This letter theoretically analyzes and minimizes the L2-sensitivity for all-pass fractional delay digital filters of which structure is given by the normalized lattice structure. The L2-sensitivity is well known as one of the useful evaluation functions for measuring the performance degradation caused by quantizing filter coefficients into finite number of bits. This letter deals with two cases: L2-sensitivity minimization problem with scaling constraint, and the one without scaling constraint. It is proved that, in both of these two cases, any all-pass fractional delay digital filter with the normalized lattice structure becomes an optimal structure that analytically minimizes the L2-sensitivity.

This paper deals with a state-space approach for adaptive second-order IIR notch digital filters with constrained poles and zeros. A simplified iterative algorithm is derived from the gradient-descent method to minimize the mean-squared output of an adaptive notch digital filter. Then, stability and parameter-estimation bias are analyzed for the simplified iterative algorithm. A numerical example is presented to demonstrate the validity and effectiveness of the proposed adaptive state-space notch digital filter and parameter-estimation bias analysis.

This paper investigates an adaptive notch digital filter that employs normal state-space realization of a single-frequency second-order IIR notch digital filter. An adaptive algorithm is developed to minimize the mean-squared output error of the filter iteratively. This algorithm is based on a simplified form of the gradient-decent method. Stability and frequency estimation bias are analyzed for the adaptive iterative algorithm. Finally, a numerical example is presented to demonstrate the validity and effectiveness of the proposed adaptive notch digital filter and the frequency-estimation bias analyzed for the adaptive iterative algorithm.

Based on the concept of polynomial operators, this paper explores generalized direct-form II structure and its state-space realization for two-dimensional separable-denominator digital filters of order (m, n) where a structure with 3(m+n)+mn+1 fixed parameters plus m+n free parameters is introduced and analyzed. An l2-scaling method utilizing different coupling coefficients at different branch nodes to avoid overflow is presented. Expressions of evaluating the roundoff noise for the filter structure as well as its state-space realization are derived and investigated. The availability of the m+n free parameters is shown to be beneficial as the roundoff noise measures can be minimized with respect to these free parameters by means of an exhaustive search over a set with finite number of candidate elements. The important role these parameters can play in the endeavors of roundoff noise reduction is demonstrated by numerical experiments.

This paper deals with the problem of minimizing roundoff noise and pole sensitivity simultaneously subject to l2-scaling constraints for state-space digital filters. A novel measure for evaluating roundoff noise and pole sensitivity is proposed, and an efficient technique for minimizing this measure by jointly optimizing state-space realization and error feedback is explored, namely, the constrained optimization problem at hand is converted into an unconstrained problem and then the resultant problem is solved by employing a quasi-Newton algorithm. A numerical example is presented to demonstrate the validity and effectiveness of the proposed technique.

Block-state realization of state-space digital filters offers reduced implementation complexity relative to canonical state-space filters while filter's internal structure remains accessible. In this paper, we present a quantitative analysis on l2 coefficient sensitivity of block-state digital filters. Based on this, we develop two techniques for minimizing average l2-sensitivity subject to l2-scaling constraints. One of the techniques is based on a Lagrange function and some matrix-theoretic techniques. The other solution method converts the problem at hand into an unconstrained optimization problem which is solved by using an efficient quasi-Newton algorithm where the key gradient evaluation is done in closed-form formulas for fast and accurate execution of quasi-Newton iterations. A case study is presented to demonstrate the validity and effectiveness of the proposed techniques.

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.

In this paper, we propose a novel method for the design of CSD (Canonic Signed Digit) coefficient FIR (Finite Impulse Response) filters based on ACO (Ant Colony Optimization). This design problem is formulated as a combinatorial optimization problem and requires high computation time to obtain the optimal solution. Therefore, we propose an ACO approach for the design of CSD coefficient FIR filters. ACO is one of the promising approaches and appropriate for solving a combinatorial optimization problem in reasonable computation time. Several design examples showed the effectiveness of our method.

We report on the fabrication of a magnetic metallic contaminant detector using multi-channel high-Tc RF-SQUIDs (superconducting quantum interference devices) for large packaged food. For food safety finding small metallic contaminants is an important issue for a food manufacturer. Hence, a detection method for small sized contaminants is required. Some detection systems for food inspection using high-Tc SQUIDs have been reported to date. The system described here is different from the previous systems in its permitted size for inspection, being larger at 150mm in height × 300mm in width. For inspection of large sized food packages, improvement of the signal to noise ratio (SNR) is an important issue because the signal intensity is inversely proportional to the cube of the distance between the SQUID sensor and the object. Therefore a digital filter was introduced and its parameters were optimized. As a result, a steel ball as small as 0.5mm in diameter at a stand-off distance of 167mm was successfully detected with more than SNR = 3.3.

Multiple notch filters are used to suppress narrow-band or sinusoidal interferences in digital signals. In this paper, we propose a novel optimization design technique of an infinite impulse response (IIR) multiple notch filter. It is based on the Nelder-Mead simplex method. Firstly, the system function of the desired notch filter is constructed to form the objective function of the optimization technique. Secondly, the design parameters of the desired notch filter are optimized by Nelder-Mead simplex method. A weight function is also introduced to improve amplitude response of the notch filter. Thirdly, the convergence and amplitude response of the proposed technique are compared with other Nelder-Mead based design methods and the cascade-based design method. Finally, the practicability of the proposed notch filter design technique is demonstrated by some practical applications.

