基于Chen-mobius变换的语音信号处理及图片传输的研究

发布时间：2018-03-19 03:21

本文选题：Chen-mobius变换　切入点：信号处理　出处：《云南师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：自从Mobius反演公式1857年被发现以来,很多学者对它进行推广运用,其最为突出的成果就是利用Mobius反演公式推导出Chen-mobius变换。运用Chen-mobius变换与其原函数自身正交而所属函数族非正交的这个特性解决了一系列重要的物理学中的逆问题,例如,玻色体系逆问题、晶格比热逆问题、晶格结合能逆问题、费米体系逆问题、黑体辐射逆问题、材料模拟计算等,开创了数论中的Mobius变换解决物理学中各种逆问题的巧妙方法。同时Chen-mobius变换也被应用于信号处理方面,创造了Chen-mobius新型通信系统。Chen-mobius通信系统就是运用mobius变换把常用信号(周期矩形脉冲,奇偶对称方波、锯齿波和三角波)的傅里叶级数进行逆变换,得到了的正余弦函数及一般周期信号的波形展开,继而求得Chen-mobius变换。Chen-mobius变换函数与原信号相互正交,但是其所属的函数族为非正交的,这样的两个函数在通信处理的调制解调过程中具有优越性。Chen-mobius变换经常用于简单信号的变换,一般情况下其主要用于一般正余弦信号和方波信号。本文试图让Chen-mobius更广泛,更具体,继而对特殊信号的Chen-mobius变换进行推导,得到了有一定运用价值的一些结论,并把其运用语音信号处理及图片传输。此篇论文主要完成三个方面的工作。首先,进行了两个特殊信号(二次函数周期波形及二次函数锯齿波形)的Chen-mobius变换的推导;然后把推导结果运用到语音信号处理及图片传输过程中,发现了此处理过程的安全性与稳定性;其次把二次函数周期波形及二次函数锯齿波形的Chen-mobius变换用在语音信号及图片传输的嵌套处理过程中,发现其相比于非嵌套系统具有加密性;最后对信号处理的波形对比图及参数进行分析,结果表明Chen-mobius在语音信号处理及图片传输过程中的可行性及优越性。
[Abstract]:Since the discovery of the Mobius inversion formula in 1857, many scholars have popularized it. The most outstanding result is the derivation of the Chen-mobius transform by using the Mobius inversion formula, which solves a series of important inverse problems in physics by using the characteristic that the Chen-mobius transform is orthogonal to its original function itself and that the family of functions belongs to it is not orthogonal, for example, Inverse problem of boson system, inverse problem of specific heat of lattice, inverse problem of lattice binding energy, inverse problem of Fermi system, inverse problem of blackbody radiation, calculation of material simulation, etc. The method of solving various inverse problems in physics by Mobius transformation in number theory was created. Meanwhile, Chen-mobius transform was also applied to signal processing. The Chen-mobius new communication system. Chen-mobius communication system is to use mobius transform to transform the Fourier series of common signals (periodic rectangular pulse, odd-even symmetric square wave, sawtooth wave and triangular wave). The obtained sine cosine function and the waveform expansion of the general periodic signal are obtained, and then the Chen-mobius transform. Chen-mobius transform function is orthogonal to the original signal, but its function family is nonorthogonal. These two functions have advantages in the process of modulation and demodulation in communication processing. Chen-mobius transform is often used in the transformation of simple signals, and in general, it is mainly used in general sinusoidal signals and square wave signals. This paper tries to make Chen-mobius more extensive and more specific. Then the Chen-mobius transform of the special signal is deduced, and some conclusions with certain application value are obtained, and the speech signal processing and picture transmission are used. This paper mainly completes three aspects of work. The Chen-mobius transform of two special signals (quadratic function periodic waveform and quadratic function sawtooth waveform) is derived, and the results are applied to the speech signal processing and picture transmission. The security and stability of the processing process are found. Secondly, the Chen-mobius transform of the quadratic function periodic waveform and the quadratic function sawtooth waveform is used in the nested processing of speech signal and picture transmission. It is found that it has encryption compared with non-nested system. Finally, the waveform contrast diagram and parameters of signal processing are analyzed. The results show that Chen-mobius is feasible and superior in the process of speech signal processing and picture transmission.
【学位授予单位】：云南师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN912.3

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