中文摘要：

针对语音信号压缩感知问题,在研究语音离散余弦变换（Discrete Cosine Transform,DCT）系数和小波包变换（Wavelet Packet Transform,WPT）特性的基础上构造了离散余弦小波包变换（Discrete Cosine Wavelet Packet Transform,DCWPT）。DCWPT首先获取语音信号的DCT域系数,结合语音频谱特性选取部分DCT系数进行WPT变换,从而得到比DCT系数更加稀疏的DCWPT系数。为将此变换直接用于压缩感知,构造了DCWPT的正交稀疏分解矩阵并分析了其稀疏表示性能。结合稀疏表示基优化了正交匹配追踪重构算法,提出了基于DCWPT的语音信号压缩感知框架。通过压缩重构对照实验,采用主客观评价指标,得出该方法优于传统基于DCT的语音压缩感知方法的结论。

英文摘要：

Concerning the compressed sensing of speech signal, the discrete cosine wavelet packet transform（DCWPT） for speech signal is proposed on basis of the properties of discrete cosine transform and wavelet packet transform. The coefficients of DCWPT can be obtained by wavelet packet transform（DWT） from the coefficients of discrete cosine transform（DCT）, and the coefficients are sparser in DCWPT domain than in DCT domain. In order to apply this new efficient transform to the compressed sensing of speech signal successfully, the sparse decomposition matrix of DCWPT is constructed and its performance analyzed. Also the orthogonal matching pursuit reconstruction algorithm is optimized according to the sparse decomposition matrix, and a new framework of the compressed sensing of speech signal based on DCWPT is put forward. It is concluded by subjective and objective indicators from the experiment that the new method is better than the traditional DCT method.