Let N(k,p^m) be the number of distinct values of x^k mod p^m for all integers x(0xp^m-1). Given a random integer a, the probability that x^ka(mod p^m) has an integer solution x is given by N(k,p^m)/p^m. Explicit and simple representations of N(k,p^m) are obtained. Asymptotic formulas of the probability N(k,p^m)/p^m as m,p and k are also shown.

The back crosstalk constant K_b of a pair of coupled transmission lines using parallel round wires on a multiwire circuit board is presented in graphical form for relative dielectric constants of 1.0, 2.65 and 5.0 and for various separation between two wires as a function of normalized wire radius. K_b, obtained numerically, is in good agreement with the experimental value.

We show that, for any simple SIMD machine M with time complexity T(n), there exists a systolic array which can simulate M in T(n)+2n+O(1) steps. Our result is an improvement on the previous (2T(n)+3n+O(1))-step systolic simulation theorem.

The aim of this paper is to investigate necessary and sufficient conditions for liveness of a class of extended marked graphs (EMG) in terms of the initial token distributions and the net structure. The results can be applied to a large class of EMG which includes the class discussed in Refs. (1) and (7).

This paper investigates the convergence property of a circuit simulation technique called an iterated timing analysis. A block strictly row-wise or column-wise diagonal dominant matrix is defined, and these matrices are shown to be nonsingular. In addition, both block Jacobi method and block Gauss-Seidel iteration are proved to converge for the equation whose coefficient matrix is one of these matrices. On the bases of these results, the following two sufficient conditions for the iterated timing analysis to converge locally are given: ) the capacitance matrix of the circuit is block strictly row-wise or column-wise diagonally dominant and a time step is sufficiently small, ) the conductance matrix of the circuit has the same property and a time step is sufficiently large.

In this paper, an argumental approach is introduced for an expression of correlation functions between two arbitrary codewords. The real parts of the correlation values are mapped onto the argument vector, then the components of the vector are plotted on a unit circle by each angle. The imaginary parts are expressed on the another unit circle by the same manner. The distinctive features of the proposed method are described in comparison with recent expression methods, and some examples of the application are demonstrated along with numerical results. The argumental expression is shown to be a generalized way to indicate correlation functions for all possible codewords.

A transmission performance design method for digital telephone sets is described, considering talker echo resulting from reflection at the four-wire to two-wire hybrid point in mixed digital-analogue networks. The method provides for complete international telephone connection, talker echo suppression and improved speech quality. To develop a design method with these features, first, the effect of talker echo on speech quality is evaluated. Next, digital telephone set loudness ratings are regulated as follows: 8.3 dB sending loudness rating 10 dB, 0.5 dB receiving loudness rating 4 dB. As a result, the Mean Opinion Score (MOS) for digital telephone sets in the ISDN is from 2.3 to 2.7 according to tests, considered acceptable for about 90% of subscribers.

A new analysis technique applicable to speech recognition is proposed considering the auditory mechanism of speech perception which emphasizes spectral dynamics as well as compensates for the spectral undershoot associated with coarticulation. A speech wave is represented by the LPC cepstrum and logarithmic energy sequences, and the time sequences over short periods are expanded by the first- and second-order polynomial functions at every frame period. The dynamics of the cepstrum sequences are then emphasized by the linear combination of their polynomial expansion coefficients, that is, derivatives, and their instantaneous values. Speaker-independent word recognition experiments using time functions of the dynamics-emphasized cepstrum and the polynomial coefficient for energy indicate that the error rate can be largely reduced by this method. The experimental results are compared with those obtained by the previous method in which the polynomial coefficients for the cepstrum and energy time functions were used in combination with the original time functions of these parameters as independent parameters.

PLL(Phase-Locked Loop) FM demodulators have been popularly used in various communication systems as a threshold extension device. However, because of the difficulty of the exact analysis, the practical design of PLL demodulators has greatly depended on the experimental results. In this paper, we will introduce the design method in which PLL parameters are approximately determined using the quasi-linear approximation. These are then checked by the time domain digital simulation. As a result, we may design the practical PLL demodulators without doing experiments.

Orchard coding scheme is a kind of convolutional coding system of rate (n₀1)/n₀. In this system. Calculation of parity bits is over perviously calculated parity bits as well as information bits. This article presents a new class of orchard codes which correct double bit errors and single byte errors within a constraint length. The rate of the codes is (n₀1)/n₀ and the constraint length is n₀(4n₀+1) bits. A byte is group of n₀ bits. In the proposed codes, the generation of a present parity bit is affected by the information bits and the parity bits for past 2n₀ clock times. The decoder generates a syndrome sequence and errors are corrected using the syndrome pattern. An error propagation occurs only when the punctuation of a syndrome pattern of length 4n₀+1 is erroneous, but if the successive 4n₀ zero-bits appear in the syndrome sequence, the error propagation does not occur beyond that.

Realization of performance requirements by scheduling strategies is investigated on a finite-source queueing model, which has often been used as a model of time-shared systems. The model consists of a single-server station (processor) and a multiple-server station (terminals); each job has a distinct mean service time at the processor. Performance requirements that are stated in terms of the performance vector, each element of which is the utilization factor of the processor for a job, are investigated, and the following results are obtained. First, the optimization of performance measures is discussed under Markovian assumptions. Linear performance measures such as the throughput and the mean response time can be optimized by preemptive priority disciplines, and their implementation may be simple. However, the optimization of nonlinear performance measures such as the average cost per interaction may lead to a linearly constrained nonlinear programming problem, and the schedules which optimize them may be hard to implement. Second, realization of the equal response ratio is discussed. The processor sharing (or preemptive-resume LCFS) discipline, although it attains the equal response ratio in M/G/1, gives a smaller response ratio to a job with a longer mean processor time. It is shown under Markovian assumptions that the equal response ratio is achievable by another scheduling strategy.

Sectioned optimization methods for image restoration is presented in order to restore the original image from the observation degraded by a point spread function and additive noise. This is a locally adaptive filter which minimizes the mean square errors of the estimate for each section of the image. The required information for this processing is derived from the observation as a proto-type and then it is modified to fit for processing in each section of the image by using an iterative algorithm. The simulation examples show that the restored image is always superior than that of the usual minimum mean square error-filter. This can not only be utilized for the usual degraded image but also for the image suffered from the band width compression in the image communication.

The use of the Constructive Solid Geometry (CSG) model has been considered in several computer-aided design systems for recent years, since its concept of powerful and multiple operations on basic object shapes to create more complex ones is intuitively easy to understand. Based on the CSG concept and a guiding principle of scene analysis, an algorithm for interpreting three-view drawings is described in this paper. In a certain process, the 3D interpretation works on local recognition to detect possible subparts of which orthographic patterns are defined in the 2D description of a part. In the subsequent process, which examines all possible solutions to the given drawing until finding one that meets some goal criteria, the combinatorial operators are applied to the possible subparts. Through those repeated processes, the final solution can be obtained in terms of consistent subparts in a CSG tree, including additional information about solids and cavities.