This paper proposes statistical analysis of phase-only correlation (POC) functions under the phase fluctuation of signals due to additive Gaussian noise. We derive probability density function of phase-spectrum differences between original signal and its noise-corrupted signal with additive Gaussian noise. Furthermore, we evaluate the expectation and variance of the POC functions between these two signals. As the variance of Gaussian noise increases, the expectation of the peak of the POC function monotonically decreases and variance of the POC function monotonically increases. These results mathematically guarantee the validity of the POC functions used for similarity measure in matching techniques.

This paper derives the balanced realizations of second-order analog filters directly from the transfer function. Second-order analog filters are categorized into the following three cases: complex conjugate poles, distinct real poles, and multiple real poles. For each case, simple formulas are derived for the synthesis of the balanced realizations of second-order analog filters. As a result, we obtain closed form expressions of the balanced realizations of second-order analog filters.

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 review presents research topics and results on digital signal processing in the last twenty years in Japan. The main parts of the review consist of design and analysis of multidimensional digital filters, multiple-valued logic circuits and number systems for signal processing, and general purpose signal processors.

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 letter presents an efficient design method of multiplierless 2-D state-space digital filters (SSDFs) based on a genetic algorithm. The resultant multiplierless 2-D SSDFs, whose coefficients are represented as the sum of two powers-of-two terms, are attractive for high-speed operation and simple implementation. The design problem of multiplierless 2-D SSDFs described by Roesser's local state-space model is formulated subject to the constraint that the resultant filters are stable. To ensure the stability for the resultant 2-D SSDFs, a stability test routine is embedded in th design procedure.

Roundoff error due to iterative computation with finite wordlength degrades the quality of decoded images in fractal image coding that employs a deterministic iterated function system. This paper presents a state-space approach to roundoff error analysis of fractal image coding for grey-scale images. The output noise variance matrix and the noise matrix are derived for the measures of error and the output noise variance is newly defined as the pixel mean of diagonal elements of the output noise matrix. A quantitative comparison of experimental roundoff error with analytical result is made for the output noise variance. The result shows that our analysis method is valid for the fractal image coding. Our analysis method is useful to design a real-time and low-cost decoding hardware with finite wordlength for fractal image coding.

This paper proposes an analysis method of scaling-factor-quantization error in fractal image coding using a state-space approach with the statistical analysis method. It is shown that the statistical analysis method is appropriate and leads to a simple result, whereas the deterministic analysis method is not appropriate and leads to a complex result for the analysis of fractal image coding. We derive the output error variance matrix for the measure of error and define the output error variance by scalar quantity as the mean of diagonal elements of the output error variance matrix. Examples are given to show that the scaling-factor-quantization error due to iterative computation with finite-wordlength scaling factors degrades the quality of decoded images. A quantitative comparison of experimental scaling-factor-quantization error with analytical result is made for the output error variance. The result shows that our analysis method is valid for the fractal image coding.

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 a design method of variable IIR digital filters based on balanced realizations and minimum round-off noise realizations of digital filters. Highly accurate variable digital filters are easily derived by the proposed method. The coefficient matrices of both realizations of second-order digital filters are obtained directly from prototype realizations. The filter coefficients of variable digital filters can be obtained by frequency transformations to the realizations. The filter coefficients are presented as truncated Taylor series for the purpose of reducing a number of calculations to tune the coefficients. However the proposed filters have highly accurate variable characteristics against the coefficient truncation since balanced realizations and minimum round-off noise realizations have very low coefficient sensitivities, which are invariant under the frequency transformations. Moreover, the dynamic ranges of the proposed filters are almost constant against the frequency transformations. Numerical examples show the effectiveness of the variable digital filters designed by the proposed method.

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.

This paper presents a novel image coding scheme based on separate coding of region and residue sources. In a subband image coding scheme, quantization errors in each subimage spread over the reconstructed image and result in a blurring or a boundary artifact. To obtain high compression ratio without considerable degradation, an input image, in our scheme, is separated into region and residue sources which are coded using different coding schemes. The region source is coded by adaptive arithmetic coder. The residue source is coded using multiresolution subimages generated by applying a subband filter. Each block in the subimages is predicted by an affine transformation of blocks in lower resolution subimages. Experimental results show that a high coding efficiency is achieved using the proposed scheme, especially in terms of the subjective visual quality and PSNR at low bit-rate compression.

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 discusses the behavior of the second-order modes (Hankel singular values) of linear continuous-time systems under typical frequency transformations, such as lowpass-lowpass, lowpass-highpass, lowpass-bandpass, and lowpass-bandstop transformations. Our main result establishes the fact that the second-order modes are invariant under any of these typical frequency transformations. This means that any transformed system that is generated from a prototype system has the same second-order modes as those of the prototype system. We achieve the derivation of this result by describing the state-space equations and the controllability/observability Gramians of transformed systems.