Research On Fast Algorithm For Speech Signal MP Sparse Decomposition And Its Application In Speech Recognition

Language is the most direct way to communicate, so it is important to research how to represent speech signals. Signal sparse decomposition based on Matching Pursuit(MP) has been applied to many areas because of its predominant way of represent signals. But the large computational cost is the bottleneck of sparse decomposition. Although MP sparse decomposition has been improved many times, the quality and the speed of the algorithm are not satisfactory for people's demands. The algorithm which is improved by FFT is based on complex function, but the speech signals and the atoms are both real. So this improved algorithm dose not match the signal model.In this thesis, according to the cyclic property of the speech signal, cosine over-complete dictionary is chosen in order to sparse decompose the speech signal. The method not only can guarantee the quality of the reconstructed signal, but also can cut down the size of the dictionary. Thereby, the memory consumption and the computational time are both reduced. Lots of simulations prove that the new dictionary is more suitable for the periodic signals.Furthermore, a new sparse decomposition algorithm is proposed.In order to reduce the storage of the over-complete dictionary, with the equal relationship, this method firstly uses set partitioning method. And then according to the characters of the speech signal and the fact that the signals and atoms are all real, this new algorithm converts inner product calculations into cyclic correlation calculations that are fast done by Fast Hartley Transform(FHT). Because of using the relationship of the inner product and the cyclic correlation as well as the relationship of the cyclic correlation and FHT, the speech of the speech signal MP sparse decomposition is increased. Compared to the algorithm of the MP based signal sparse decomposition with FFT, this algorithm can not only get over the instability of the results, but also can reduce the memory consumption by half, and heighten the speed of the decomposition. Last, the atoms and the projects gotten by sparse decomposition with Gabor dictionary contain the speech signals' important message. Every atom is determined by parameters, so the atoms' parameters and projects can be regarded as the speech signals' characteristics. The speech recognition can be realized using this new characteristics.In this paper, the computer simulations verify the efficiency of every new improved method.