Hans Journal of Wireless Communications
Vol.08 No.04(2018), Article ID:26130,7 pages
10.12677/HJWC.2018.84016

Speech Enhancement Algorithm Combining Speech Absence Probability

Ruirui Han, Ying Gao, Chen Chen

School of Opto-Electronic Information, Yantai University, Yantai Shandong

Received: Jul. 1st, 2018; accepted: Jul. 18th, 2018; published: Jul. 30th, 2018

ABSTRACT

The research work of this paper is mainly on the basis of the amplitude squared spectrum least mean square estimator and proposes a new algorithm. Due to the uncertainty of the speech in the statistical model of noisy speech, the unified processing of speech signals will inevitably result in the loss of speech components, which will affect the performance of speech enhancement. Therefore, this paper mainly studies and estimates the frequency of each signal. The speech probability is then combined with the gain function of the squared spectrum least mean square error algorithm to derive a new gain function. Finally, we can see through the experimental simulation, the algorithm proposed in this paper can significantly improve the voice quality and improve the intelligibility of the voice.

Keywords:Speech Enhancement, Speech Absence Probability, Minimum Mean-Squared Error, Gain Function

1. 引言

2. 语音增强算法基本理论

${Y}_{k}^{2}={X}_{k}^{2}+{D}_{k}^{2}$ (1)

${\stackrel{^}{X}}_{k}^{2}=E\left\{{X}_{k}^{2}|{Y}_{k}^{2}\right\}={\int }_{0}^{{Y}_{k}^{2}}{X}_{k}^{2}f\left({X}_{k}^{2}|{Y}_{k}^{2}\right)\text{d}{X}_{k}^{2}$ (2)

$f\left({X}_{k}^{2}|{Y}_{k}^{2}\right)=\frac{f\left({Y}_{k}^{2}|{X}_{k}^{2}\right)f\left({X}_{k}^{2}\right)}{f\left({Y}_{k}^{2}\right)}=\left\{\begin{array}{l}{\Psi }_{k}\mathrm{exp}\left(-\frac{{X}_{k}^{2}}{\lambda \left(k\right)}\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\sigma }_{x}^{2}\ne {\sigma }_{d}^{2}\\ \frac{1}{{Y}_{k}^{2}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{ }\text{ }\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\sigma }_{x}^{2}={\sigma }_{d}^{2}\end{array}$ (3)

$\frac{1}{\lambda \left(k\right)}=\frac{1}{{\sigma }_{x}^{2}\left(k\right)}-\frac{1}{{\sigma }_{x}^{2}\left(k\right)}$ (4)

${\Psi }_{k}=\frac{1}{\lambda \left(k\right)\left\{1-\mathrm{exp}\left[-\frac{{Y}_{k}^{2}}{\lambda \left(k\right)}\right]\right\}}$ (5)

${X}_{k}^{2}=\left\{\begin{array}{l}\left(\frac{1}{{v}_{k}}-\frac{1}{\mathrm{exp}\left({v}_{k}\right)-1}\right){Y}_{k}^{2},\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\sigma }_{x}^{2}\ne {\sigma }_{d}^{2}\\ \frac{1}{2}{Y}_{k}^{2},\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{\hspace{0.17em}}\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }{\sigma }_{x}^{2}={\sigma }_{d}^{2}\end{array}$ (6)

${G}_{\text{MMSE-MSS}}=\left\{\begin{array}{l}\sqrt{\frac{1}{{v}_{k}}-\frac{1}{\mathrm{exp}\left({v}_{k}\right)-1}},\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{\hspace{0.17em}}{\sigma }_{x}^{2}\ne {\sigma }_{d}^{2}\\ \sqrt{\frac{1}{2},}\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }{\sigma }_{x}^{2}={\sigma }_{d}^{2}\end{array}$ (7)

3. 本文提出的融合无语音概率的语音增强算法

${f}_{{X}_{k}^{2}}\left({X}_{k}^{2}\right)=\frac{1}{{\sigma }_{x}^{2}}\mathrm{exp}\left[-\frac{{X}_{k}^{2}}{{\sigma }_{x}^{2}}\right]$ (8)

${f}_{{D}_{k}^{2}}\left({D}_{k}^{2}\right)=\frac{1}{{\sigma }_{d}^{2}}\mathrm{exp}\left[-\frac{{D}_{k}^{2}}{{\sigma }_{d}^{2}}\right]$ (9)

${f}_{{Y}_{k}^{2}}\left({Y}_{k}^{2}\right)=\frac{1}{{\sigma }_{x}^{2}-{\sigma }_{d}^{2}}\left(\mathrm{exp}\left(-\frac{{Y}_{k}^{2}}{{\sigma }_{x}^{2}}\right)-\mathrm{exp}\left(-\frac{{Y}_{k}^{2}}{{\sigma }_{d}^{2}}\right)\right)$ (10)

$\left\{\begin{array}{l}{H}_{0}^{k}:{Y}_{k}^{2}={D}_{k}^{2}\\ {H}_{1}^{k}:{Y}_{k}^{2}={X}_{k}^{2}+{D}_{k}^{2}\end{array}$ (11)

$P\left({Y}_{k}^{2}|{H}_{1}^{k}\right)=\frac{1}{{\sigma }_{x}^{2}-{\sigma }_{d}^{2}}\left(\mathrm{exp}\left(-\frac{{Y}_{k}^{2}}{{\sigma }_{x}^{2}}\right)-\mathrm{exp}\left(-\frac{{Y}_{k}^{2}}{{\sigma }_{d}^{2}}\right)\right)$ (12)

$P\left({Y}_{k}^{2}|{H}_{0}^{k}\right)=\frac{1}{{\sigma }_{d}^{2}}\mathrm{exp}\left(-\frac{{Y}_{k}^{2}}{{\sigma }_{d}^{2}}\right)$ (13)

$P\left({Y}_{k}^{2}|{H}_{1}^{k}\right)=\frac{P\left({Y}_{k}^{2}|{H}_{1}^{k}\right)P\left({H}_{1}^{k}\right)}{P\left({Y}_{k}^{2}|{H}_{0}^{k}\right)P\left({H}_{0}^{k}\right)+P\left({Y}_{k}^{2}|{H}_{1}^{k}\right)P\left({H}_{1}^{k}\right)}=\frac{\Lambda \left({Y}^{2}\right)}{1+\Lambda \left({Y}^{2}\right)}=G$ (14)

${G}_{\text{new}}={G}_{\text{MMSE-MSS}}\cdot \sqrt{G}$ (15)

${\stackrel{^}{X}}_{k}^{2}={G}_{\text{new}}\cdot {Y}_{k}^{2}$ (16)

4. 仿真实验结果分析

(a) 纯净语音信号语谱图 (b) 带噪语音信号语谱图 (c) 基于MMSE-MSS算法的增强语音语谱图 (d) 基于本文算法的增强语音信号语谱图

Figure 1. The spectrum of speech signal of different algorithms under white noise. (SNR = 10 dB)

Table 1. The data comparison table of the two algorithms

5. 小结

Speech Enhancement Algorithm Combining Speech Absence Probability[J]. 无线通信, 2018, 08(04): 141-147. https://doi.org/10.12677/HJWC.2018.84016

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