Generalised distributions and digital signal processing applications

1. 第一个目标是将候选人最近引入的新的扩展双边拉普拉斯、z和傅立叶相关变换应用于物理、化学、生物医学信号的数字信号处理以及音乐信号的谐波分析，这要归功于他对分布理论的推广。2009年6月刚刚出版的候选人的一本书，“信号，系统，变换和DSP…”，1346页，泰勒和弗朗西斯（CRC），被出版商宣布为该领域的新参考书。这本书，介绍了广义分布和新的变换，应该是通过新的研究领域指导研究生的工具。两名博士和四名硕士生正在进行有关新转换应用的项目。建议撰写关于分布理论的推广和变换的推广的第二本书。此外，一名博士候选人已经申请加入该团队。

1. A first objective is to apply the new extended Bilateral Laplace, z, and Fourier-related transforms recently introduced by the candidate, thanks to his generalisation of distribution theory, to digital signal processing of physical, chemical, biomedical signals, as well as to the harmonic analysis of music signal. A book by the candidate, just published June 2009, "Signals, Systems, Transforms and DSP...", 1346 pages, Taylor and Francis (CRC), is announced by the publisher as the new Reference Book of the domain. The book, which introduces the generalised distributions and the new transforms, should be instrumental in guiding graduate students through new areas of research. Two Ph.D. and four Masters students are pursuing projects on the applications of the new transforms. Writing a second book on the generalization of distribution theory and the extension of transforms is proposed. Moreover, one Ph.D, candidate has applied to be admitted to the team.