A new gradient type adaptive algorithm is proposed in this paper. It is formulated based on the least squares criteria while the conventional gradient algorithms are based on the least mean square criteria. The proposed algorithm has two variable parameters and by changing them we can adjust the characteristic of the algorithm from the RLS to the LMS depending on the environment. This capability of adjustment achieves the possibility of providing better solutions. However, not only it provides better solutions than the conventional algorithms under some conditions but also it provides a very interesting theoretical view point. It provides a unified view point of the adaptive algorithms including the conventional ones, i.e., the LMS or the RLS, as limited cases and it enables us to analyze the bounds for those algorithms.

Kalman filter is an essential tool in signal processing, modern control and communications. The filter estimates the states of a given system from noisy measurements, using a mean-square error criterion. Although Kalman filter has been shown to be very versatile, it has always been computationally intensive since a great number of matrix computations must be performed at each iteration. Thus the exploitation of this technique in broadband real time applications is restricted. The solution to these limitations appears to be in VLSI (very large scale integration) architectures for the parallel processing of data, in the form of systolic architectures. Systolic arrays are networks of simple processing cells connected only to their nearest neighbors. Each cell consists of some simple logic and has a small amount of local memory. Overall data flows through the array are synchronously controlled by a single main clock pulse. In parallel with the development of Kalman filter, the square root covariance and the square root information methods have been studied in the past. These square root methods are reported to be more accurate, stable and efficient than the original algorithm presented by Kalman. However it is known that standard SRIF is less efficient than the other algorithms, simply because standard SRIF has additional matrix inversion computation and matrix multiplication which are difficult to implement in terms of speed and accuracy. To solve this problem, we use the modified Faddeeva algorithm in computing matrix inversion and matrix multiplication. The proposed algorithm avoids the direct matrix inversion computation and matrix multiplication, and performs these matrix manipulations by Gauss elimination. To evaluate the proposed method, we constructed an efficient systolic architecture for standard SRIF using the COMPASS design tools. Actual VLSI design and its simulation are done on the circuits of four type processors that perform Gauss elimination and the modified Givens rotation.

Exact analytical solutions for the steady-state transmission and reflection characteristics of a nonlinear Fabry-Perot resonator applicable to bistable optical devices are derived. The resonator consists of a Kerr-like nonlinear film sandwiched by reflection mirrors made of a quarter-wave dielectric stack. An equivalent mirrorless model has been introduced to facilitate the analysis. For both positive and negative nonlinear coefficients, the rigorous solutions have been simply expressed in terms of Jacobian elliptic functions.

A rigorous radar cross section (RCS) analysis of a two-dimensional parallel-plate waveguide cavity with three-layer material loading is carried out for the E- and H-polarized planc wave incidence using the Wiener-Hopf technique. Introducing the Fourier transform for the scattered field and applying boundary conditions in the transform domain, the problem is formulated in terms of the simultaneous Wiener-Hopf equations satisfied by the unknown spectral functions. The Wiener-Hopf equations are solved via the factorization and decomposition procedure together with rigorous asymptotics, leading to the efficient approximate solution. The scattered field in the real space is evaluated by taking the inverse Fourier transform and applying the saddle point method. Representative numerical examples on the RCS are given for various physical parameters. It is shown that the three-layer lossy material loading inside the cavity results in significant RCS reduction over broad frequency range.

The relation between computing part of the FFT spectrum and the so-called generalized FFT (GFFT) is clarified, leading to a new algorithm for performing partial FFTs. The method can be applied when only part of the output is required or when the input data sequence contains many zeros. Such cases arize for example in decimation and interpolation and also in computing linear convolutions. The technique consists of decomposing the DFT into several generalized DFTs. Efficient algorithms for these generalized DFTs exist. The computational complexity of the new approach is roughly equal to the complexity of previous techniques, but the structure is superior, because only one type of butterfly is used and a few lines of code are sufficient. The theoretical properties of the GDFT are given. The case of multidimensional signals, defined on arbitrary sampling lattices is also considered.

