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In this paper, a formulation of the convergence property of the NLMS method, an updating algorithm for an adaptive Volterra filter, is discussed. To date, much research has been carried out on the convergence property of the updating algorithm in a linear adaptive filter. However, there has been insufficient study of the updating algorithm for the second-order adaptive Volterra filter. In this paper, the convergence property of the E-NLMS method, an updating algorithm in the second-order adaptive Volterra filter, is formulated and the convergence property of the second-order adaptive Volterra filter is theoretically determined. In the formulation of the convergence property we use the first-order recursive filter expression, which is effective for studying various characteristics of the NLMS method in linear adaptive filters. In addition, it is recognized that the nature of the input signal to the diagonal (D) elements of the second-order Volterra system is different from that of the input to the other (ED) components. By means of computer simulation, it is confirmed that the convergence property given by the derived theoretical equation can sufficiently express the actual convergence property. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 85(10): 40–50, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.1124 [ABSTRACT FROM AUTHOR]

In this paper, we propose an active noise control (ANC) system without secondary path model (Ĉ filter). The proposed system is based on the simultaneous perturbation optimization method with block process. Consequently, the coefficients of the adaptive filter in the proposed system are updated by error signals only. The conventional ANC system using the Filtered-x algorithm becomes unstable due to the error between the secondary path from a secondary source to an error sensor and its model. On the other hand, the proposed ANC system has the advantage of becoming stable because of not using the model. In this paper, we show the principle of the proposed ANC system and also the effectiveness of this system by computer simulations. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 83(10): 47–55, 2000 [ABSTRACT FROM AUTHOR]

gggggAssume that an n × n dot matrix is stored in consecutive n words of a computer with one word being n bit. This paper discusses eight operations to rotate or transpose the dot matrix in horizontal/vertical! slant direction. As is well known, such operations form a group. This paper presents a unified description of the algorithms, and it is shown that all eight algorithms can be derived by suit- ably setting the constants in the unified algorithm. Then it is shown that the algorithms can be transformed to each other by simple transformation rules for the constants, and those transformation rules are shown to form a group. The foregoing algorithms for the dot matrix are not unique, and there can be different descriptions for the algorithm producing the same result. Consequently, there can be various versions of the eight algorithms as well as versions of transformation rules. This paper shows that one of the two groups formed by the transformation rules is isomorphic to the group of algorithms, but the other is not isomorphic. [ABSTRACT FROM AUTHOR]

When synchronization phenomena are analyzed, the phase equations are known to often provide useful qualitative and quantitative information [1]. The target of this paper is to examine through comparisons of the derivation algorithm of the phase equations a realistic system including the case where the equations are not necessarily given explicitly. In other words, the equivalence of two different conventional algorithms [1, 4] is shown, and the advantages and cautions when specific phenomena use both in an example are each explained. © 2007 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 90(12): 1– 9, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20284 [ABSTRACT FROM AUTHOR]

The standardization of video coding, such as MPEG, has been based on a combination of the discrete cosine transform (DCT) and interframe motion estimation. Recently, on the other hand, there has been interest in algorithms that also apply the transform along the time axis, so that the video picture is transformed in 3D and encoded. The purpose of this paper is to utilize the correlation along the time axis more effectively. Motion estimation based on the phase correlation is introduced. A new 3D coding algorithm for video pictures is proposed in which several error frames are combined as a CUBE, and the frequency transform is also applied in the time direction. In order to encode the transformed CUBE more effectively, 3D EZW-IP (embedded zero-tree wavelet image codec based on intraband partitioning) coding, which is a 3D extension of EZW-IP coding, is applied. By computer simulation, it is shown that the method is better than MPEG2 (TM5) and the effectiveness of introducing the motion estimation is verified, indicating the usefulness of the proposed method. © 2006 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 89(5): 32–38, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20206 [ABSTRACT FROM AUTHOR]

In this paper, we present a new structure for a complex adaptive infinite impulse response (IIR) notch filter which is useful for the detection of complex sinusoids in communication and radar systems. The proposed structure is based on the gradient algorithm. The adaptive detection of a complex sinusoid with additive complex white noise has been investigated. A quantitative analysis for the steady-state coefficient fluctuation has been developed. Analytical expressions for the steady-state variance of complex variable coefficient fluctuation have been obtained. It has been shown that the variance of the complex coefficient fluctuation does not depend on the angular frequency of the input sinusoid. Finally, the results of computer simulations which confirm the theoretical predictions are presented. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 85(1): 32–40, 2002 [ABSTRACT FROM AUTHOR]

