SIMULATIONS

To show that the proposed method can segregate the desired signal f₁(t) from a noisy signal f(t) precisely even in waveforms, we ran three simulations using the following signals:
(a) noisy synthesized AM-FM harmonic complex tone [6];
(b) noisy real vowel (/a/, /i/, /u/, /e/, /o/); and
(c) noisy real continuous vowel (/aoi/),
where noise was a pink noise and the SNRs of noisy signals were from 5 to 20 dB in 5-dB steps. The speech signals were the Japanese vowels of four speakers (two males and two females) in the ATR-database [8].

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

$$10\log_{10} \frac{\int_{0}^T f_1(t)^2dt}{\int_{0}^T (f_1(t)-\hat{f}_1(t))^2dt} \qquad (\mbox{dB}).$$ (9)

Next, to show the advantages of the constraints in Table 1, we compared the performance of our method in the following three conditions:
(1) extract the harmonics using the Comb filter and predict A_k(t) and $\theta_{1k}(t)$ 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.