Numerical integration by gaussian quadrature
Gauss quadrature formula for approximate integration by computer - numerical integration
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Gauss quadrature formula for approximate integration by computer - numerical integration
Energy of interaction between two hydrogen atoms in their ground states described by Gauss-type functions
Timing error and noisy phase reference joint effect on system performance of coded partially phase coherent reception
Circuit limits the positive and negative peaks of a random-noise signal. It accurately establishes a known limiting level relative to any given RMS value of the random-noise signal input.
Simulation of service load distributions using digital computers with FORTRAN 4 program
Probability density functions for quantization noise, continuous wave interference, impulse noise, and atmospheric noise
Maximum likelihood receiver /MLR/ to detect pulsed signal propagated through turbulent medium, assuming optical propagation over long path in atmosphere
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The improvement in db due to concatenation over conventional M-ary coding is studied to reduce the probability of a bit error and to increase the available bit rate for the same system parameters of error rate, transmitter power, and range. The results of calculations for orthogonal modulation with noncoherent detection and Q-level correlator quantization are presented. It is shown that the correlator outputs are quantized to one of the Q levels, and the receiver output is a vector consisting of a list of the M correlator quantum levels. The channel has Q(M) possible outputs and M possible inputs. Optimum output is approached by increasing fine quantization
The role of the linear-quadratic stochastic control problem in engineering design is reviewed in tutorial fashion. The design approach is motivated by considering the control of a nonlinear uncertain plant about a desired input-output response. It is demonstrated how a design philosophy based on (1) deterministic perturbation control, (2) stochastic state estimation, and (3) linearized stochastic control leads to an overall closed-loop control system. The emphasis of the paper is on the philosophy of the design process, the modeling issue, and the formulation of the problem; the results are given for the sake of completeness, but no proofs are included. The systematic off-line nature of the design process is stressed throughout.
An FM/FM system is one in which the signal information frequency modulates a subcarrier, which, in turn, frequency modulates a main carrier for transmission. The detection process then involves two frequency demodulators in sequence. Using Rice's click model for both FM demodulators, we obtain the average click rate and an approximate output spectrum that include the effect of the impulses generated by the carrier demodulator on the subcarrier demodulation at and below threshold. We then focus on the threshold behavior of these systems and the proportioning of their modulation parameters so as to provide certain desired characteristics. We find that due to the filtering action of the second demodulator, the number of output clicks from carrier generated spikes can be orders of magnitude smaller, yet their contribution to the output noise can be much greater than that produced by the first demodulation.
The effect of the grating-induced phase and spatial modulations by multiple transverse modes simultaneously present in mode-locked laser pulses is investigated. Our analysis shows that the dispersions of the grating pair become strongly dependent on wavelength because of the energy exchanges occurring among transverse modes. As a result, the maximum-intensity trace at the output of the grating is shown to be curved and the grating-induced pulse-compression rate is shown to vary significantly across the beam cross section. Also, a discussion is presented relating our analysis to existing experimental data on the wavelength-dependent chirping rates of mode-locked laser beams.
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A detailed study is presented of some statistical properties of a stochastic process that consists of the sum of two sine waves of unknown relative phase and a normal process. Since none of the statistics investigated seem to yield a closed-form expression, all the derivations are cast in a form that is particularly suitable for machine computation. Specifically, results are presented for the probability density function (pdf) of the envelope and the instantaneous value, the moments of these distributions, and the relative cumulative density function (cdf).
Lagrange-type equations are often used in planetary theory and sometimes in satellite theory. The equations express the variation of osculating Keplerian elements in terms of derivatives of a disturbing function or a perturbing potential. When the perturbing force is derivable from a potential, it is possible to convert the Lagrange-type equations to another form. This form, usually, attributed to Gauss, contains the perturbing forces instead of the derivatives of the potential. The case of an arbitrary separable reference orbit is discussed together with a lemma, a Keplerian check, and questions of the applicability of the equations to the spheroidal method.
The effectiveness of a lubricant film preventing metallic contact between two rolling surfaces (such as in ball bearings) as a function of surface roughness parameters was investigated. The parameters considered are the spectral moments of the two-dimensional surface obtained by superposition of the two rolling surfaces. The peak height distribution, estimation of one-dimensional profile spectral moments, and the estimation of two-dimensional surface moments from several profile measurements were considered. Also given is an asymptotic relation between the mean film thickness and contact occurrences.
Theoretical investigation of how effectively a lubricant film prevents metallic contact between two rolling surfaces (such as in ball bearings) as a function of surface roughness parameters. The parameters considered are the spectral moments of the two-dimensional surface obtained by superposition of the two rolling surfaces. We consider the peak height distribution, estimation of one-dimensional profile spectral moments, and the estimation of two-dimensional surface moments from several profile measurements are taken into account. Also given is an asymptotic relation between the mean film thickness and contact occurrences.