Soft decision decoding is a decoding method which can cut the decoding error probability as compared with hard decision decoding by utilizing the channel measurement information effectively. In this paper, a new soft decision decoding method by which decoding operations can be efficiently carried out by utilizing the hierarchy of linear block codes is proposed. In addition, an improved algorithm which can reduce significantly the maximum computational complexity is also proposed. The proposed decoding algorithm utilizing the hierarchical structure of codes is a decoding method by which decoding is carried out sequentially from codes with high coding rates or codes of higher hierarchy in the inclusion order, and soft decision decoding can be efficiently carried out by utilizing a number of classes of codes having inclusion relationships in a manner which is superior to Chase algorithm 2 in the decoding error probability and the computational complexity for decoding. Computer simulation results confirm that the proposed algorithm realizes decoding error probability characteristics close to those of the maximum likelihood decoding method and that decoding can be carried out efficiently at a lower computational complexity than Chase algorithm 2 when the SNR is large. In addition, the improved algorithm which can reduce significantly the maximum computational complexity can realize decoding error probability characteristics close to those of the maximum likelihood decoding method on practical communication channels with relatively large SNR. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 83(3): 108–114, 2000 [ABSTRACT FROM AUTHOR]

The geometric learning algorithm (GLA) was proposed as an application of the affine projection algorithm for an adaptive filter to the perceptron. In the GLA, the connection weight vector w(n) is updated vertically toward the orthogonal complement of k patterns. The GLA demonstrates some typical behavior when the learning rate λ is 2, which means that w(n) and w(n + 1) are symmetric with respect to the complement. Therefore, in this paper, the GLA with λ = 2 is discriminated as the symmetric learning algorithm (SLA) and the convergence properties of the SLA are analyzed. The convergence conditions regarding the order k of the SLA, the number P of patterns, and the dimension N of patterns are analyzed theoretically. It is proved that k < N is the necessary condition for convergence when P > 2N. The relation between k and the learning speed is analyzed theoretically. It becomes clear that the maximum learning speed on average can be obtained when k = N/2. These properties are supported by computer simulations. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 82(4): 18–25, 1999 [ABSTRACT FROM AUTHOR]

In this paper, an adaptive array is proposed in which the CMA (Constant Modulus Algorithm) and LMS algorithms are combined so that a pass diversity effect is obtained without using training signals. The basic operations of the proposed algorithm are as follows. CMA captures the direct wave with maximum power. Based on the output of the CMA adaptive filter, a reference signal is generated. The LMS algorithm, using this reference signal, captures the delayed wave. By combining the direct wave and the delayed wave at maximum rate, the receiving quality is improved. By means of a computer simulation, we confirmed that the convergence property is improved and that the effect of the reference signal error on the system convergence characteristics is small. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(7): 37–44, 1998 [ABSTRACT FROM AUTHOR]

Learning identification is one of the most widely utilized adaptive algorithms due to its small computational complexity. A problem with this algorithm is that a division by the square norm of the state vector is includ- ed in the coefficient update process which easily produces an instability when the nonstationary such as speech is given as the input. A method known to cope with such a problem and to realize the stable convergence involves not updating the coefficient when small input signals continue. This paper discusses this approach. As a first step, the situation is assumed where the square norm of the state vector is less than the specified threeshold and the effect of interrupting the coefficient update is analyzed. The convergence and the time-constant are formulated and the guarantee of the estimation accuracy for the convergence value is discussed. Then, the step gain is derived for the specified guarantee value so that the convergence speed is the fastest in the stochastic sense while ensuring stability. Lastly, the effectiveness of the proposed method is verified by computer simulation. It is shown that, even if the input signal is annotation, the fastest convergence speed is realized, together with the satisfactory estimation accuracy, which is always obtained according to the specified guarantee value after the convergence. [ABSTRACT FROM AUTHOR]

A novel adaptive filter is proposed that adapts to the sample spacing as well as to the tap weights. Although in adaptive digital processing, the tapped-delay line usually has uniformly spaced taps, with the spacing equal to symbol period or a fraction of symbol period, an adaptive filter with a few taps should be adaptively arranged for nonuniform spacing for better convergence as the sampling timing varies. The conventional non-uniformly spaced filters are not adaptively changed or not arranged under the constraint of the acceptable mean-square error. In this paper, a least-mean square (LMS)- type algorithm is derived in which an adaptive filter adaptively changes the amount of delay, as well as the filter coefficients. The performance of the proposed algorithm is investigated by computer simulation. [ABSTRACT FROM AUTHOR]

This paper proposes the parallel construction of the second-order infinite impulse response (IIR) adaptive digital filter (ADF) as an adaptive digital filter for eliminating multiple narrowband signals mixed in the broadband signal. Then the pole-control method for the filter is proposed. In the proposed pole-control, the pole radius and the pole argument are controlled separately by different algorithms. In this study, the pole argument is corrected by estimating the deviation of the central frequency of the signal to be eliminated from the convergent value of the multiplier coefficient that determines the zero. The pole radius is controlled by the method that determines the direction of correction, using the parallel-connected three ADFs with the same pole argument and a slightly different pole radius. It is verified by a simulation that those pole-control methods work effectively. It is demonstrated that the pole radius and the pole argument can be controlled simultaneously. [ABSTRACT FROM AUTHOR]

