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��ࡱ�>�� =?��<��%` �r�l:bjbjn�n�2<,�,��zzzzzzz��$��"""""��$=h�:qz��zz""�o��z"z"��zz�"� �d��0��z�� 2��2��zzzzzz��f[/g�bjt xidian university, china ��v�fractional order signal processing: techniques, applications and urgency ;n�� dr. yangquan chen, director of center for self-organizing and intelligent systems (csois), associate professor of electrical and computer engineering, utah state university, usa. �e��2009-5-26�tuesday � 11�45-12�45�r�[ � synopsis: in recent years, fractional order signal processing (fosp) is becoming an active research area, due to the demand on analysis of long-range dependence/ self-similarity in time series, such as financial data, communications networks data and biocorrosion noise. we will show that fosp is essentially based on the idea of fractional order calculus (foc). fractional order calculus is a generalization of the differential and integral operators. it is the root of the fractional systems described by fractional order differential equations. the simplest fractional order dynamic systems include the fractional order integrators and fractional order differentiators. the autoregressive fractional integrated moving average (arfima) model is a typical fractional order system. it is a generalization of autoregressive moving average (arma) model. the traditional models can only capture short-range dependence; for example, poisson processes, markov processes, autoregressive (ar), moving average (ma), autoregressive moving average (arma) and autoregressive integrated moving average (arima) processes. for time series which possesses long-range dependence, arfima models give a good fit. in lrd (long range dependent) processes, there is a strong coupling between values at different times. this indicates that the decay of the autocorrelation function is hyperbolic and decays slower than exponential decay, and that the area under the function curve is infinite. we can also say that their autocorrelation functions are power-law distributed. 1/f noise is a signal that possesses long-range dependence. the power or square of some variable associated with the random process, measured in a narrow bandwidth, is roughly proportional to reciprocal frequency. we will illustrate that the 1/f noise could be the output of a fractional order system with input of white noise. the degree of lrd in time series is analyzed by estimating their hurst parameter. fractional fourier transform based estimator has been proved by this research to have a better performance than the other existing estimators for many time series including fractional gaussian noise, biocorrosion processes data and great salt lake water-surface-elevation data. according to the concept of fractional fourier transform, some other fractional linear transforms have been developed in the literature such as fractional hartley transform, fractional sine transform and fractional cosine transform. a brief explanation of fractals and fractional splines is presented. finally, a concise introduction to fractional lower order moments (flom) or fractional lower order statistics (flos) and fractional delay is presented to make the fosp techniques more inclusive. the purpose of this lecture is to present a brief overview of various fractional order signal processing techniques. meanwhile, through examples, we will show that in real world applications, we need to use fosp techniques. as we pursue higher performance in the competitive world, we feel an urgency in applying fosp techniques. short biography of yangquan chen yangquan chen is an associate professor of electrical and computer engineering. his current areas of research interests include: distributed measurement and distributed control of distributed parameter systems using mobile actuator and sensor networks, mechatronics and controls (intelligent, optimal, robust, nonlinear and adaptive), applied fractional calculus, uav cooperative control for remote sensing and real time water management and irrigation control. he holds 13 granted and 2 pending us patents. he is an author of three research monographs (springer verlag 1999, 2007, 2009), six textbooks (siam press 2007; taylor & francis/crc 2008 and tsinghua university press 2002, 2004, 2007, 2008) and over 100 refereed journal papers. longer biography of yangquan chen yangquan chen (sm 95 srm 98) received the b.s. degree in industrial automation from the university of science and technology of beijing, beijing, china, in 1985, the m.s. degree in automatic control from the beijing institute of technology, beijing, in 1989, and the ph.d. degree in advanced control and instrumentation from the nanyang technological university, singapore, singapore, in 1998. he is currently an associate professor of electrical and computer engineering at utah state university, logan, and the director of the center for self-organizing and intelligent systems. he is the holder of 13 granted and two pending u.s. patents in various aspects of hard disk drive servomechanics. he has published over 100 refereed journal papers, over 20 refereed book chapter papers, over 200 refereed conference papers, and more than 50 industrial technical reports. he has coauthored three research monographs �iterative learning control: convergence, robustness and applications� (with changyun wen, lecture notes series in control and information science, springer-verlag, 1999), � iterative learning control: robustness and monotonic convergence for interval systems� (with hyo-sung ahn and kevin l. moore, communication and control engineering series, springer-verlag, 2007), �optimal observation for cyber-physical systems a fisher-information-matrix-based approach� (with song, z., sastry, c.r., tas, n.c., springer-verlag, 2009) and six textbooks �system simulation: techniques and applications based on matlab/simulink� (with dingy� xue, tsinghua university press, beijing, china, april 2002), �solving advanced applied mathematical problems using matlab� (with dingy� xue, tsinghua university press, august 2004, 2nd edition nov. 2008), �solving control related mathematical problems using matlab� (with dingy� xue, tsinghua university press, november 2007), �linear feedback control: analysis and design with matlab� (with dingy� xue, siam press, philadelphia, pa, 2007) and "solving applied mathematical problems with matlab" (with dingyu xue, crc press, nov. 2008). his current areas of research interests include: distributed measurement and distributed control of distributed parameter systems using mobile actuator and sensor networks, mechatronics and controls (intelligent, optimal, robust, nonlinear and adaptive), applied fractional calculus, uav cooperative control for remote sensing and real time water management and irrigation control. dr. chen is an associate editor on the conference editorial board of the control systems society of the ieee and an associate editor on the <b��b h z \ j l n r t ~ � � � � � bcq��í��vbvk-hzrw5�b*khojpjqj\�^jajph'hzrwb*khojpjqj^jajph%hzrw5�b*cjkhpj\�ajph'hzrwb*cjkhojpj^jajphhzrwb*cjkhpjajph*hzrwb*cjkhojpj^jajo(ph%hzrw5�b*cj"khpj\�aj"ph'hzrwb*cj"khojpj^jaj"ph*hzrwb*cj"khojpj^jaj"o(ph <�� b � � v c� o � ~�)��-~�2��5��$7$8$h$a$gdzrwl:�5��b��f��x�a�bc��5`��:r(��$7$8$h$a$gdzrw��b� ��w�z�>��v � !k!�! 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