Results

First, simulation of segregation are conducted using 10 mixed signals f_M(t). f_M(t) is decomposed by a wavelet filterbank, and is then applied to the segregation algorithm as shown in Fig. . S_k(t) and $\phi_k(t)$ are determined as shown in Fig. . Onset time and offset time of f₁(t), $T_{\rm {on}}$ and $T_{{\rm {off}}}$, are determined as shown in Fig. . The results of simulation for a sinusoidal signal (m=0) as shown in Fig. are shown in Fig. . From this figure, it can be seen that the proposed method can extract a sinusoidal signal from mixed signal.

Similarly, simulations of segregation are carried out using 10 mixed signals f_R(t). The proposed model extracts so little of f₁(t) that f₂(t)becomes approximately the same as f(t).

When the extracted signal corresponds to 10 mixed signals, the mean value of SNR in the time region is calculated as

$${\rm {SNR}}=10\log_{10}\frac{\int_0^T f_i^2(t)dt}{\int_0^T (f_i(t)-\hat{f}_i(t))^2dt},\qquad i=1,2.$$ (30)

It is shown that in the case of f_M(t), the SNR of $\hat{f}_1(t)$ is 12.9 dB (standard deviation 2.58) and the SNR of $\hat{f}_2(t)$ is 10.1 dB (standard deviation 1.58). In the case of f_R(t), the SNR of $\hat{f}_1(t)$ is 1.6 dB (standard deviation 1.58) and the SNR of $\hat{f}_2(t)$ is 8.7 dB (standard deviation 0.48). If f(t) can also enhanced using a bandpassed filter (BPF) with a center frequency of 600 Hz and a bandwidth of 23 Hz and if $\hat{f}_1(t)$ is the enhanced signal, the SNR of $\hat{f}_1(t)$ is only 8.1 dB. From these results, it can be stated that the proposed method is superior in improving SNR in comparison with method using BPF. In the case of f_M(t), the proposed method can not only extract a sinusoidal signal more accurately than f_R(t) but can also a bandpassed noise. While engineering application call for a method of segregating all signals from noisy signals, the proposed method successfully extracts signals by taking advantage of the constraints of ASA (c. f. f_M(t)). Note that the above results show of CMR which is as the human auditory phenomenon. To examine this similarity, we will carry out a simulation of CMR in next section by setting the model parameters to the human auditory properties.