over (d)}, and for the remaining components from Xk+1 to Xd, a larger threshold is set as τc=σc√{square root over (2log10 N)}, where σc is the variance of component Xc;
- (4) soft threshold de-noise:
- all components Xc(c=2, . . . ,d) except the first component are de-noised using soft threshold, namely, if the absolute value of the numerical value of a certain noisy signal of each component is lower than the threshold for this component, the output is zero;
- if the signal value is larger than the threshold, the output is the signal value minus the threshold;
- otherwise, the output is the signal value plus the threshold, where the sum of all soft threshold de-noised components {tilde over (X)}c(c=2, . . . ,d) and x1 is a first estimated signal {tilde over (x)} and the estimated noise is set as ñ=xin−{tilde over (x)};
- (5) estimate the variance of ñ, using the estimated noise {tilde over (x)} as an input signal, repeat steps (1) to (4);
- (6) compare the variance of the noise obtained in successive iterations, if the noise variance is no longer decreased significantly or reaches the predetermined iteration times, the iteration stops;
- otherwise, repeat steps (1) to (5);
- and
- (7) the de-noised signal {tilde over (x)} is the sum of the trend x1 with the minimal noise variance or the predetermined iteration times and all de-noised components {tilde over (x)}c(c=2, . . . ,d).
Dependencies are inferred from the claim text.