Audio Signal Processing And Application Based On Compressed Sensing

The compressed sensing is applied in the project to reconstruct the original signal by a small amount of sampling data.For different types of signal,the applicable sparse basis,observation matrix and reconstruction algorithm are different.Therefore,the compressed sensing theory and its application about the acoustic signal is researched in this paper.The development and application of compressed sensing theory is introduced briefly in this paper,and the basic concepts and principles of sparse basis,observation matrix and reconstruction algorithm are studied.Three kinds of observation matrices are analyzed particularly,and two improved observation matrices according to the random Bernoulli observation matrix and part Hadamard observation matrix are proposed.The two improved matrices are proved to follow the RIP properties,and their performance is studied by reconstructing the simulating sparse signal in Matlab.The results show that performance of the two improved observation matrices is improved compared with their prototype observation matrix.In order to get the acoustic signal data for further research,the wireless acoustic signal acquisition system is designed by the microphone,MSP430G2553 MCU and nRF24L01 wireless module.In the experiment,the sparse effect of acoustic signal based on different sparse matrices are studied firstly,and the applicable sparse matrix is obtained.Then applicability of various observation matrices to acoustic signal are analyzed,and the two improved observation matrices are used to reconstruct the acoustic signal.The results show that the improved part Hadamard observation matrix based on random sequence can reconstruct the acoustic signal well and its performance is improved obviously.Besides,it can be realized easier by hardware circuit,which is very suitable for the compressed sampling of acoustic signal in project.Secondly,several reconstruction algorithms are adopted to reconstruct the acoustic signal,and their reconstruction effects are studied and compared.Finally,to solve the packet-loss problem in the wireless transmission of the acoustic signal,the CS anti-packet loss algorithm based on the sender and the CS anti-packet loss algorithm based on the receiver are proposed.The acoustic signal is used to verify the algorithms effect,and the simulation results show that the two algorithms have a significant anti-packet loss effect,and the algorithm based on the receiver can recover the signal very well particularly.The acoustic signal can be recovered well even when the packet loss rate is 60%.