All the analysis filters are cosine modulated versions of a prototype filter. The design cost of the filter bank is equivalent to that of the prototype and the implementation complexity is comparable to that of the prototype plus a low-complexity matrix. It is well-known that the 1D lossless systems can be characterized by state space description. In 1D, the connection between the losslessness of a transfer matrix and the unitariness of the realization matrix is well-established. We will present the developments on the study of 2D lossless systems.

As in 1D case, the 2D FIR lossless systems can be characterized in terms of state space realizations. We will review this, and then address the factorizability of 2D FIR lossless systems by using the properties of state space realizations. The parameter uncertainties are assumed to be norm-bounded. Firstly, a new delay-dependent sufficient condition for the robust asymptotical stability of uncertain 2-D continuous systems with state delay is developed.

All results are developed in terms of linear matrix inequalities. Finally, two examples are provided to validate the effectiveness of the proposed method. Lower bounds for the stability margins of 2-D digital systems are extended to n-D systems. These bounds are then improved for n-D including 2-D systems which have characteristic polynomials with 1-D factor polynomials.

An example is presented to illustrate the theoretical results, and it is shown that the lower bound on coefficient wordlength could be considerably improved for the partial factorable denominator n-D digital systems. All the discussions are based on the n-D Lyapunov equation. The linear quadratic Gaussian LQG control for one-dimensional 1D systems has been known to be one of the fundamental and significant methods in linear system theory. However, the LQG control problem for two-dimensional 2D systems has not been satisfactorily solved due to their structural and dynamical complexity.

In this paper, sufficient conditions for evaluation of the quadratic performance indices of 2D systems in terms of the system state and control variables are proposed. Using these conditions, systematic design methods for finite horizon and infinite horizon LQG controls of 2D systems are developed using a convex optimization method. The high-resolution eigenspace-based methods such as, estimation of signal parameters via rotational invariance technique ESPRIT , multiple signal classification, etc.

In order to employ these methods, a new pre-processing method is developed based on the spatial smoothing in MIMO radar with the EmV sensors. Monte-Carlo simulations are performed to investigate the estimation-accuracy and resolution-capability of the proposed approach, and to compare with no pre-processing and the existing method.

The simulation result shows that, the proposed methodology improves the performance significantly. In this paper, a method to design the two-channel FIR linear-phase LP face-centred orthorhombic FCO filter banks with equiripple magnitude responses and perfect-reconstruction PR is presented. An interior-point algorithm is utilized to optimize the peak ripples of the analysis filters and a first-order approximation skill is introduced to satisfy the PR constraint.

The simulation example is presented to illustrate the effectiveness of this proposed design technique. This paper addresses systems of linear functional equations from an algebraic point of view. We give an introduction to and an overview of recent work by a small group of people including the author of this article on effective methods which determine structural properties of such systems. We focus on parametrizability of the behavior, i. Flatness of the linear system corresponds to the existence of an injective parametrization.

Using an algebraic analysis approach, we associate with a linear system a module over a ring of operators. For systems of linear partial differential equations we choose a ring of differential operators, for multidimensional discrete linear systems a ring of shift operators, for linear differential time-delay systems a combination of those, etc. Module theory and homological algebra can then be applied effectively to study a linear system via its system module, the interpretation depending on the duality between equations and solutions.

In particular, the problem of computing bases of finitely generated free modules i.

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Some work on computer algebra packages, which have been developed in this context, is summarized. The contribution of this paper is three-fold: first, we propose a novel scheme for generalized minor subspace extraction by extending an idea of dimension reduction technique. The proposed scheme can employ any algorithm capable of estimating the first minor generalized eigenvector.

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Second, we propose a pair of such iterative algorithms and analyze their convergence properties in the general case where the generalized eigenvalues are not necessarily distinct. Third, by using these algorithms inductively, we present adaptive implementations of the proposed scheme for estimating an orthonormal basis of the generalized minor subspace.

Numerical examples show that the proposed adaptive subspace extraction algorithms have better numerical stability than conventional algorithms. A multidimensional Hough transform is used in conjunction with continuous wavelet transforms to aid in solving a parameterized inverse problem.

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The inverse problem under consideration is the characterization of distributed scatterers by means of active wideband remote sensing. From a noisy wavelet transform estimate, the Hough transform is used to estimate a support region which is directly related to the physical parameters describing the distributed object. A novel algorithm for estimating the motion parameters of air maneuvering target by means of reconstructing time samples and signal is proposed in this paper.

