This paper proposes the statistical analysis of phase-only correlation functions between two real signals with phase-spectrum differences. For real signals, their phase-spectrum differences have odd-symmetry with respect to frequency indices. We assume phase-spectrum differences between two signals to be random variables. We next derive the expectation and variance of the POC functions considering the odd-symmetry of the phase-spectrum differences. As a result, the expectation and variance of the POC functions can be expressed by characteristic functions or trigonometric moments of the phase-spectrum differences. Furthermore, it is shown that the peak value of the POC function monotonically decreases and the sidelobe values monotonically increase as the variance of the phase-spectrum differences increases.

A new approach to design variable IIR digital filters by using a cascade of N identical individual filters of any order n is proposed in this paper. First, the approximation method for lowpass filter specifications is outlined, then the general limitations of the new method are investigated and a compact formula is derived. Next, the limitations for the main canonic approximations (Butterworth, Chebyshev and Elliptic) are investigated and compared and convenient expressions for design and evaluation are obtained. New first- and second-order filter sections, permitting very easy tuning of the cutoff frequency by recalculating and reprogramming of a single multiplier coefficient value, are developed and the design and tuning strategies for highpass, bandpass and bandstop filters are proposed. Finally design examples are given and the sound superiority of the new method compared to other known is demonstrated experimentally.

This paper proposes an efficient design method of three-dimensional (3-D) recursive digital filters for video signal processing via decomposition of magnitude specifications. A given magnitude specification of a 3-D digital filter is decomposed into specifications of 1-D digital filters with three different (horizontal, vertical, and temporal) directions. This decomposition can reduce design problems of 3-D digital filters to design problems of 1-D digital filters, which can be designed with ease by conventional methods. Consequently, design of 3-D digital filters can be efficiently performed without complicated tests for stability and large amount of computations. In order to process video signal in real time, the 1-D digital filters with temporal direction must be causal, which is not the case in horizontal and vertical directions. Since the proposed method can approximate negative magnitude specifications obtained by the decomposition with causal 1-D R filters, the 1-D digital filters with temporal direction can be causal. Therefore the 3-D digital filters designed by the proposed method is suitable for real time video signal processing. The designed 3-D digital filters have a parallel separable structure having high parallelism, regularity and modularity, and thus is suitable for high-speed VLSI implementation.

This paper presents FIR digital filters based on stochastic/binary hybrid computation with reduced hardware complexity and high computational accuracy. Recently, some attempts have been made to apply stochastic computation to realization of digital filters. Such realization methods lead to significant reduction of hardware complexity over the conventional filter realizations based on binary computation. However, the stochastic digital filters suffer from lower computational accuracy than the digital filters based on binary computation because of the random error fluctuations that are generated in stochastic bit streams, stochastic multipliers, and stochastic adders. This becomes a serious problem in the case of FIR filter realizations compared with the IIR counterparts because FIR filters usually require larger number of multiplications and additions than IIR filters. To improve the computational accuracy, this paper presents a stochastic/binary hybrid realization, where multipliers are realized using stochastic computation but adders are realized using binary computation. In addition, a coefficient-scaling technique is proposed to further improve the computational accuracy of stochastic FIR filters. Furthermore, the transposed structure is applied to the FIR filter realization, leading to reduction of hardware complexity. Evaluation results demonstrate that our method achieves at most 40dB improvement in minimum stopband attenuation compared with the conventional pure stochastic design.

This paper proposes an analysis method of the roundoff error due to finite-wordlength decoding in fractal image coding. The proposed method can be applied to large images such as 256 256 or 512 512 images because it needs no complex matrix computation. The simplified model used here ignores the effect of decimation ratio on the roundoff error because it is negligible. As an analysis result, the proposed method gives the output error variance which consists of grey-tone scaling coefficients and an iteration number. This method is tested on various types of 12 standard images which have 256 256 size or 512 512 size with 256 grey levels. Comparisons of simulation results with analysis results are given. The results show that our analysis method is valid for the fractal image coding.

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.