From the signal processing transform point of

From the signal processing transform point of view [9], the Fourier transform (FT) has been applied widely in many scientific disciplines, and has played important role in almost all the science and technology domains. However, with the extension of research objects and scope, FT has been discovered to have many shortcomings [4]. In order to overcome these shortcomings, a series of novel signal analysis theories and tools have been put forward to process nonstationary or no Gauss signals, such as fractional Fourier transform [4], short-time Fourier transform, time-frequency distribution [3], wavelet transform [2], cyclic statistics, AM/FM signal analysis and linear canonical transform [10] and so on. On the other hand, from mathematical point of view, a set of signals can be looked as a vector space, and all of the filters can be looked as another space, therefore, the linear signal processing progress can be looked as the actions between the signal space and the filter space. As shown in Ref. [11], the signal models used in signal processing are actually the algebraic objects that have more structures than the vector spaces. And from these mathematical structures we can obtain more insights into the signal processing technology and derive novel signal processing tools [12–17]. It is therefore worthwhile and interesting to investigate the mathematical structures of the signal processing tools and transforms. The main goal of this paper is to provide an overview of recent developments regarding the algebraic and geometric signal processing technologies and their applications in signal processing community. Section 2 describes the algebraic signal processing (ASP), Section 3 presents the recent results about the geometric signal processing, and the conclusions and potential research directions along this way are provided in Section 4.
Algebraic signal processing The goal of this section is to give a short introduction to the algebraic signal processing (ASP) ido1 inhibitor that has been recently developed [11–17]. First a short review of the basic knowledge of algebra is given.
Geometric signal processing
Conclusions In this paper, we introduce the algebraic and the geometric approaches of signal processing. In Section 2, the canonical methods of signal processing are recalled, and then the main concepts of the algebraic methods of signal processing, including some important applications, are introduced. In Section 3, the method of information geometrical signal processing is introduced. We recall the concepts of information geometry, including the classical information geometry and the information geometry based on matrix group. Also we introduce the applications of information geometry in several fields, including signal processing, blind signal separation, neural network, Boltzmann machine, Doppler radar detection, fractional Fourier transformation and so on. At last, we propose some problems for the further consideration.
Acknowledgment The author would like to thank the program for Changjiang scholars and Innovative Research Team in Univeristy (IRT1005), the National Natural Science Foundations of China (61171195, 61331021 and 61179031), and Program for New Century Excellent Talents In University (Ncet-12-0042) for the support.
Introduction At present, the research on one-dimensional trajectory correction technology is relatively mature. In order to obtain the force used to adjust the lateral trajectory for TDTCP, the rotational speed of projectile must be reduced if the actuator or impulse engines arranged around its body are used, so its complexity and cost may be high, all these factors limit the development of TDTCP. According to the theory of exterior ballistics, a large diameter spin-stabilized projectile has a systematic deviator at the impact point, namely ballistic drift which is usually of order of magnitude of several hundred meters, much more than the lateral dispersion. If a damping disk (as shown in Fig. 1) is added in the one-dimensional correction mechanism (damping ring) to adjust the roll damping moment and further correct the trajectory by changing the ballistic drift, then the whole correction mechanism is cheaper and easier to implement, which provides an effective way for the development of TDTCP. At present, the researches on TDTCP in those countries such as France, Sweden, etc. have achieved considerable progresses. The corresponding research has been also developed in China, but is still in the stage of preliminary theoretical analysis.