This paper analyzes frequency tracking characteristics of a complex-coefficient adaptive infinite impulse response (IIR) notch filter with a simplified gradient-based algorithm. The input signal to the complex notch filter is a complex linear chirp embedded in a complex zero-mean white Gaussian noise. The analysis starts with derivation of a first-order real-coefficient difference equation with respect to steady-state instantaneous frequency tracking error. Closed-form expression for frequency tracking mean square error (MSE) is then derived from the difference equation. Lastly, closed-form expressions for optimum notch bandwidth coefficient and step size constant that minimize the frequency tracking MSE are derived. Computer simulations are presented to validate the analysis.

In this paper we analytically investigate the generalization performance of learning using correlated inputs in the framework of on-line learning with a statistical mechanical method. We consider a model composed of linear perceptrons with Gaussian noise. First, we analyze the case of the gradient method. We analytically clarify that the larger the correlation among inputs is or the larger the number of inputs is, the stricter the condition the learning rate should satisfy is, and the slower the learning speed is. Second, we treat the block orthogonal projection learning as an alternative learning rule and derive the theory. In a noiseless case, the learning speed does not depend on the correlation and is proportional to the number of inputs used in an update. The learning speed is identical to that of the gradient method with uncorrelated inputs. On the other hand, when there is noise, the larger the correlation among inputs is, the slower the learning speed is and the larger the residual generalization error is.

This paper presents a closed form solution to a problem of constructing the best lower bound of a convex function under certain conditions. The function is assumed (I) bounded below by -ρ, and (II) differentiable and its derivative is Lipschitz continuous with Lipschitz constant L. To construct the lower bound, it is also assumed that we can use the values ρ and L together with the values of the function and its derivative at one specified point. By using the proposed lower bound, we derive a computationally efficient deep monotone approximation operator to the level set of the function. This operator realizes better approximation than subgradient projection which has been utilized, as a monotone approximation operator to level sets of differentiable convex functions as well as nonsmooth convex functions. Therefore, by using the proposed operator, we can improve many signal processing algorithms essentially based on the subgradient projection.

In this letter, a computational approach for solving cross-coupled algebraic Riccati equations (CAREs) is investigated. The main purpose of this letter is to propose a new algorithm that combines Newton's method with a gradient-based iterative (GI) algorithm for solving CAREs. In particular, it is noteworthy that both a quadratic convergence under an appropriate initial condition and reduction in dimensions for matrix computation are both achieved. A numerical example is provided to demonstrate the efficiency of this proposed algorithm.

This paper proposes a new adaptive filter algorithm for system identification by using an independent component analysis (ICA) technique, which separates the signal from noisy observation under the assumption that the signal and noise are independent. We first introduce an augmented state-space expression of the observed signal, representing the problem in terms of ICA. By using a nonparametric Parzen window density estimator and the stochastic information gradient, we derive an adaptive algorithm to separate the noise from the signal. The proposed ICA-based algorithm does not suppress the noise in the least mean square sense but to maximize the independence between the signal part and the noise. The computational complexity of the proposed algorithm is compared with that of the standard NLMS algorithm. The stationary point of the proposed algorithm is analyzed by using an averaging method. We can directly use the new ICA-based algorithm in an acoustic echo canceller without double-talk detector. Some simulation results are carried out to show the superiority of our ICA method to the conventional NLMS algorithm.

In this paper, we propose a novel bicubic method for digital image interpolation. Since the conventional bicubic method does not consider image local features, the interpolated images obtained by the conventional bicubic method often have a blurring problem. In this paper, the proposed bicubic method adopts both the local asymmetry features and the local gradient features of an image in the interpolation processing. Experimental results show that the proposed method can obtain high accuracy interpolated images.

This paper proposes a suboptimal algorithm for the maximum likelihood detection (MLD) in multiple-input multiple-output (MIMO) communications. The proposed algorithm regards transmitted signals as continuous variables in the same way as a common method for the discrete optimization problem, and then searches for candidates of the transmitted signals in the direction of a modified gradient vector of the metric. The vector is almost proportional to the direction of the noise enhancement, from which zero-forcing (ZF) or minimum mean square error (MMSE) algorithms suffer. This method sets the initial guess to the solution by ZF or MMSE algorithms, which can be recursively calculated. Also, the proposed algorithm has the same complexity order as that of conventional suboptimal algorithms. Computer simulations demonstrate that it is much superior in BER performance to the conventional ones.

