Using a matrix approach based on a Markov process, we investigate the reliability of a circular connected-(1,2)-or-(2,1)-out-of-(m,n):F lattice system for the i.i.d. case. We develop a modified linear lattice system that is equivalent to this circular system, and propose a methodology that allows the systematic calculation of the reliability. It is based on ideas presented by Fu and Hu [6]. A partial transition probability matrix is used to reduce the computational complexity of the calculations, and closed formulas are derived for special cases.

In this paper, a threshold-based I-Q diversity combining scheme for ultra-high frequency (UHF) radio frequency identification (RFID) readers with a quadrature receiver is proposed in the aspect of improving the tag detection performance. In addition, the performance of the proposed scheme is evaluated as the closed-form expressions. In particular, its statistical characteristics are detailed and its performance is compared to that of conventional schemes over independent and identically distributed Rician fading conditions in terms of average signal-to-noise ratio (SNR), bit error rate (BER), and the average number of required combining process. Numerical results indicate that the proposed scheme enables processing power control through threshold control while meeting the required quality of service compared to conventional schemes.

Maximally flat digital differentiators (MFDDs) are widely used in many applications. By using MFDDs, we obtain the derivative of an input signal with high accuracy around their center frequency of flat property. Moreover, to avoid the influence of noise, it is desirable to attenuate the magnitude property of MFDDs expect for the vicinity of the center frequency. In this paper, we introduce a design method of linear phase FIR band-pass MFDDs with an arbitrary center frequency. The proposed transfer function for both of TYPE III and TYPE IV can be achieved as a closed form function using Jacobi polynomial. Furthermore, we can easily derive the weighting coefficients of the proposed MFDDs using recursive formula. Through some design examples, we confirm that the proposed method can adjust the center frequency arbitrarily and the band width having flat property.

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.

Flat Panel Displays (FPDs) are manufactured using many pieces of different processing equipment arranged sequentially in a line. Although the constant inter-arrival time (i.e., the tact time) of glass substrates in the line should be kept as short as possible, the collision probability between glass substrates increases as tact time decreases. Since the glass substrate is expensive and fragile, collisions should be avoided. In this paper, we derive a closed form formula of the approximate collision probability for a model, in which the processing time on each piece of equipment is assumed to follow Erlang distribution. We also compare some numerical results of the closed form and computer simulation results of the collision probability.

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.

Both adaptive modulation and diversity combining are attractive techniques to combat fading and these two can be applicable to each digital-modulated symbol in OFDM transmission. In this letter, aiming to combat severe fading more effectively than the adaptive modulation, we theoretically analyze the benefit of a frequency diversity scheme within one OFDM symbol, which is a simple kind of coded OFDM (COFDM) based on IEEE 802.16 protocols. A simple closed form equation of bit error rate (BER) is derived, and then the advantages of correlated diversity gain and interference suppression by the diversity scheme are verified by both theoretical analysis and Monte Carlo simulation.

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.