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The performance of wavelet de‐noising depends on the determination of two factors, the threshold value λ and the threshold function. In this section, the wavelet de‐noising algorithm adopts the soft thresholding method to adaptively filter the specific spectrums of the noisy signals to obtain modified wavelet coefficients . Let at level j.

The soft thresholding method sets every wavelet coefficient c_j[n] to zero if |c_j[n]| is less than or equal to a chosen threshold λ; otherwise, the threshold is subtracted from any c_j[n]. Then, all modified coefficients = at level j can be defined as:

(2.4)

(2.5)

where

 cj[n] nth wavelet coefficients at level j;

  nth modified wavelet coefficients at level j;

 λ threshold of cj[n]; and

 MAD(cL − 1[n]) mean absolute deviation of cL − 1[n].