One of 3-D devices to achieve high density arrays was adopted in this study, where source and drain junctions are formed along the silicon fin. The screening by adjacent high fins for large sensing margin makes it hard to ion-implant with high angle so that vertical ion implantation is inevitable. In this study, the dependency of current characteristics on doping profiles is investigated by 3-D numerical analysis. The position of concentration peak and the doping gradient are varied to look into the effects on driving currents. Through these analyses, the optimum condition of ion implantation for 3-D devices is estimated.

An adaptive array code acquisition for direct-sequence/code-division multiple access (DS/CDMA) systems was recently proposed to enhance the performance of the conventional correlator-based method. The scheme consists of an adaptive spatial and an adaptive temporal filter, and can simultaneously perform beamforming and code-delay estimation. Unfortunately, the scheme uses a least-mean-square (LMS) adaptive algorithm, and its convergence is slow. Although the recursive-least-squares (RLS) algorithm can be applied, the computational complexity will greatly increase. In this paper, we solve the dilemma with a low-complexity conjugate gradient (LCG) algorithm, which can be considered as a special case of a modified conjugate gradient (MCG) algorithm. Unlike the original conjugate gradient (CG) algorithm developed for adaptive applications, the proposed method, exploiting the special structure inherent in the input correlation matrix, requires a low computational-complexity. It can be shown that the computational complexity of the proposed method is on the same order of the LMS algorithm. However, the convergence rate is improved significantly. Simulation results show that the performance of adaptive array code acquisition with the proposed CG algorithm is comparable to that with the original CG algorithm.

The element-by-element finite element method (EBE-FEM) combined with the preconditioned conjugate gradient (PCG) technique is employed in this paper to calculate the coupling capacitances of multi-level high-density three-dimensional interconnects (3DIs). All capacitive coupling 3DIs can be captured, with the effects of all geometric and physical parameters taken into account. It is numerically demonstrated that with this hybrid method in the extraction of capacitances, an effective and accurate convergent solution to the Laplace equation can be obtained, with less memory and CPU time required, as compared to the results obtained by using the commercial FEM software of either MAXWELL 3D or ANSYS.

The estimation of the point-spread function (PSF) is one of very important and indispensable tasks for the practical image restoration. Especially, for the motion blur, various PSF estimation algorithms have been developed so far. However, a majority of them becomes useless in the low blurred signal-to-noise ratio (BSNR) environment. This paper describes a new robust PSF estimation algorithm based on Hough transform concerning gradient vectors, which can accurately and robustly estimate the motion blur PSF even in low BSNR case. The effectiveness and validity of the proposed algorithm are verified by applying it to the PSF estimation and the image restoration for noisy and motion blurred images.

In this paper, we propose a methodology for calculating on-chip temperature gradient and leakage power distributions. It considers the interdependence between leakage power and local temperature using a general circuit simulator as a differential equation solver. The proposed methodology can be utilized in the early stages of the design cycle as well as in the final verification phase. Simulation results proved that consideration of the temperature dependence of the leakage power is critically important for achieving reliable physical designs since the conventional temperature analysis that ignores the interdependence underestimates leakage power considerably and may overlook potential thermal runaway.

In this letter we present steady-state analyses of a gradient algorithm (GA) for second-order adaptive infinite impulse response (IIR) notch filters. A method for deriving more accurate estimation mean square error (MSE) expressions than the recently proposed method is presented. The method is based on the estimation error power spectral density (PSD). Moreover, an expression for the estimation bias for the adaptive IIR notch filter with constrained poles and zeros is shown to be obtained from the estimation MSE expression. Simulations are presented to confirm the validity of the analyses.

