Simulations and Results

We carried out two simulations on segregating two-acoustic sources using noise-added signal f(t) to show that the proposed method can extract the desired signal f₁(t) from it. The two simulations are composed as follows:

1.

Extracting an AM complex tone from a noise-added AM complex tone.

2.

Extracting a speech signal from a noisy speech.

We use two types of measures to evaluate the performance of the segregation using the proposed method.

One is the power ratio in terms of the amplitude envelope A_k(t), i.e., the likely SNR. The aim of using this measure is to evaluate the segregation in terms of the amplitude envelope where signal and noise exist in the same frequency region. This measure is called ``Precision,'' and is defined by

$${\rm {Precision}}(k):=10\log_{10}\frac{\int_0^T A_k^2(t)dt}{\int_0^T (A_k(t)-\hat{A}_k(t))^2dt},$$ (11)

where A_k(t) is the amplitude envelope of original signal f₁(t) and $\hat{A}_k(t)$ is the amplitude envelope of the segregated signal $\hat{f}_1(t)$.

The other is spectrum distortion (SD). The aim of using this measure is to evaluate the extraction of a desired signal $\hat{f}_1(t)$ from noise-added signal f(t). This measure is defined by

$${\rm {SD}}:=\sqrt{\frac{1}{W}\sum_{\omega}^{W}\left(20\log_{1... ...rac{\tilde{F}_1(\omega)}{\tilde{\hat{F}}_1(\omega)}\right)^2},$$ (12)

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

The reduced SD of f₁(t) is the SD difference between f(t) and $\hat{f}_1(t)$.

  

Figure: f₁(t) and f(t) (SNR=10 dB).

  

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

  

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