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.

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 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.

This paper proposes a closed form solution to L2-sensitivity minimization of second-order state-space digital filters. Restricting ourselves to the second-order case of 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, the L2-sensitivity minimization problem can be converted into a problem to find the solution to a fourth-degree polynomial equation of constant coefficients, which can be algebraically solved in closed form without iterative calculations.

This paper presents a hardware-efficient folding technique for high-order FIR filtering while considering the tradeoff between the number of processing elements and throughput rate. Given the throughput rate, one can always employ the minimum number of processing elements for saving the implementation cost and figure out a folded architecture. However, applying inefficient folding techniques may result in costly switches and registers. Therefore, our work intends to evaluate the efficiency for folding techniques in terms of the number of registers, and the power dissipation of registers. As shown in the estimation results, while comparing with the published folded architectures under the same throughput rate, the proposed folding technique can turn out less power dissipation and low hardware complexity than the others. The proposed design has been implemented using TSMC 0.18 µm 1P6M technology. As seen in the post-layout simulation, our design can meet the requirement of IS-95 WCDMA pulse shaping FIR filter while the power consumption can be as low as 16.66 mW.

The minimization problem of an L2-sensitivity measure subject to L2-norm dynamic-range scaling constraints is formulated for a class of two-dimensional (2-D) state-space digital filters. First, the problem is converted into an unconstrained optimization problem by using linear-algebraic techniques. Next, the unconstrained optimization problem is solved by applying an efficient quasi-Newton algorithm with closed-form formula for gradient evaluation. The coordinate transformation matrix obtained is then used to synthesize the optimal 2-D state-space filter structure that minimizes the L2-sensitivity measure subject to L2-norm dynamic-range scaling constraints. Finally, a numerical example is presented to illustrate the utility of the proposed technique.

In this paper, we treat a design problem for IIR digital filters described by rational transfer function in discrete space. First, we form the filter design problem using the modified least-squares (MLS) criterion and express it as the quadratic form with respect to the numerator and denominator coefficients. Next, we show the relaxation method using the Lagrange multiplier method in order to search for the good solution efficiently. Additionally we can check the filter stability when designing the denominator coefficients. Finally, we show the effectiveness of the proposed method using a numerical example.

In this paper, we propose a new error feedback (EF) structure for 2-D separable-denominator digital filters described by a rational transfer function. In implementing two-dimensional separable-denominator digital filters, the minimum delay elements structures are common. In the proposed structure, the filter feedback-loop corresponding to denominator polynomial is placed at a different location compared to the commonly used structures. The proposed structure can minimize the roundoff noise more than the previous structure though the number of multipliers is less than that of previous one. Finally, we present a numerical example by designing the EF on the proposed structure and demonstrate the effectiveness of the proposed method.

Classical designs of maximally flat finite impulse response digital filters need to perform inverse discrete Fourier transformation of the frequency responses, in order to calculate the impulse response coefficients. Several attempts have been made to simplify the designs by obtaining explicit formulas for the impulse response coefficients. Such formulas have been derived for digital differentiators having maximal linearity at zero frequency, using different techniques including interpolating polynomials and the Taylor series etc. We show that these formulas can be obtained directly by application of maximal linearity constraints on the frequency response. The design problem is formulated as a system of linear equations, which can be solved to achieve maximal linearity at an arbitrary frequency. Certain special characteristics of the determinant of the coefficients matrix of these equations are explored for designs centered at zero frequency, and are used in derivation of explicit formulas for the impulse response coefficients of digital differentiators of both odd and even lengths.

This paper presents an algorithm for fingerprint image restoration using Digital Reaction-Diffusion System (DRDS). The DRDS is a model of a discrete-time discrete-space nonlinear reaction-diffusion dynamical system, which is useful for generating biological textures, patterns and structures. This paper focuses on the design of a fingerprint restoration algorithm that combines (i) a ridge orientation estimation technique using an iterative coarse-to-fine processing strategy and (ii) an adaptive DRDS having a capability of enhancing low-quality fingerprint images using the estimated ridge orientation. The phase-only image matching technique is employed for evaluating the similarity between an original fingerprint image and a restored image. The proposed algorithm may be useful for person identification applications using fingerprint images.

This paper presents a digital reaction-diffusion system (DRDS)--a model of a discrete-time discrete-space reaction-diffusion dynamical system--for designing new image processing algorithms inspired by biological pattern formation phenomena. The original idea is based on the Turing's model of pattern formation which is widely known in mathematical biology. We first show that the Turing's morphogenesis can be understood by analyzing the pattern forming property of the DRDS within the framework of multidimensional digital signal processing theory. This paper also describes the design of an adaptive DRDS for image processing tasks, such as enhancement and restoration of fingerprint images.

For low-complexity linear-phase FIR digital filters which have coefficients expressed as canonic signed digit (CSD) code, a design method to impose power-of-two DC gain is proposed. Output signal level can easily be compensated to that of input so that cascading many stages do not cause any gain errors, which are harmful in, for example, high precision measurement systems. The design is formulated as an optimization problem with magnitude response constraints. The integer linear programming modified for CSD codes is solved by the branch and bound method. The design example shows the effectiveness of the obtained filter in comparison with existing CSD filters. Also, an evaluation method for the area to implement the filter into field programmable gate array (FPGA) is proposed. The implementation example shows that the minimum critical path is obtained with only a little increase in the die area.

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.

Explicit formulas for the tap-coefficients of Taylor series based type III FIR digital differentiators have already been presented. However, those formulas were not derived mathematically from the Taylor series and were based on observation of different sets of the results. In this paper, we provide a mathematical proof of the formulas by deriving them mathematically from the Taylor series.

New designs of MAXFLAT discrete and differentiating Hilbert transformers are presented using their interrelationships with digital differentiators. The new designs have the explicit formulas for their tap-coefficients, which are further modified to obtain a new class of narrow transition band filters, with a performance comparable to the Chebyshev filters.

New explicit formulas for tap-coefficients of halfband low/high pass MAXFLAT non-recursive filters are presented by using their relationship with already presented maximally linear type IV differentiators. These formulas are modified to give a new class of narrow transition band filters, with a performance comparable to that of optimal filters.

This paper proposes a private communication system with chaos using fixed-point digital computation. When fixed-point computation is adopted, chaotic properties of the modulated signal should be checked carefully as well as calculation error problems (especially, overflow problems). In this paper, we propose a novel chaos modem system for private communications including a chaotic neuron type nonlinearity, an unstable digital filter and an overflow function. We demonstrate that the modulated signal reveals hyperchaotic property within 10,000 data point fixed-point computation, and evaluate the security of this system in view of the sensitivity of coefficients for demodulation.

The authors have proposed a design method for two-dimensional (2-D) separable-denominator (SD) periodically time-variant digital filters (PTV DFs) and confirmed their superiority over 2-D time-invariant DFs. In that result, the periodicity matrix representing the periodicity of the varying filter coefficients is, however, restricted to two cases. This paper extends that idea so that the input-output relation of 2-D SD PTV DFs with an arbitrary periodicity matrix can be determined. This enables us to design wide range of 2-D PTV DFs.