In this paper, we study a novel method to avoid a local minimum stagnation in the design problem of IIR (Infinite Impulse Response) filters using PSO (Particle Swarm Optimization). Although PSO is appropriate to solve nonlinear optimization problems, it is reported that a local minimum stagnation occurs due to a strong intensification of particles during the search. Then, multi-swarm PSO based on the particle reallocation strategy is proposed to avoid the local minimum stagnation. In this method, a reallocation space is determined by using some global bests. In this paper, the relationship between the number of swarms and the best value of design error is shown and the effectiveness of the proposed method is shown through several design examples.

In this paper, we propose a method for designing finite impulse response (FIR) filters with canonic signed digit (CSD) coefficients using particle swarm optimization (PSO). In such a design problem, a large number of local minimums appear in an evaluation function for the optimization. An updating procedure of PSO tends to stagnate around such local minimums and thus indicates a premature convergence property. Therefore, a new framework for avoiding such a situation is proposed, in which the evaluation function is modified around the stagnation point. Several design examples are shown to present the effectiveness of the proposed method.

For a large-sized touch screen, we designed and evaluated a real-time touch microarchitecture using a field-programmable gate array (FPGA). A high-speed hardware accelerator based on a parallel touch algorithm is suggested and implemented in this letter. The touch controller also has a timing control unit and an analog digital convert (ADC) control unit for analog touch sensing circuits. Measurement results of processing time showed that the touch controller with its proposed microarchitecture is five times faster than the 32-bit reduced instruction set computer (RISC) processor without the touch accelerator.

Recently a simple algorithm was presented by the first author which enables one to successively compute the transformation matrix of various order for the general 1-D to 1-D polynomial transformation. This letter extends the result to the general 1-D to 2-D polynomial transformation. It is also shown that the matrix obtained can be used for the 2-D to 2-D polynomial transformation as well.

In this paper, we present a numerical method for the equiripple approximation of IIR digital filters. The conventional rational Remez algorithm quickly finds the squared magnitude response of the optimal IIR digital filters, and then by factorizing it the equiripple filter is obtained. Unlike the original Remez algorithm for FIR filters, it is difficult for the rational Remez algorithm to explicitly control the ratio of ripples between different bands. In the conventional lowpass filter design, for example, when different weights are given for its passband and stopband, one needs to iteratively design the filter by manually changing the weights in order to achieve the ratio of the weights exactly. To address this problem, we modify the conventional algorithm and make it possible to directly control the ripple ratio. The method iteratively solves eigenvalue problems with controlling the ripple ratio. Using this method, the equiripple solutions with desired weights are obtained automatically.

Several methods for testing stability of first quadrant quarter-plane two dimensional (2-D) recursive digital filters have been suggested in 1970's and 80's. Though Jury's row and column algorithms, row and column concatenation stability tests have been considered as highly efficient mapping methods. They still fall short of accuracy as they need infinite number of steps to conclude about the exact stability of the filters and also the computational time required is enormous. In this paper, we present procedurally very simple algebraic method requiring only two steps when applied to the second order 2-D quarter - plane filter. We extend the same method to the second order Non-Symmetric Half-plane (NSHP) filters. Enough examples are given for both these types of filters as well as some lower order general recursive 2-D digital filters. We applied our method to barely stable or barely unstable filter examples available in the literature and got the same decisions thus showing that our method is accurate enough.

This paper demonstrates an efficient modelling method for artificial materials using digital filtering (DF) techniques. To demonstrate the efficiency of the DF technique it is applied to an electromagnetic bandgap (EBG) structure and a capacitively-loaded loop the so-called, CLL-based metamaterial. Firstly, this paper describes fine mesh simulations, in which a very small cell size (0.10.10.1 mm3) is used to model the details of an element of the structures to calculate the scattering parameters. Secondly, the scattering parameters are approximated with Padé forms and then factorised. Finally the factorised Padé forms are converted from the frequency domain to the time domain. As a result, the initial features in the fine meshes are effectively embedded into a numerical simulation with the DF boundary, in which the use of a coarse mesh is feasible (1,000 times larger in the EBG structure simulation and 680 times larger in the metamaterial simulation in terms of the volumes). By employing the coarse mesh and removal of the dielectric material calculations, the heavy computational burden required for the fine mesh simulations is mitigated and a fast, efficient and accurate modelling method for the artificial materials is achieved. In the case of the EBG structure the calculation time is reduced from 3 hours to less than 1 minute. In addition, this paper describes an antenna simulation as a specific application example of the DF techniques in electromagnetic compatibility field. In this simulation, an electric field radiated from a dipole antenna is enhanced by the DF boundary which models an artificial magnetic conductor derived from the CLL-based metamaterial. As is shown in the antenna simulation, the DF techniques model efficiently and accurately large-scale configurations.

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 proposes closed form solutions to the L2-sensitivity minimization subject to L2-scaling constraints for 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. The proposed approach reduces the constrained optimization problem to an unconstrained optimization problem by appropriate variable transformation. 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 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.