Calculation of electric fields due to lines of charge

The amplitude of the electric field due to a straight line segment of uniform electric charges is shown to be given by E=2q (4πDε₀)^-1 sen (α/2) where q is the linear charge density, α is the viewing angle (from the observation point to the filament extremities), and D is the distance to the filament; furthermore, the direction of the vector E lies on the bisector of the viewing angle. This result can greatly reduce the computation time in the analysis of EMC (electromagnetic compatibility) problems involving static or quasi-static charge distributions     

An efficient non-recursive algorithm for computing the reliabilityof k-out-of-n systems

An algorithm for computing the reliability of k-out-of- n systems is proposed. It is simple, easy to implement on a computer, time and memory efficient, and good for numerical computation. The memory complexity is O(n-k), and for a given value of n-k the computation time is proportional to n . Its FORTRAN implementation is presented     

Energy consumption in multilective and boundary VLSI computations

A VLSI computation is said to be m-way multilective when each input bit is available m times in either space or time or both. The repeated availability of input bits can save computational energy. For a uniswitch m-way multilective computation, where a wire can switch at most once, it is shown that the energy savings can be as much as a factor of m. A multiswitch m-way multilective computation can save up to a factor of √ m switching energy. Tighter energy lower bounds are derived for a circuit with the input/output (I/O) pads located on the border. These boundary computations seem to cost an additional factor ranging from √log n to log n in switching energy. The author extends the energy lower bounds for the multilective case, for a chip with aspect ratio a. The additional energy cost ranges from a factor of √a to a factor of a     

Fast cosine transform of Toeplitz matrices, algorithm andapplications

A fast algorithm for the discrete cosine transform (DCT) of a Toeplitz matrix of order N is derived. Only O(N log N)+O(M) time is needed for the computation of M elements. The storage requirement is O(N). The method carries over to other transforms (DFT, DST) and to Hankel or circulant matrices. Some applications of the algorithm are discussed     

The inductance matrix of a multiconductor transmission line inmultiple magnetic media

A simple relationship between the inductance matrix and the auxiliary capacitance matrix is given. For a multiconductor transmission line consisting of N_c conducting cylinders in inhomogeneous media consisting of N_d homogeneous regions with permeabilities μ_i and permittivities ϵ _i, the inductance matrix [L] for the line is obtained by solving the magnetostatic problem of N_c conductors in N_d regions with permeabilities μ _i. The capacitance matrix [C] for the line is obtained by solving the electrostatic problem of N_c conductors in N_d regions with permittivities ϵ _i. It is shown that [L]=μ₀ϵ₀[C^'] ^-1, where [C^'] is the capacitance matrix of an auxiliary electrostatic problem of N_c conductors in N_d regions with relative permittivities set equal to the reciprocals of the relative permeabilities of the magnetostatic problem, i.e. ϵ^' _i/ϵ₀=μ₀/μ_i     

Pipelined recursive filter with minimum order augmentation

Pipelining is an efficient way for improving the average computation speed of an arithmetic processor. However, for an M-stage pipeline, the result of a given operation is available only M clock periods after initiating the computation. In a recursive filter, the computation of y(n) cannot be initiated before the computations of y(n-1) through y(n-N) are completed. H.B. Voelcker and E.E. Hartquist (1970) and P.M.Kogge and H.S. Stone (1973) independently devised augmentation techniques for resolving the dependence problem in the computation of y(n). However, the augmentation required to ensure stability may be excessively high, resulting in a very complex numerator realization. A technique which results in a minimum order augmentation is presented. The complexity of the resulting filter design is very much lower. Various pipelining architectures are presented. It is demonstrated by an example that when compared to the prototype filter, the augmented filter has a lower coefficient sensitivity and better roundoff noise performance     

A storage-efficient method for solving banded Toeplitz systems

A method is presented for solving the banded Toeplitz system Tx=y by decomposing T into its asymptotic upper and lower triangular factors (which are banded and Toeplitz) and a rank-p correction matrix, where p is the bandwidth of T. This way of representing T requires only O(p²) words of storage and allows computation of x in O(2Np) operations. A similar method is presented for the case in which T is bi-infinite and y is zero outside a finite region     