## Multidimensional Systems Signal Processing Algorithms and Application Techniques, Volume 77

Firstly, the received data of multiple antennas are spliced together to reconstruct time samples of a single antenna by compensating a proper phase. This reconstruction is equivalent to increasing time samples within a single coherent processing interval for a single antenna. After that, an ideal signal whose time sample number is equal to the length of the reconstructed time samples is constructed. At last, the estimation results of initial velocity and acceleration of the air maneuvering target are obtained by applying the nonlinear least squares method to compare the similarity between the reconstructed time samples and signal.

The proposed algorithm can achieve accurate parameter estimation with limited pulses. The effectiveness of this algorithm is verified and its performance is very close to the Cramer—Rao bound as shown by our simulation results. We then use state-of-the-art computer algebra algorithms to check this last condition, and thus the structural stability of multidimensional systems.

Identification for closed-loop two-dimensional 2-D causal, recursive, and separable-in-denominator CRSD systems in the Roesser form is discussed in this study. For closed-loop 2-D CRSD systems, under feedback control condition, there exists some correlation between the unknown disturbances and future inputs which offers the fundamental limitation for utilizing standard open-loop 2-D CRSD systems subspace identification methods.

In other words, the existing open-loop subspace approaches will result in biased estimates of plant parameters from closed-loop data. In this study, based on orthogonal projection and principal component analysis, novel 2-D CRSD subspace identification methods are developed, which are applicable to both open-loop and closed-loop data.

Additionally, the whiteness external excitation case is discussed and subsequently modified instrument variables are adopted to improve the proposed subspace algorithm. An illustrative example of the injection molding process and several numerical examples are used to validate consistency and efficiency of the proposed subspace approaches for 2-D CRSD systems.

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This paper introduces a new selection rule for network connections that implements stable KWTA networks. To widen the applications of WTA networks, a new class of WTA networks is proposed, and their efficient design methods are presented.

We demonstrate the properties of the generalized class of WTA networks, through three application examples. The spectrum envelope reconstructed from the converted features usually deviates from its natural form. This aberration from the natural form observed in cases such as over-smoothing, over-fitting, and widening of formants is partially caused by two factors: 1 there is an error in the reconstruction of spectrum envelope from the features, and 2 the set of features extracted from the spectrum envelope of the speech signal is not closed.

The elements of these sets are generated by forming a group of extended vectors of features and applying a quantization scheme on the features of a speech signal. The use of this method in speech synthesis leads to a noticeable reduction of error in spectrum reconstruction from the features. Furthermore, the final spectrum envelope extracted from voice conversions maintains its natural form and, consequently, the problems arising from the deviation of voice from its natural state are resolved. The above method can be generally used as one phase of speech synthesis.

It is independent of the voice conversion technique used and its parallel or non-parallel training method, and can be applied to improve the naturalness of the generated speech signal in all common voice conversion methods. Moreover, this method can be used in other fields of speech processing like texts to speech systems and vocoders to improve the quality of the output signal in the synthesis step. We illustrate this inapplicability of the above-mentioned result in Sect. We then provide an answer to this open problem of characterizing characteristic cones for discrete n D autonomous systems with general n ; we prove an algebraic condition that is necessary and sufficient for a given cone to be a characteristic cone for a given system of linear partial difference equations with real constant coefficients.

In the second part of the paper, we convert this necessary and sufficient condition to another equivalent algebraic condition, which is more suited from algorithmic perspective. In this paper, a new algorithm is proposed for two-dimensional parameter estimation of coherently distributed noncircular signals. Based on the special sensor array geometry of L-shaped uniform linear arrays, 2D angular parameters are obtained independently by using the modified propagator method. Specifically, two selection matrices are employed to obtain rotation invariance matrices under considering signal noncircularity.

By making use of the rotation invariance matrices, we then obtain the central elevation and azimuth direction-of-arrivals, respectively. After that, the pair-matching of them is accomplished by searching the minimums of a cost function of the estimated 2D angular parameters. Finally, numerical results to testify the effectiveness of the proposed algorithm are provided.

It is also shown that the proposed algorithm performs well in a wide signal-to-noise ratio range. The present study addresses the problem of two-dimensional autoregressive estimation in the presence of additive white noise.

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The estimation method is based on combining the low-order and high-order Yule-Walker equations. The noise-compensated YW equations are solved using an iterative algorithm. The proposed method is also applied to joint frequency and direction of arrival estimation in uniform linear arrays. Using simulation study, the performance of the proposed algorithm is evaluated and compared with other methods. A novel feedback beamformer is proposed for receiving multipath coherent signals. First, a subtraction-based minimum variance distortionless response beamformer is utilized to obtain an estimation of the desired signal.

Then its output is fed back to the original full aperture array where a minimum mean square error MMSE beamformer is applied. Due to multipath-matched feature of the MMSE beamformer, the novel feedback beamformer can combine multipath signals without aperture loss. Two feedback schemes are proposed and their effectiveness is verified via simulation.