Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : On general filtering problem of stationary processes with fixed transformation | Li Journal of Inequalities and Applications 2011 2011 68 Ỡ Journal of Inequalities and Applications http content 2011 1 68 a SpringeiOpen Journal RESEARCH Open Access On general filtering problem of stationary processes with fixed transformation Long suo Li Correspondence lilongsuo6982@ Department of Mathematics Harbin Institute of Technology Harbin 150001 Abstract A fixed transformation are given for one-dimensional stationary processes in this paper. Based on this we propose a general filtering problem of stationary processes with fixed transformation. Finally on a stationary processes with no any additional conditions we get the spectral characteristics of pHn t in the space L2 FX dl and then we calculate the value of the best predict quantity Q of the general filtering problem. Keywords stationary processes fixed transformation fillering 1. Introduction The Prediction theory is an important part of stationary processes also linear filter problems is an important part of Prediction theory. The linear filtering problem of multidimensional stationary sequence and processes for a linear system are firsted studied by Rosanov in 1 and then a series of general filter problem of stationary process for a linear system are studied in 2-9 . Theoretically this problem is a extend of the classic prediction problem. But it has high practical value it also widely applied in communication exploration space technology and automatic control etc. 2. Propose the problem Let X t t e R be simple wide stationary process. Let Hx L X t t e R HX t L X s s t s e R Suppose the complex-value function b t statisfing the following conditions 1 b t e L 0 rc n L2 0 rc 2 - 1 2 b t for t 0 2 - 2 Let B k f b t e-iudt 2 - 3 Jo Springer 2011 Li licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License http licenses by which permits unrestricted use .
