Simulation 2

  

Figure: f₁(t) and f(t) (SNR=10dB).

    

Figure: SDs of $\hat{f}_1(t)$ and f(t).
Figure: Precision property for $\hat{f}_1(t)$.

This simulation assumes that f₁(t) is a synthetic vowel, as shown in Fig. 5, where F₀=125 Hz, N_F0=40, and it is the vowel /a/ synthesized by LMA, and that f₂(t) is a bandpassed random noise with a bandwidth of about 6 kHz. Three types of f(t) are used as simulation stimuli, where the SNRs of f(t) are from 0 to 20 dB in 10-dB steps. The mixed signal for SNR=10 dB is plotted in Fig. 5.

The simulations were carried out using the three mixed signals. The average SDs of f₁(t) and f(t) are shown in Fig. 6. Hence, it is possible to reduce the SD by about 15 dB as noise reduction by using the proposed method. For example, when the SNR of f(t) is 10 dB, the proposed method can segregate A_k(t) with high precision, as shown in Fig. 7, and it can extract the $\hat{f}_1(t)$ shown in Fig. 7 from the f(t) shown in Fig. 5. Therefore, the proposed model can also extract the amplitude information of speech f₁(t) from a noisy speech f(t) with high precision when speech and noise exist in the same frequency region. Hence, this method can be used to extract a speech signal from noisy speech.