Probability of error for the fixed-length lossy coding of general sources

In this correspondence, we are interested in the error exponent of fixed-length lossy source coding, where the sources are general sources, in the sense of Han and Verduacute, including all nonstationary and/or nonergodic sources. The aim of the correspondence is to establish a unified formula for the minimum (D, r)-achievable rate which is the minimum achievable coding rate under asymptotic constraints of the form epsiv_n(D) ~ e^-nr (n rarr infin), where r is the prescribed error exponent, epsiv_n(D) is the probability of the distortion exceeding a level D, and n is the code-length. For the stationary memoryless source with finite alphabet, Marton (1974) obtained a formula for the reliability function which is expressed in terms of the minimum (D,r)- achievable rate. Recently, Ihara and Kubo proved that the Marton's formula remains true for the stationary memoryless Gaussian source under a mean-squared fidelity criterion. In this correspondence, it is shown that a formula similar to Marton's formula holds for the general sources. The error exponent of correct decoding is also investigated and a formula for the minimum achievable rate of correct decoding in lossy coding is established     

Microwave (1-100 GHz) dielectric model of leaves

A semiempirical formula for the complex dielectric permittivity of leaves from different plants is found from a comparison of published measurements covering the frequency range from 1 to 100 GHz. The explicit parameters are the dry-matter fraction m_d of the leaf and the permittivity ϵ_SW of saline water with a salinity of about 1 percent. The physical part of the formula is its basis on ϵ_SW while the empirical part is its linearity with m_d. The formula is applicable to fresh leaves; their m _d values are in the range 0.1d<0.5. A test indicates that besides the m_d variation and the spectral dependence the formula also describes the temperature variation correctly     

A relationship for temperature dependence of threshold current for 1.3-/spl mu/m compressively strained-layer multiple-quantum-well lasers

Assuming that the differential gain is a linear function of temperature, a formula is derived to describe the threshold current as a function of temperature. A maximum operating temperature, T/sub max/ which is related to the fundamental physical properties (such as differential gain, free carrier loss and intervalence band absorption) of the lasers appears naturally in the formula, at which lasing ceases. To experimentally investigate the relationship, studies were carried out on 1.3-/spl mu/m strained-layer multiple quantum well (SL-MQW) lasers with variant 0.7% compressively strained wells. The formula shows a good correlation with threshold current versus temperature data over the temperature range 200 K to 450 K.     

An investigation of the high-frequency limit of a miniaturizedcommercial voltage-controlled oscillator used in 900-MHz-bandmobile-communication handset

The 900-MHz-band voltage-controlled oscillator (VCO) currently used in a commercial mobile-communication handset has the features of light weight, small size, low phase noise, and low DC current consumption. This paper investigates the problems that may occur when these types of VCO's are employed in next-generation high-frequency mobile-communication handsets. The results show that oscillation may not commence above frequency f_T/² √(R_eq /T_bb), which is significantly below the f_max of the device itself, due to the effects of the circuit elements. In addition, a new formula is proposed which provides a practical guideline for selection of the active devices. The procedure for extraction of the small-signal model required by the proposed formula is also described in detail. The results obtained with the formula are in good agreement with those obtained from the measured S-parameters     

Study of the relation between doping profile and diode CVcharacteristics

An explicit formula relating Schottky-diode junction capacitance (C_j) as a function of diode bias (V_dc) and Gaussian doping profile (k) has been curve fitted to a one-dimensional numerical analysis. Two-dimensional physical simulation and the explicit formula have been applied to a Schottky diode with both simulated and analytic results compared against measurement. Incomplete ionization, edge effects, and additional charge created by traps have also been investigated using a physical simulation package, and results are presented for different trap densities. The stated formula has been implemented for a Schottky diode model using a symbolically defined device within the HP-MDS harmonic-balance simulator. This has been used as a building block for a nonlinear transmission-line (NLTL) doubler design with simulated and measured second harmonic-power output being presented. The formula, which is easily implemented in computer-aided design tools, is important for NLTL modeling and design     

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     

An approximate formula for calculating the directivity of an antenna

An approximate general formula to calculate the directivity of an antenna based upon theE-plane andH-plane patterns is proposed. For narrow beam patterns, the directivity is expressed in terms of the half-power beam widths of the main patterns. The better approximation of the formula presented here over the geometrical mean formula is pointed out.     

