Evaluation of the extracted signal

We used spectrum distortion to evaluate the segregation performance of the proposed method, as defined by

$$\sqrt{\frac{1}{W}\sum_{\omega}^{W}\left(20\log_{10} \frac{\tilde{F}_1(\omega)}{\tilde{\hat{F}}_1(\omega)}\right)^2},$$ (10)

where $\tilde{F}_1(\omega)$ and $\tilde{\hat{F}}_1(\omega)$ are the amplitude spectra of f₁(t) and $\hat{f}_1(t)$, respectively. In the above equation, the frame length is 51.2 ms, the frame shift is 25.6ms, W is the analyzable bandwidth of the filterbank (about 6 kHz), and the window function is Hamming.

Next, in order to show the advantages of the constraints in Table 1, we compare the performance of our method under the following three conditions: (1) extract the harmonics using the Comb filter and predict A_k(t) using the Kalman filtering; (2) extract the harmonics using the Comb filter; and (3) do nothing. Here, condition 1 corresponds to the smoothness of constraint (ii) being omitted; condition 2 corresponds to constraints (ii) and (iii) being omitted; and condition 3 corresponds to no constraints being applied at all.

  

Figure: Segregation accuracies for simulations: (top) simulation 1, (middle) simulation 2, (bottom) simulation 3.

Segregation accuracies of the three simulations are shown in Fig. . For example, when the SNR of f(t) was 10 dB as shown in Fig. (b) for simulation 3, the proposed method could segregate A_k(t) with high accuracy and could extract $\hat{f}_1(t)$, shown in Fig. (d), from f(t). In addition, we compared our proposed method with the other method (under three conditions) for the above simulations. The results show that the segregation accuracy using the proposed method was better than that using the other three conditions. The results for these three simulations and three conditions show that the proposed method can segregate the desired harmonic tone from a noisy harmonic tone with high accuracy. Improvements in spectrum distortion for simulations 1, 2, and 3 are about 17.6, 7.0, and 5.4 dB, respectively.