基于压缩感知的信号时频表示重构  

Time-Frequency Representation and Reconstruction Based on Compressive Sensing

作　　者：李秀梅[1] 吕军[1] 

机构地区：[1]杭州师范大学信息科学与工程学院,杭州311121

出　　处：《计算机系统应用》2016年第7期176-181,共6页Computer Systems & Applications

基　　金：国家自然科学基金(61571174);浙江省自然科学基金(LY15F010010);浙江省信号处理重点实验室开放项目(ZJKL_4_SP-OP2013-02)

摘　　要：传统的时频分析方法受限于Nyquist采样定理,信息量的增加提高了对采样速率、传输速度和存储空间的要求;同时,双线性魏格纳-维尔分布处理多分量信号时会产生交叉项,常用的核函数法在抑制交叉项时降低了信号的时频聚集性.该文将压缩感知与时频分析方法相结合,在时频分析中突破采样定理的限制,抑制交叉项的同时获得较高的时频聚集性.针对单分量信号、多分量信号、蝙蝠声音信号,利用不同的窗函数如矩形窗或高斯窗,得出仿真结果,验证了基于压缩感知的信号时频表示重构优于传统的基于傅里叶变换进行重构的方法.并利用最小均方误差MSE和时频聚集度CM作为衡量参数,分析了不同样本空间与所重构信号时频表示性能之间的关系.Traditional time-frequency analysis is restricted by the Nyquist sampling theorem. As the amount ot .information increases, higher requirements are needed in sampling rate, transmission velocity, and storage space. Moreover, bilinear Wigner-Ville distribution is suffered from cross terms when processing multi-component signals. Using the kernel function based methods to suppress cross terms can decrease time-frequency concentration. In this paper, compressive sensing is combined with time-frequency analysis to solve the above problems. Under the framework ~f compressive sensing based time-frequency analysis, the restriction of Nyquist sampling theorem can be lessened, and the Wigner-Ville distribution can achieve suppressed cross terms with high time-frequency concentration. Simulations are provided for mono-eomponent signal, multi-component signal, and bat sound signal, based on different window functions such as the rectangular window or the Gaussian window, to verify that the compressive sensing based time-frequency representation reconstruction is superior to the traditional reconstruction method. Moreover, we analyze the relationship between different sample regions and the performance of the reconstructed time-frequency representations, in terms of the mean-square-error （MSE） and time-frequency concentration measurement （CM）.

关 键 词：压缩感知 时频分析 模糊函数 时频表示 重建 

分 类 号：TN911.7[电子电信—通信与信息系统]