Natural, continuous tone images have a very important property of high correlation of adjacent pixels. Images which we wish to compress are usually non-stationary and can be reasonably modeled as smooth and textured areas separated by edges. This property has been successfully exploited in LOCO-I and CALIC by applying gradient based predictive coding as a major de-correlation tool. However, they only examine the horizontal and vertical gradients, and assume the local edge can only occur in these two directions. Their over-simplified assumptions hurt the robustness of the prediction in higher complex areas. In this paper, we propose an accurate gradient selective prediction (AGSP) algorithm which is designed to perform robustly around any type of image texture. Our method measures local texture information by comparison and selection of normalized scalar representation of the gradients in four directions. An adaptive predictor is formed based on the local gradient information and immediate causal pixels. Local texture properties are also exploited in the context modeling of the prediction error. The results we obtained on a test set of several standard images are encouraging. On the average, our method achieves a compression ratio significantly better than CALIC without noticeably increasing of computational complexity.

Optical flow is usually computed only on the basis of intensity information of images. Therefore, if we use color information in addition to the intensity, it is expected that more accurate optical flow can be computed. However, this intuition will be correct only when the following conditions are satisfied. First, the images should contain rich color variations. Moreover, it is also required that the image gradient of each color band differs in its direction. In this report, we empirically examined the difference of gradient directions on each band using 500 images, and evaluated quantitatively the advantage of using color information for optical flow computation.

An RF adaptive array antenna (RF-AAA) configured with variable capacitors is proposed. This antenna system can control the power combining ratio and phase value of received signals. In this paper, we focus on the diversity effects of RF-AAA. First, we show the design methodology of the combiner circuit to realize the effective combining. Second, the perturbation method and the steepest gradient method are compared for the optimization algorithms to provide fast convergence and suboptimum solutions among the variable circuit constants. Finally, in simulation, we show the RF-AAA can achieve diversity antenna gains of 7.7 dB, 10.9 dB and 12.6 dB for 2-branch, 3-branch and 4-branch configuration, respectively, which have higher performance than the selection combining.

This paper presents method that offers the fast and accurate analysis of large-scale periodic array antennas by conjugate-gradient fast Fourier transform (CG-FFT) combined with an equivalent sub-array preconditioner. Method of moments (MoM) is used to discretize the electric field integral equation (EFIE) and form the impedance matrix equation. By properly dividing a large array into equivalent sub-blocks level by level, the impedance matrix becomes a structure of Three-level Block Toeplitz Matrices. The Three-level Block Toeplitz Matrices are further transformed to Circulant Matrix, whose multiplication with a vector can be rapidly implemented by one-dimension (1-D) fast Fourier transform (FFT). Thus, the conjugate-gradient fast Fourier transform (CG-FFT) is successfully applied to the analysis of a large-scale periodic dipole array by speeding up the matrix-vector multiplication in the iterative solver. Furthermore, an equivalent sub-array preconditioner is proposed to combine with the CG-FFT analysis to reduce iterative steps and the whole CPU-time of the iteration. Some numerical results are given to illustrate the high efficiency and accuracy of the present method.

In this paper, we introduce a new method for depth perception from a 2D natural scene using scale variation of patterns. As the surface from a 2D scene gets farther away from us, the texture appears finer and smoother. Texture gradient is one of the monocular depth cues which can be represented by gradual scale variations of textured patterns. To extract feature vectors from textured patterns, higher order local autocorrelation functions are utilized at each scale step. The hierarchical linear discriminant analysis is employed to classify the scale rate of the feature vector which can be divided into subspaces by recursively grouping the overlapped classes. In the experiment, relative depth perception of 2D natural scenes is performed on the proposed method and it is expected to play an important role in natural scene analysis.

This paper quantitatively analyzes thermal gradient of SoC and proposes a thermal flattening procedure. First, the impact of dominant parameters, such as area occupancy of memory/logic block, power density, and floorplan on thermal gradient are studied quantitatively. Temperature difference is also evaluated from timing and reliability standpoints. Important results obtained here are 1) the maximum temperature difference increases with higher memory area occupancy and 2) the difference is very floorplan sensitive. Then, we propose a procedure to amend thermal gradient. A slight floorplan modification using the proposed procedure improves on-chip thermal gradient significantly.

To cut down the sidelobe level of radiation pattern, a novel adaptive algorithm is proposed for electronic steering parasitic antenna. The composite objective function in this algorithm takes both directivity and sidelobe level of pattern into account, and the steepest gradient algorithm is selected to search the optimum value of reactive load. Simulations are carried out to validate the algorithm, simulated results show that the levels of sidelobe are both below -4 dB in different beamforming cases, and the front to back ratios are better than 10 dB.