ACk is the class of problems solvable by an alternating Turing machine in space O(log n) and alternation depth O(logk n) [S. A. Cook, A taxonomy of problems with fast parallel algorithms, Inform. Contr. vol. 64]. We consider a game played by two persons: each player alternately moves a marker along an edge of a given digraph, and the first palyer who cannot move loses the game. It is shown that the problem to determine whether the first player can win the game on a digraph with n nodes exactly after logk n moves is complete for ACk nuder NC1 reducibility.

In this paper we propose an effective Peak Rate Spacer (PRS) which can guarantee the negotiated peak cell rate almost perfectly even though contention of cells in the output link of the spacer occurs. We also propose a state-dependent Mean cell Rate Policer-Spacer (MRPS) which can manage the cell loss rate properly by controlling the buffer read rate according to the buffer state. As the MRPS has a cell buffer, it intrinsically has a traffic shaping function. Simulation results clearly show effectiveness of our PRS and MRPS.

A method for evaluating the degradation of subband adaptive digital filters (ADF) is presented. The performance of a simple ADF that uses critical sampling is mainly influenced by the subband filter bank's characteristics and the finite precision arithmetic operations used. This paper considers a two-channel mirror filter bank and a normalized least mean square algorithm with floating point arithmetic. The theoretical ERLE (Echo Return Loss Enhancement) and the theoretical relationships between the output error of the ADF and the circuit parameters considering finite precision A/D conversion and finite word length effects in floating point arithmetic operation are obtained using an equivalent noise model. Simulation results are found to be in good agreement to analytical values; the difference is only 3 to 5 dB.

This paper presents a new approach to the recovery of 3-D structure from multiple pairs of images from different viewpoints. Searching for the corresponding points between images, which is common in stereopsis, is avoided. Extracted edges from input images are projected back into 3-D space, and their intersections are calculated directly. Many false intersections may appear, but if we have many pair images, true intersections are extracted by appropriate thresholding. Octree representation of the intersections enables this approach. We consider a way to treat adjacent edge piexels as a line segment rather than as individual points, which differs from previous works and leads to a new algorithm. Experimental results using both synthetic and actual images are also described.

Dynamic programming based one dimensional-two dimensional adaptive pattern matching methods were investigated. In these methods, the reference pattern is represented as a sequence of directional vectors and the input pattern as two dimensional dot pattern. The input pattern needs no preskeletization or local feature analysis, and thus stroke order free top-down pattern matching is carried out. As the starting point, Rubber String Matching algorithm using fixed direction vectors was newly investigated. At latter stages, the reference pattern vectors were permitted some freedom in their directions to cope with abrupt aberrations in input pattern line segments, improving the flexibility of matching. Two cases were considered, allowing 45and approximately 20deviations from the vector directions. The 20version gave the best recognition score.

We developed a simple, practical, adaptive data compression algorithm of the LZ78 class. According to the Lempel-Ziv greedy parsing, a string boundary is not related to the statistical history modeled by finite-state sources. We have already reported an algorithm classifying data into subdictionaries (CSD), which uses multiple subdictionaries and conditions the current string by using the previous one to obtain a higher compression ratio. In this paper, we present a practical implementation of this method suitable for any kinds of data, and show that CSD is more efficient than the LZC which is the method used by the program compress available on UNIX systems. The CSD compression performance was about 10% better than that of LZC with the practical dictionary size, an 8k-entry dictionary when the test data was from the Calgary Compression Corpus. With hashing, the CSD processing speed became as fast as that of LZC, although the CSD algorithm was more complicated than LZC.

This paper proposes a new subband adaptive filtering algorithm for adaptive FIR filters. The number of taps for each subband filter is adaptively controlled based on a sum of the absolute coefficients or the coefficient power in conjunction with the subband signal power. Keeping the total number of taps constant, redundant taps are redistributed to subbands where the number of taps is insufficient. Simulation results with a white signal show that the number of taps in each subband approaches an optimum as each subband filter converges. For a colored signal, tap assignment by the new algorithm is as stable as for a white signal.

