*2.3. Evalution Measures*

In this section, the optimal choice will be derived based on the quantitative experimental results. Since the SNR is one of the measures that evaluates the denoising performance [44,45], the following performance indexes were used to evaluate the denoised signal with *j* and *k*.

$$SNR\_{j,k} = 10 \log\_{10} \frac{\sum\_{i=1}^{N} s^2[i]}{\sum\_{i=1}^{N} \left| s[i] - s\_{j,k}[i] \right|} \,\tag{6}$$

$$\eta(k) = \log\_{10}((s\_l - l(m[k]))) \times l(m[k])),\tag{7}$$

$$eff(j,k) = \frac{SNR\_{j,k}}{\eta(k)}\tag{8}$$

where *s* ˆ *j*,*k* [*i*] and *SNRj*, *<sup>k</sup>* in (10) denote the denoised signal and the SNR when the decomposed level is *j* and the wavelet function index is *k*. The *η*(*k*) (11) is the execution complexity of the wavelet transform in case the wavelet function index is *k*. The *η*(*k*) is defined as the common logarithm value of the number of multiplication operations required for the wavelet transform that can be obtained by the length of the signal *s<sup>l</sup>* and the length of the mother wavelet function *l*(*m*[*k*]). For the denoising process, the higher SNR value shows that a better performance and lower execution complexity represents higher efficiency [46]. Therefore, the new criterion *e f f*(*j*, *k*) (12) is proposed in this study to evaluate denoising performance efficiency.