Traveling wave lobe locations

A simple and reasonably accurate formula for the angular locations of traveling wave lobes has been available for many years, but the formula holds only for surface waves that travel at the speed of light. It is shown how the formula may be modified to account for propagation velocities less than the speed of light. It is shown that when the equation derived by the author is used to estimate a starting value for cosQ in the Newton-Raphson method, the solution usually requires no more than three iterations for an accuracy of 10^-6 in the solution for Q     

Receiver Model for Depolarized Signal Due to Polarization-Mode Dispersion and Partially Polarized Noise Due to Polarization-Dependent Loss in an Optical Fiber Communication System

We systematically investigate the combined effect on the system performance in an optical fiber communication system of a signal that is depolarized due to polarization-mode dispersion (PMD) and noise that is partially polarized due to polarization-dependent loss. We derive a formula for the variance of the electric current of the signal due to the signal–noise beating between a depolarized signal and partially polarized noise. We validate this theoretical formula by comparing the $Q$ -factor calculated using the theory to results obtained from Monte Carlo simulations and experiments. We show that the system performance strongly depends on the power-splitting ratio, the degree of polarization of the noise, and the angle between the states of polarization of the signal and the polarized part of the noise. Although the theoretical formula is derived assuming that the optical fiber only has first-order PMD, we show that for arbitrary fiber, this formula still produces a reliable estimate of the $Q$-factor provided that the second-order PMD is on the order of 300 ${hbox {ps}}^{2}$ or less.      

An efficient representation of radiation from a circular aperturewith tapered amplitude and quadratic phase

An efficient series representation is derived for I_pab, a quadratic phase integral commonly encountered in aperture-antenna theory. The accuracy and efficiency of the series formula relative to ordinary numerical integration are discussed. This formula may be useful in solving such problems as quadratic-phase error effects on beamwidth, field in the Fresnel-region, on-axis defocus characteristics of a paraboloidal reflector, or shadow-region field behind a disk     

On the input impedance of a Hertzian dipole over a flat surface

An explicit formula is derived for the change of input impedance of a vertical electric dipole as a function of the distance of the dipole to a horizontal boundary with a prescribed surface impedancen. It is shown that, ifn ll 120pi, the result is consistent with the formula obtained by the compensation-theorem approach.     

Optimum tapered buffer

Driver stages in MOS circuitry have been extensively investigated during the last decade. recently a tapering rule for CMOS buffers was derived showing that the tapering factor (β) is determined by the ratio of output to input capacitance. The derivation fails to account for the correlation between the short-circuit current and β. As a result, the derived formula consistently overpredicts the value of optimum β, especially for large input/output capacitance ratios. The authors present a modified formula and a method to account for the effect of the short-circuit current that is viable for buffer stages over a wide range of output/input capacitance ratios; this newly derived formula accurately predicts the optimum tapering factors for BiCMOS as well as CMOS buffer chains     

Recurrence formula for impulse response coefficients of Sinc/sup N/ FIR filter

A simple recurrence formula for computing the impulse response coefficients of the Sinc/sup N/ FIR made of a cascade of N Sinc filters each of length M is presented. The formula allows for a much lower mathematical operation compared to the previously published format and thus leads to a faster execution time and simpler circuitry.     

Equivalent capacity for on/off sources in ATM

A formula is presented for the `equivalent capacity' required to support a given cell loss probability in an ATM buffer fed by a single on/off source. This formula can be applied as a component in connection admission control and bandwidth management algorithms in ATM telecommunications networks     

APPROXIMATION OF THE QUEUE LENGTH DISTRIBUTION OF GENERAL QUEUES

In this paper we develop an approximation formalism on the queue length distribution for general queueing models. Our formalism is based on two steps of approximation; the first step is to find a lower bound on the exact formula, and subsequently the Chernoff upper bound technique is applied to this lower bound. We demonstrate that for the M/M/1 model our formula is equivalent to the exact solution. For the DIM/1 queue, we find an extremely tight lower bound below the exact formula. On the other hand, our approach shows a tight upper bound on the exact distribution for both the ND/D/1 and M/D/1 queues. We also consider the M+Σ N_jD/D/1 queue and compare our formula with other formalisms for the Σ N_jD/D/1 and M+D/D/1 queues.     

