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Multidimensional Signal Processing
Published in Richard C. Dorf, Circuits, Signals, and Speech and Image Processing, 2018
Yun Q. Shi, Wei Su, Chih-Ming Chen, Sarah A. Rajala, N.K. Bose, L.H. Sibul
Multidimensional signal processing tools apply to aperture and sensor array processing. Planar sensor arrays can be considered to be sampled apertures. Three-dimensional or volumetric arrays can be viewed as multidimensional spatial filters. Therefore, the topics of sensor array processing, aperture processing, and multidimensional signal processing can be studied under a unified format. The basic function of the receiving array is transduction of propagating waves in the medium into electrical signals. Propagating waves are fundamental in radar, communication, optics, sonar, and geophysics. In electromagnetic applications, basic transducers are antennas and arrays of antennas. The large body of literature that exists on antennas and antenna arrays can be exploited in the areas of aperture and sensor array processing. Much of the antenna literature deals with transmitting antennas and their radiation patterns. Because of the reciprocity of transmitting and receiving transducers, key results that have been developed for transmitters can be used for analysis of receiver aperture and/or array processing. Transmitting transducers radiate energy in desired directions, whereas receiving apertures/arrays act as spatial filters that emphasize signals from a desired look direction while discriminating against interferences from other directions. The spatial filter wavenumber response is called the receiver beam pattern. Transmitting apertures are characterized by their radiation patterns.
Multi-Dimensional Photonic Processing by Discrete-Domain Approach
Published in Le Nguyen Binh, Photonic Signal Processing, 2019
Multi-dimensional signal processing enables processing of signals that depend on more than one co-ordinate. Although many concepts of multi-dimensional signal processing are straightforward extensions of 1-D signal processing theory, there are also significant differences that need to be clarified, particularly when referred to photonics. Discussions of Multi-dimensional signal processing in this paper is limited to 2-D signal processing applicable to photonics that is by far the most important class of multi-dimensional signal processing.
Wavelet Transforms with Optics
Published in Francis T. S. Yu, Entropy and Information Optics, 2017
We have discussed the semicontinuous STFT, the semicontinuous WT, and their optical implementation. We have shown that one of the best substitutions for the Gaussian function in the Fourier domain is a squared sinusoid function that can form a biorthogonal window function in the time domain. A couple of optical architectures for the STFT and WT are illustrated. Although our discussions are confined to one-dimensional signal processing, the basic concepts can be easily extended to multidimensional signal processing.
Improved closed-loop subspace identification with prior information
Published in International Journal of Systems Science, 2018
Youqing Wang, Ling Zhang, Yali Zhao
Two-dimensional (2-D) systems are wildly existed in many engineering fields and can be used to solve many complex problems, such as the achievement of multi-variable network, multidimensional signal processing, image processing and batch process control. Some traditional methods have extended to 2-D systems, such as fault diagnosis and compensation (Wang, Zhao, Li, & Ding, 2017; Zhao, Shen, & Wang, 2017), performance assessment (Wang, Zhang, Wei, Zhou, & Huang, 2018). However, due to the complexity of subspace identification on 2-D systems, the closed-loop subspace identification for 2-D systems is rare (Cheng, Fang, & Wang, 2017), leaving many problems to be settled. Therefore, it is interesting and important to extend the current study into 2-D systems in the future.