This paper proposes the Gramian-preserving frequency transformation for linear discrete-time state-space systems. In this frequency transformation, we replace each delay element of a discrete-time system with an allpass system that has a balanced realization. This approach can generate transformed systems that have the same controllability/observability Gramians as those of the original system. From this result, we show that the Gramian-preserving frequency transformation gives us transformed systems with different magnitude characteristics, but with the same structural property with respect to the Gramians as that of the original system. This paper also presents a simple method for realization of the Gramian-preserving frequency transformation. This method makes use of the cascaded normalized lattice structure of allpass systems.

This letter proposes closed form solutions to the L2-sensitivity minimization of second-order state-space digital filters with real poles. We consider two cases of second-order digital filters: distinct real poles and multiple real poles. In case of second-order digital filters, we can express the L2-sensitivity of second-order digital filters by a simple linear combination of exponential functions and formulate the L2-sensitivity minimization problem by a simple polynomial equation. As a result, the minimum L2-sensitivity realizations can be synthesized by only solving a fourth-degree polynomial equation, which can be analytically solved.

This paper discusses the behavior of the second-order modes (Hankel singular values) of linear continuous-time systems under variable transformations with positive-real functions. That is, given a transfer function H(s) and its second-order modes, we analyze the second-order modes of transformed systems H(F(s)), where 1/F(s) is an arbitrary positive-real function. We first discuss the case of lossless positive-real transformations, and show that the second-order modes are invariant under any lossless positive-real transformation. We next consider the case of general positive-real transformations, and reveal that the values of the second-order modes are decreased under any general positive-real transformation. We achieve the derivation of these results by describing the controllability/observability Gramians of transformed systems, with the help of the lossless positive-real lemma, the positive-real lemma, and state-space formulation of transformed systems.

This paper presents a new analysis of power complementary filters using the state-space representation. Our analysis is based on the bounded-real Riccati equations that were developed in the field of control theory. Through this new state-space analysis of power complementary filters, we prove that the sum of the controllability/observability Gramians of a pair of power complementary filters is represented by a constant matrix, which is given as a solution to the bounded-real Riccati equations. This result shows that power complementary filters possess complementary properties with respect to the Gramians, as well as the magnitude responses of systems. Furthermore, we derive new theorems on a specific family of power complementary filters that are generated by a pair of invertible solutions to the bounded-real Riccati equations. These theorems show some interesting relationships of this family with respect to the Gramians, zeros, and coefficients of systems. Finally, we give a numerical example to demonstrate our results.

This letter proposes evolutionary digital filters (EDFs) as new adaptive digital filters. The EDF is an adaptive filter which is controlled by adaptive algorithm based on the evolutionary strategies of living things. It consists of many linear/time-variant inner digital filters which correspond to individuals. The adaptive algorithm of the EDF controls and changes the coefficients of inner filters using the cloning method (the asexual reproduction method) or the mating method (the sexual reproduction method). Thus, the search algorithm of the EDF is a non-gradient and multi-point search algorithm. Numerical examples are given to show the effectiveness and features of the EDF such that they are not susceptible to local minimum in the multiple-peak performance surface.

This paper proposes a fast, efficient detection algorithm of missing data (also referred to as blotches) based on Markov Random Field (MRF) models with less computational load and a lower false alarm rate than the existing MRF-based blotch detection algorithms. The proposed algorithm can reduce the computational load by applying fast block-matching motion estimation based on the diamond searching pattern and restricting the attention of the blotch detection process to only the candidate bloch areas. The problem of confusion of the blotches is frequently seen in the vicinity of a moving object due to poorly estimated motion vectors. To solve this problem, we incorporate a weighting function with respect to the pixels, which are accurately detected by our moving edge detector and inputed into the formulation. To solve the blotch detection problem formulated as a maximum a posteriori (MAP) problem, an iterated conditional modes (ICM) algorithm is used. The experimental results show that our proposed method results in fewer blotch detection errors than the conventional blotch detectors, and enables lower computational cost and the more efficient detecting performance when compared with existing MRF-based detectors.

In this paper, we propose Affine Combination Lattice Algorithm (ACLA) as a new lattice-based adaptive notch filtering algorithm. The ACLA makes use of the affine combination of Regalia's Simplified Lattice Algorithm (SLA) and Lattice Gradient Algorithm (LGA). It is proved that the ACLA has faster convergence speed than the conventional lattice-based algorithms. We conduct this proof by means of theoretical analysis of the mean update term. Specifically, we show that the mean update term of the ACLA is always larger than that of the conventional algorithms. Simulation examples demonstrate the validity of this analytical result and the utility of the ACLA. In addition, we also derive the step-size bound for the ACLA. Furthermore, we show that this step-size bound is characterized by the gradient of the mean update term.