Computing the probability of undetected error for shortened cycliccodes

The authors present a general technique for computing P _e for all possible shortened versions of cyclic codes generated by any given polynomial. The technique is recursive, i.e. computes P_e for a given code block length n from that of the code block length n-1. The proposed computation technique for determining P_e does not require knowledge of the code weight distributions. For a generator polynomial of degree r, and |g| nonzero coefficients, the technique yields P_e for all code block lengths up to length n in time complexity O(n|g |2^r+|g|). Channels with variable bit error probabilities can be analyzed with the same complexity. This enables the performance of the code generator polynomials to be analyzed for burst errors     

Evaluation of the quantization error in denominator-separable 2-Drecursive filters

The evaluation of the quantization error in two-dimensional (2-D) digital filters involves the computation of the infinite square sum J=Σ^∞_m=φΣ ^∞_n=φy² (m, n). A simple method is presented for evaluating J based on partial fraction expansion and using the residue method provided the Z-transform Y(Z₁, Z₂) of the sequence y(m, n) having quadrant support is a causal bounded input, bounded output (BIBO) stable denominator-separable rational function. The value of J is expressed as a sum of simple integrals which can easily be evaluated. The simple integrals are tabulated for ready reference. The proposed method is suitable for analytical as well as numerical computation and can easily be programmed     

A (16, 9, 6, 5, 4) error-correcting DC free block code

A (2n, k, l, c, d) DC free binary block code is a code of length 2n, constant weight n, 2^k codewords, maximum runlength of a symbol l , maximum accumulated charge c, and minimum distance d . The purpose of this code is to achieve DC freeness and error correction at the same time. The goal is to keep the rate k/2 n and d large and l and c small. Of course, these are conflicting goals. H.C. Ferreira (IEEE Trans. Magn., vol.MAG-20, no.5, p.881-3, 1984) presented a (16, 8, 8, 5, 4) DC free code. Here, a (16, 9, 6, 5, 4) DC free code is presented. Easy encoding and decoding algorithms are also given     

Realization of IIR LDM digital filters

A method is presented of realizing an infinite impulse response (IIR) digital filter (DF) using linear delta modulation (LDM) as a simple analog/digital (A/D) converter. This method makes the realization of IIR digital filters much simpler than that of conventional ones because it does not require hardware multipliers or a pulse code modulation (PCM) A/D converter. Compared to the finite impulse response (FIR) LDMDF, this IIR LDMDF requires significantly less computation time     

Rapid optimal scheduling for time-multiplex switches using acellular automaton

Many time-multiplex switching systems require that the incoming traffic be scheduled to avoid conflict at the switch output (two or more users converging simultaneously upon a single output). Optimal scheduling provides a means to assign traffic on demand such that either blocking probability is minimized (unbuffered system) or packet waiting time is minimized (buffered system). However, computation of an optimal schedule for switches of a reasonable size (i.e. N=100) may require many seconds or even minutes, whereas the traffic demand may vary much more rapidly. Since the computation time varies as O(N²), the problem becomes readily intractable for large N. This computational bottleneck is overcome by using a scheduling algorithm which is run on a simple special-purpose parallel computer (cellular automaton). A schedule is produced in O(N) time if signal propagation time in the automaton is considered negligible, and therefore increases in computation speed by several orders of magnitude should be possible; the time to compute a schedule for a 1000-input switch would be measured in milliseconds rather than minutes     

Longitudinal and transverse current distributions on coupledmicrostrip lines

The normalized longitudinal and transverse current distributions on coupled microstrip lines are obtained for even and odd modes by using the charge conservation formula and the charge distributions calculated by a Green's function technique. Their dependence on the shape ratios w/h and s/h and on the relative permittivity ε* of the substrate is shown     

The number of failed components in aconsecutive-k-of-n:F system

For a consecutive-k-out-of-n:F system an exact formula and a recursive relation are presented for the distribution of the number of components, X, that fail at the moment the system fails. X estimates how many cold spares are needed to replace all failed components upon system failure. The exact formula expresses the dependence of the distribution of X upon parameters k , n. The recursive formula is suitable for efficient numerical computation of the distribution of X     

