In this paper we treat the two-variable positive extension problem for trigonometric polynomials where the extension is required to be the reciprocal of the absolute value squared of a stable polynomial. This problem may also be interpreted as an autoregressive ﬁlter design problem for bivariate stochastic processes. We show that the existence of a solution is equivalent to solving a ﬁnite positive deﬁnite matrix completion problem where the completion is required to satisfy an additional low rank condition. ...
Digital Image Processing: Image Restoration Matrix Formulation - Duong Anh Duc provides about matrix Formulation of Image Restoration Problem; constrained least squares filtering (restoration); a brief review of matrix differentiation; Pseudo-inverse Filtering; Minimum Mean Square Error (Wiener) Filter; Parametric Wiener Filter.
LEAST-SQUARES AND MINIMUM– VARIANCE ESTIMATES FOR LINEAR TIME-INVARIANT SYSTEMS
4.1 GENERAL LEAST-SQUARES ESTIMATION RESULTS In Section 2.4 we developed (2.4-3), relating the 1 Â 1 measurement matrix Y n to the 2 Â 1 state vector X n through the 1 Â 2 observation matrix M as given by Y n ¼ MX n þ N n ð4:1-1Þ
It was also pointed out in Sections 2.4 and 2.10 that this linear time-invariant equation (i.e., M is independent of time or equivalently n) applies to more general cases that we generalize further here. Speciﬁcally we assume Y n is a 1 Â ðr...
GIVENS ORTHONORMAL TRANSFORMATION
11.1 THE TRANSFORMATION The Givens orthonormal transformation for making a matrix upper triangular is made up of successive elementary Givens orthonormal transformations G 1 ; G 2 ; . . . to be deﬁned shortly. Consider the matrix T expressed by 2 3 t 11 t 12 t 13 6t t t 7 ð11:1-1Þ T ¼ 6 21 22 23 7 4 t 31 t 32 t 33 5 t 41 t 42 t 43 First, using the simple Givens orthonormal transformation matrix G 1 the matrix T is transformed to 2 3 ðt 11 Þ 1 ðt...
VOLTAGE LEAST-SQUARES ALGORITHMS REVISITED
10.1 COMPUTATION PROBLEMS The least-squares estimates and minimum-variance estimates described in Section 4.1 and 4.5 and Chapter 9 all require the inversion of one or more matrices. Computing the inverse of a matrix can lead to computational problems due to standard computer round-offs [5, pp. 314–320]. To illustrate this assume that s¼1þ" ð10:1-1Þ
Assume a six-decimal digit capability in the computer. Thus, if s ¼ 1:000008, then the computer would round this off to 1.00000.
HOUSEHOLDER ORTHONORMAL TRANSFORMATION
In the preceding chapter we showed how the elementary Givens orthonormal transformation triangularized a matrix by successfully zeroing out one element at a time below the diagonal of each column. With the Householder orthonormal transformation all the elements below the diagonal of a given column are zeroed out simultaneously with one Householder transformation.
Ultra wideband (UWB) has advanced and merged as a technology, and many more people are aware of the potential for this exciting technology. The current UWB field is changing rapidly with new techniques and ideas where several issues are involved in developing the systems. Among UWB system design, the UWB RF transceiver and UWB antenna are the key components. Recently, a considerable amount of researches has been devoted to the development of the UWB RF transceiver and antenna for its enabling high data transmission rates and low power consumption.
GRAM–SCHMIDT ORTHONORMAL TRANSFORMATION
13.1 CLASSICAL GRAM–SCHMIDT ORTHONORMAL TRANSFORMATION The Gram–Schmidt orthonormalization procedure was introduced in Section 4.3 in order to introduce the orthonormal transformation F applied to the matrix T. The Gram–Schmidt orthonormalization procedure described there is called the classical Gram–Schmidt (CGS) orthogonilization procedure. The CGS procedure was developed in detail for the case s ¼ 3, m 0 ¼ 2, and then these results were extrapolated to the general case of arbitrary s and m 0 .
LINEAR TIME-VARIANT SYSTEM
15.1 INTRODUCTION In this chapter we extend the results of Chapters 4 and 8 to systems having time-variant dynamic models and observation schemes [5, pp. 99–104]. For a time-varying observation system, the observation matrix M of (4.1-1) and (4.1-5) could be different at different times, that is, for different n. Thus the observation equation becomes Y n ¼ M nX n þ N n ð15:1-1Þ
For a time-varying dynamics model the transition matrix È would be different at different times. In this case È of (8.
Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: A New Pipelined Systolic Array-Based Architecture for Matrix Inversion in FPGAs with Kalman Filter Case Study
The first block is responsible for receiving and amplifying the brain signal, allocating
electrodes into specific places on the scalp in the case of the use of electrodes on the surface, or inside
brain in the intracortical use cases, in the second block signal is sampled, the quantity
and periodic system of time to digitize it, to simplify the following
digitized phase signal can be filtered, for example to reduce the noise level is
Better SNR or signal identification and processing artifacts....
Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Multiuser Detection Using Adaptive Multistage Matrix Wiener Filtering Schemes with Stage-Selection Criteria in DS-UWB
Two of the most important functions for signal processing are not in the Signal Processing Toolbox at all, but are built-in MATLAB functions: • filter applies a digital filter to a data sequence. • fft calculates the discrete Fourier transform of a sequence. The operations these functions perform are the main computational workhorses of classical signal processing. Both are described in this chapter.
Characterizing the Performance of Adaptive Filters 19.3 Analytical Models, Assumptions, and Deﬁnitions
System Identiﬁcation Model for the Desired Response Signal • Statistical Models for the Input Signal • The Independence Assumptions • Useful Deﬁnitions
19.4 Analysis of the LMS Adaptive Filter
Mean Analysis • Mean-Square Analysis
19.5 Performance Issues
Basic Criteria for Performance • Identifying Stationary Systems • Tracking Time-Varying Systems Normalized Step Sizes • Adaptive and Matrix Step Sizes • Other Time-Varying Step Size Methods
In this paper, we present a computational method for transforming a s y n t a c t i c g r a p h , which represents all syntactic interpretations of a sentence, into a s e m a n t i c g r a p h which filters out certain interpretations, but also incorporates any remaining ambiguities. We argue that the resulting ambiguous graph, supported by an exclusion matrix, is a useful data structure for question answering and other semantic processing. Our research is based on the principle that ambiguity is an inherent aspect of natural...