Simulation 1

This simulation assumes that f₁(t) is an AM complex tone as shown in Fig. 2, where F₀=200 Hz, N=10, and envelope of f₁(t) is sinusoidal (10 Hz), and f₂(t) is a bandpassed random noise, where the bandwidth of f₂(t) is about 6 kHz. Seven types of f(t) are used as simulation stimuli, where the SNRs of f(t) are from -10 to 20 dB in 5-dB steps. The mixed signal for SNR=10 dB is plotted in Fig. 2.

The simulations were carried out using the seven mixed signals. The average SDs of f₁(t) and f(t) are shown in Fig. 3. As a result, it is possible to reduce the SD by about 20 dB as noise reduction by using the proposed method. For example, when the SNR of f(t) is 10dB, the proposed method can segregate A_k(t) with high precision as shown in Fig. 4, and it can extract the $\hat{f}_1(t)$ shown in Fig. 4 from the f(t) shown in Fig. 2. The signal is reconstructed by considering $\theta_{1k}(t)=\phi_k(t)$, because phase information can not be determined by the assumption $\theta_{1k}(t)=0$. The proposed model can extract the amplitude information of AM complex tone from a noise-added signal f(t) with a high precision in which signal and noise exist in the same frequency region. Moreover, the proposed model can also extract the desired AM complex tone from mixed AM complex tones with different fundamental frequencies.