A fast signature scheme based on congruential polynomial operations

A novel digital signature scheme is proposed in which the computation time is much shorter than that of the Rivest-Shamir-Adelman (RSA) scheme, while the key length and signature length are comparable to those for the RSA scheme. Moreover, the proposed scheme can be implemented easily and is, therefore, more practical for many digital signature applications. The scheme is based on congruential polynomial operations whose degrees are more than three. The secret key consists of two large prime numbers, p and q, and the public key is their product, n=p²q. The security of this scheme depends on the difficulty of factorizing the number n. Variations using the number of zeros succeeding the significant bit are also proposed     

A new technique for measuring MOSFET inversion layer mobility

An experimental technique for accurately determining both the inversion charge and the channel mobility μ of a MOSFET is presented. With this new technique, the inversion charge is measured as a function of the gate and drain voltages. This improvement allows the channel mobility to be extracted independent of drain voltage V_DS over a wide range of voltages (V_DS=20-100 mV). The resulting μ(V_GS) curves for different V_DS show no drastic mobility roll-off at V _GS near V_TH. This suggests that the roll-off seen in the mobility data extracted using the split C- V method is probably due to inaccurate inversion charge measurements instead of Coulombic scattering     

Fast capacitance extraction of general three-dimensional structures

K. Nabors and J. White (1991) presented a boundary-element-based algorithm for computing the capacitance of three-dimensional m-conductor structures whose computational complexity grows nearly as mn, where n is the number of elements used to discretize the conductor surfaces. In that algorithm, a generalized conjugate residual iterative technique is used to solve the n×n linear system arising from the discretization, and a multipole algorithm is used to compute the iterates. Several improvements to that algorithm are described which make the approach applicable and computationally efficient for almost any geometry of conductors in a homogeneous dielectric. Results using these techniques in a program which computes the capacitance of general 3D structures are presented to demonstrate that the new algorithm is nearly as accurate as the more standard direct factorization approach, and is more than two orders of magnitude faster for large examples     

Maximum likelihood estimation of the parameters of discretefractionally differenced Gaussian noise process

A maximum-likelihood estimation procedure is constructed for estimating the parameters of discrete fractionally differenced Gaussian noise from an observation set of finite size N. The procedure does not involve the computation of any matrix inverse or determinant. It requires N²/2+O(N) operations. The expected value of the loglikelihood function for estimating the parameter d of fractionally differenced Gaussian noise (which corresponds to a parameter of the equivalent continuous-time fractional Brownian motion related to its fractal dimension) is shown to have a unique maximum that occurs at the true value of d. A Cramer-Rao bound on the variance of any unbiased estimate of d obtained from a finite-sized observation set is derived. It is shown experimentally that the maximum-likelihood estimate of d is unbiased and efficient when finite-size data sets are used in the estimation procedure. The proposed procedure is extended to deal with noisy observations of discrete fractionally differenced Gaussian noise     

On optimum time-hopping patterns

Time-hopping patterns can be constructed from simple difference sets. By studying such constructions, it has been proven that whenever n-2, n-1, or n+1 is a prime power, then time-hopping patterns that have n terms can be constructed and are of length less than n². By computation it is shown that such patterns can have length less than n²-n^1.44 for all n⩽150. It is also shown that time-hopping patterns for n terms can have length less than n²+O(n^1.55) for all n     

Intensity noise and spontaneous emission coupling insuperluminescent light sources

A simple expression for the noise in the photocurrent generated by the detection of light from an ideal superluminescent source is derived using a quantum amplifier model. The excess noise factor X is found to be related to the photocurrent I_d, electronic charge e, spontaneous emission coupling factor K , and full width at half maximum power of the emission spectrum Δv_1/2 by the expression X=0.664 I _d/eKΔv_1/2. Implications of this result for the performance of fiber-optic gyroscopes using superluminescent-diode (SLD) light sources and for the design of low-noise SLDs are discussed