Understanding electromagnetic scattering phenomena at high frequencies is important in specifying the location of the local scattered wave (scattering center). This procedure also is available for the practical radar target recognition. Detection of the scattering center also is possible by means of the Fourier transform in the frequency data measured by a network analyzer. However, since its resolution is limited by the measured frequency bandwidth, practical applications may often be difficult. In this paper, the use of the MUSIC algorithm which has a higher resolution than the Fourier transform is proposed for the time-domain estimation method of the electromagnetic scattering. As an example, the detection of the scattering center in the backscattering measurement of a conductive sphere is discussed. It is pointed out that the algorithm can be applied without significant modifications. Most of the super-resolution methods require many snapshots. It is found by computer simulation that the noise suppression preprocessing by time domain gating is effective for reduction of the snapshots. The setting of the number of incident signals (scattering center) of the MUSIC algorithm in the time-gated data is discussed. Further, by experiments, these investigations were verified and the high-resolution nature of the present method is proven. [ABSTRACT FROM AUTHOR]

This paper presents a new adaptive filter whose adaptive weights are modified via discrete cosine transform (DCT) bases. It is shown first that the principal axes of a mean-square error surface are identical to the eigenvectors of the autocorrelation matrix R with the Toeplitz form. It is well known that these eigenvectors of the Toeplitz matrix approximate the bases of the DCT so that then a new adaptation algorithm is presented which modifies the weight vectors along with the DCT bases. Ideally, the proposed algorithm converges (in the mean-square sense) adaptive weights in N iterations. Finally, soma computer simulations with additive noises are presented to show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, a new algorithm for the detection of a single sinusoid corrupted by Gaussian noise using IIR adaptive bandpass/notch filter is presented. As the first step, the relation between the convergence speed and the filter Q-factor in IIR adaptive bandpass filter is analyzed. Based on the result of analysis, an algorithm is derived in which the filter Q-factor and the adaptive control signal generator Q-factor are made continuously variable so that they are inversely proportional to the distance between the filter center frequcncy f0 and the frequency f of the sinusoid to be detected. This makes both the convergence speed of f0 and f and the resolution high. Then it Is found that limiting the maximum amplitude response of the adaptive control signal generator to a value proportional to sin 2&pie;f can suppress the coefficient fluctuation after convergence effectively. By this approach, an IIR adaptive filter with a high Q can easily be realized. As the next step, an additional high-speed and highly stable adaptive algorithm is proposed in which the step size of the filter coefficient update is made to vary inversely with the fitter Q-factor. A realization of the IIR adaptive notch filter is also presented. Finally, the usefulness of the proposed adaptive algorithm is verified by a computer simulation. [ABSTRACT FROM AUTHOR]

Two methods have been proposed for calculating the block orthogonal projection algorithm using the Moore-Penrose generalized inverse matrix. One is the conjugate gradient method, and the other is the block adaptive algorithm composed of the Gram-Schmidt orthogonalization and the learning identification. Both computation methods are suited to the high-speed estimation of the optimal coefficients with a small computational complexity. However, the operation may become very unstable due to the effects of observation error, quantization error, and other factors. This paper proposes a method of realizing the block orthogonal projection algorithm with the learning identification, where the orthogonal basis of the space spun by the state matrix in the block adaptive filter is used as the direction of modification. A feature of this method is that the orthogonal basis is calculated using the orthogonal projection matrix. Computer simulation shows that the proposed adaptive algorithm realizes a very stable operation without being affected by either the quantization error, the operational error, or the observation noise. [ABSTRACT FROM AUTHOR]

This paper proposes an efficient method to detect the hazard existing in the logic circuit using the five-valued logic simulator. The proposed method is effective in logic verification for the combination and asynchronous and sequential logic circuits as well as the verification for the hazard (race). Using the proposed method, the timing of the logic circuit is analyzed, including the rise/fall delay considering the signal transition time. The hazard is detected based on the output of the gate and the scheduled time. Also discussion is a method of event cancellation, which is a problem in the delayed simulation. Through the results of experiments using several circuits, the proposed algorithm is shown to be useful. [ABSTRACT FROM AUTHOR]

The real-time processing of the recursive least-square algorithm is difficult to execute by the conventional Neumann-type processor because of its large computational complexity. On the other hand, it is known that the recursive least-square algorithm based on the UD decomposition, which is equivalent to the recursive least-square algorithm, can be realized by the systolic array proposed by Rung. The systolic array to execute this algorithm is difficult to realize since it requires a tremendous number of elements and corrections. In the construction of the dedicated hardware, in general, the word length of the processor affects the processing speed and the hardware area. From such a viewpoint, it is important in the construction of the systolic array to execute the recursive least-square algorithm based on the UD decomposition that the word length of the processor should be minimized. To evaluate the word length, an error analysis is required for the finite word length operation of the recursive least-square algorithm based on the UD decomposition. This paper presents the finite word length floating-point error analysis for the recursive least-square algorithm, based on the UD decomposition, and evaluates the operation error. Then the convergence of the algorithm and the number of updates of the algorithm are evaluated analytically. Finally, by a computer simulation, the validity of the theoretical analysis for the convergence and the number of updates is verified. [ABSTRACT FROM AUTHOR]