The stability of a terminated two-port network is investigated, and the stability conditions with only one inequality are obtained. Furthermore, the stability conditions with two inequalities, which are in the same form as those for the passive terminations known at the present time, are also obtained.

In this paper we introduce the Piecewise Linear Radial Basis Function Model (PWL-RBFM), a new nonlinear model that uses the well known RBF framework to build a PWL functional approximation by combining an l1 norm with a linear RBF function. A smooth generalization of the PWL-RBF is proposed: it is obtained by substituting the modulus function with the logistic function. These models are applied to several time series prediction tasks.

For system identification problems, such as noise and echo cancellation, FIR adaptive filters are mainly used for their simple adaptation and numerical stability. When the unknown system is a high-Q resonant system, having a very long impulse response, IIR adaptive filters are more efficient for reduction in the order of a transfer function. One way to realize the IIR adaptive filter is a separate form, in which the numerator and the denominator are separately realized and adjusted. In the actual applications, the order of the unknown system is not known. In this case, it is very important to estimate the total order and the order assignment on the numerator and the denominator. In this paper, effects of the order estimation error on the residual error are investigated. In this form, indirect error evaluation called "equation error" is used. Through theoretical and numerical investigation, the following results are obtained. First, under estimation of the order of the denominator causes large degradation. Second, over estimation can improve the performance. However, this improvement is saturated to some extent due to cancellation of the redundant poles and zeros. Third, the system identification error is proportional to the equation error as the adaptive filter approaching the optimum. Finally, there is possibility of recovering from the unstable state as the order assignment approaches to the optimum in an adaptive process using the equation error. Computer solutions are provided to aid in gaining insight of the order assignment and stability problem.

In this paper, we present Branching Oriented System Equation based on-line error correction scheme for recursive digital signal processing. The target digital signal processing is linear and time-invariant, and the algorithm includes multiplications with constant coefficient, additions and delays. The difficulties of the algorithm-level fault tolerance for such algorithm without structural regularity include error distribution problem and right timing of error correction. To escape the error distribution problem, multiple fan-out nodes in an algorithm are specified as the nodes at which error corrections are performed. The Branching Oriented Graph and Branching Oriented System Equation are so introduced to formulate on-line correction schemes based on this strategy. The Branching Oriented Graph is treated as the collection of computation sub-blocks. Applying checksum code independently to each sub-block is our most trivial on-line error correction scheme, and it results in, with appropriate selection of error identification process, TMR in sub-block level. One of the advantages of our method is in the reduction of redundant operations performed by merging some computation sub-blocks. On the other hand, the schedulability of the system is an important issue for our method since our on-line error correction mechanism induces additional data dependencies. In this paper, the schedulability condition and some modifications on the scheme are also discussed.

Mode separation of a multiplex mode in a mode-division multiplexing system is studied. The clear, desired single-mode pattern, which is separated from the multiplex mode by using a holographic filter, is observed in the experiment.

The classical supervised learning algorithms for optimizing multi-layered feedforward neural networks, such at the original back-propagation algorithm, suffer from several weaknesses. First, they have the possibility of being trapped at local minima during learning, which may lead to failure in finding the global optimal solution. Second, the convergence rate is typically too slow even if the learning can be achieved. This paper introduces a new learning algorithm which employs a genetic-type search during the learning phase of back-propagation algorithm so that the above problems can be overcome. The basic idea is to evolve the network weights in a controlled manner so as to jump to the regions of smaller mean squared error whenever the back-propagation stops at a local minimum. By this, the local minima can always be escaped and a much faster learning with global optimal solution can be achieved. A mathematical framework on the weight evolution of the new algorithm in also presented in this paper, which gives a careful analysis on the requirements of weight evolution (or perturbation) during learning in order to achieve a better error performance in the weights between different hidden layers. Simulation results on three typical problems including XOR, 3-bit parity and the counting problem are described to illustrate the fast learning behaviour and the global search capability of the new algorithm in improving the performance of back-propagated network.