In this paper, we compare the performance of evolutionary digital filters (EDFs) for IIR adaptive digital filters (ADFs) in terms of convergence behavior and stability, and discuss their advantages. The authors have already proposed the EDF which is controlled by adaptive algorithm based on the evolutionary strategies of living things. This adaptive algorithm of the EDF controls and changes the coefficients of inner digital filters using the cloning method or the mating method. Thus, the adaptive algorithm of the EDF is of a non-gradient and multi-point search type. Numerical examples are given to demonstrate the effectiveness and features of the EDF such that (1) they can work as adaptive filters as expected, (2) they can adopt various error functions such as the mean square error, the absolute sum error, and the maximum error functions, and (3) the EDF using IIR filters (IIR-EDF) has a higher convergence rate and smaller adaptation noise than the LMS adaptive digital filter (LMS-ADF) and the adaptive digital filter based on the simple genetic algorithm (SGA-ADF) on a multiple-peak surface.

This paper proposes a new method that reduces the computational cost of the phase-only correlation (POC)-based methods for displacement estimation in old film sequences. Conventional POC-based methods calculate all the points of the POC and only use the highest peak of the POC and its neighboring points to estimate the displacement with subpixel accuracy. Our proposed method reduces the computational cost by calculating the POC in a small region, instead of all the points of the POC. The proposed method combines a displacement pre-estimation with a modified inverse discrete Fourier transform (IDFT). The displacement pre-estimation uses the 1-D POCs of frame projections to pre-estimate the displacement with pixel accuracy and chooses a small region in the POC including the desired points for displacement estimation. The modified IDFT is then used to calculate the points in this small region for displacement estimation. Experimental results show that use of the proposed method can effectively reduce the computational cost of the POC-based methods without compromising the accuracy.

This paper proposes distributed evolutionary digital filters (EDFs) as an improved version of the original EDF. The EDF is an adaptive digital filter which is controlled by adaptive algorithm based on evolutionary computation. In the proposed method, a large population of the original EDF is divided into smaller subpopulations. Each sub-EDF has one subpopulation and executes the small-sized main loop of the original EDF. In addition, the distributed algorithm periodically selects promising individuals from each subpopulation. Then, they migrate to different subpopulations. Numerical examples show that the distributed EDF has a higher convergence rate and smaller steady-state value of the square error than the LMS adaptive digital filter, the adaptive digital filter based on the simple genetic algorithm and the original EDF.

In this paper, we propose to employ a characteristic function based non-Gaussianity measure as a one-unit contrast function for independent component analysis. This non-Gaussianity measure is a weighted distance between the characteristic function of a random variable and a Gaussian characteristic function at some adequately chosen sample points. Independent component analysis of an observed random vector is performed by optimizing the above mentioned contrast function (for different units) using a fixed-point algorithm. Moreover, in order to obtain a better separation performance, we employ a mechanism to choose appropriate sample points from an initially selected sample vector. Finally, some computer simulations are presented to demonstrate the validity and effectiveness of the proposed method.

This paper proposes a closed form solution to L2-sensitivity minimization of second-order state-space digital filters subject to L2-scaling constraints. The proposed approach reduces the constrained optimization problem to an unconstrained optimization problem by appropriate variable transformation. Furthermore, restricting ourselves to the case of second-order state-space digital filters, we can express the L2-sensitivity by a simple linear combination of exponential functions and formulate the L2-sensitivity minimization problem by a simple polynomial equation. As a result, L2-sensitivity is expressed in closed form, and its minimization subject to L2-scaling constraints is achieved without iterative calculations.

This paper discusses the behavior of the second-order modes (Hankel singular values) of linear discrete-time systems under bounded-real transformations, where the transformations are given by arbitrary transfer functions with magnitude bounded by unity. Our main result reveals that the values of the second-order modes are decreased under any of the above-mentioned transformations. This result is the generalization of the theory of Mullis and Roberts, who proved that the second-order modes are invariant under any allpass transformation, i.e. any lossless bounded-real transformation. We derive our main result by describing the controllability/observability Gramians of transformed systems with the help of the discrete-time bounded-real lemma.

A new wide-dynamic-range CMOS image sensor with pixel-level analog-to-digital (A/D) converters is proposed. The pulse-counters in the sensor are arranged outside the pixel area in order to reduce pixel size, which is a key requirement for making high-definition cameras. A new scheme called variable threshold operation is also presented as a suitable readout operation method for the sensor. Experimental measurements on a prototype sensor show that the prototype can obtain linear output response proportional to illumination by applying the new readout operation.