Computation of the Para-Pseudoinverse for Oversampled Filter Banks: Forward and Backward Greville Formulas

Frames and oversampled filter banks have been extensively studied over the past few years due to their increased design freedom and improved error resilience. In frame expansions, the least square signal reconstruction operator is called the dual frame, which can be obtained by choosing the synthesis filter bank as the para-pseudoinverse of the analysis bank. In this paper, we study the computation of the dual frame by exploiting the Greville formula, which was originally derived in 1960 to compute the pseudoinverse of a matrix when a new row is appended. Here, we first develop the backward Greville formula to handle the case of row deletion. Based on the forward Greville formula, we then study the computation of para-pseudoinverse for extended filter banks and Laplacian pyramids. Through the backward Greville formula, we investigate the frame-based error resilient transmission over erasure channels. The necessary and sufficient condition for an oversampled filter bank to be robust to one erasure channel is derived. A postfiltering structure is also presented to implement the para-pseudoinverse when the transform coefficients in one subband are completely lost.      

用粒子计数法测量颗粒物质量浓度

为了测量颗粒物的质量浓度,基于米散射理论,在偏振入射光条件下,通过数值计算研究了球形颗粒的散射光通量与粒径之间的关系,得到了利用光学粒子计数器测量颗粒物质量浓度的计算公式。该公式重点考虑了粒子数目和大小对质量浓度的影响。实验结果表明,在0.001mg/m3~2mg/m3的质量浓度范围内,该公式的计算值与实验测量值具有显著的相关性,相关系数为0.9953。     

Singularity in Green's function and its numerical evaluation

The free-space scalar Green's functionghas anR^{-1}singularity, whereRis the distance between the source and observation points. The second derivatives ofghaveR^{-3}singularities, which are not generally integrable over a volume. The derivatives ofgare treated as generalized functions in the manner described by Gel'fand and Shilov, and a new formula is derived that regularizes a divergent convolution integral involving the second derivatives ofg. When the formula is used in the dyadic Green's function formulation for calculating theEfield, all previous results are recovered as special cases. Furthermore, it is demonstrated that the formula is particularly suitable for the numerical evaluation of the field at a source point, because it allows the exclusion of an arbitrary finite region around the singular point from the integration volume. This feature is not shared by any of the previous results on the dyadic Green's function.     

An Error Probability Formula for M-ary DPSK in Fast Rician Fading and Gaussian Noise

A formula for the symbol error probability is derived which applies to differential detection ofM-ary phase-shift keying (MDPSK) in fast Rician fading and white Gaussiau noise. This formula is an extension of a result already known for MDPSK in Gaussian noise interference.     

Analytical Evaluation of Via-Plate Capacitance for Multilayer Printed Circuit Boards and Packages

The via-plate capacitance for a via transition to a multilayer printed circuit board is evaluated analytically in terms of higher order parallel-plate modes. The Green's function in a bounded coaxial cavity for a concentric magnetic ring current is first derived by introducing reflection coefficients for cylindrical waves at the inner and outer cavity walls. These walls can be perfect electric conductor (PEC)/perfect magnetic conductor (PMC) or a nonreflective perfectly matched layer. By further assuming a magnetic frill current on the via-hole in the metal plate, an analytical formula is derived for the via barrel-plate capacitance by summing the higher order modes in the bounded coaxial cavity. The convergence of the formula with the number of modes, as well as with the radius of the outer PEC/PMC wall is discussed. The analytical formula is validated by both quasi-static numerical methods and measurements. Furthermore, the formula allows the investigation of the frequency dependence of the via-plate capacitance, which is not possible with quasi-static methods.