Glenn A. Gibson

Accurate Formula for Gaseous Transmittance in the Infrared

By considering the infrared transmittance model of Zachor as the equation for an elliptic cone, a quadratic generalization is proposed that yields significantly greater computational accuracy. The strong-band parameters are obtained by iterative nonlinear, curve-fitting methods using a digital computer. The remaining parameters are determined with a linear least-squares technique and a weighting function that yields better results than the one adopted by Zachor. The model is applied to CO(2) over intervals of 50 cm(-1) between 550 cm(-1) and 9150 cm(-1) and to water vapor over similar intervals between 1050 cm(-1) and 9950 cm(-1), with mean rms deviations from the original data being 2.30 x 10(-3) and 1.83 x 10(-3), respectively.

Fast implementations of fuzzy arithmetic operations using fast Fourier transform (FFT)

Abstract In engineering applications of fuzzy logic, the main goal is not to simulate the way the experts really think, but to come up with a good engineering solution that would (ideally) be better than the experts control. In such applications, it makes perfect sense to restrict ourselves to simplified approximate expressions for membership functions. If we need to perform arithmetic operations with the resulting fuzzy numbers, then we can use simple and fast algorithms that are known for operations with simple membership functions. In other applications, especially the ones that are related to humanities, simulating experts is one of the main goals. In such applications, we must use membership functions that capture every nuance of the experts opinion; these functions are therefore complicated, and fuzzy arithmetic operations with the corresponding fuzzy numbers become a computational problem. In this paper, we design a new algorithm for performing such operations. This algorithm uses Fast Fourier Transform (FFT) to reduce computation time from O( n 2 ) to O( n log( n )) (where n is the number of points x at which we know the membership functions μ ( x )). To compute FFT even faster, we propose to use special hardware. The results of this paper were announced in the work of Kosheleva et al. [Proc. 1996 IEEE Int. Conf. on Fuzzy Systems, Vol. 3, pp. 1958–1964].

Sensitivity of atmospheric spectral transmittance to line and meteorological parameters

Abstract A study is made of the variance of the monochromatic molecular absorption coefficient and of the corresponding slant-path transmittance due to variations in the tabulated Lorentzian line-parameter data and atmospheric meteorological variables. General expressions are derived from five basic assumptions, which are useful for calculations involving specific atmospheric profiles and spectral line-parameter data. The results of calculations for 8 representative frequencies, assuming typical variations in the parameters, indicate that transmittance errors greater than 0.01 should be expected for transmittance calculations in the range from about 0.1 to 0.9.

Design issues in a CMOS implementation of a modularly-configured attached processor

Abstract Implementation of a novel modularly-configured attached processor architecture has been evaluated using I μm CMOS logic on deposited interconnect multichip module technology. The transistor count was approximately 9 million, distributed on 25 chip dies. Delay, area and power calculations were performed using the SUSPENS model. Rents rule was found to be not applicable. Speed was calculated to be in the 150MFLOPS range. The module footprint was calculated as 90 cm2 Power dissipation per unit area was low enough to allow air cooling.

Approximation to the Lorentzian coefficient for efficient calculation of transmittance profiles

A major problem in the calculation of line-by-line profiles of atmospheric transmittance lies in the excessive computational times associated with the evaluation of the Lorentzian coefficient for every gas, wavenumber, line, temperature, and pressure along the path. An approach to the solution of this problem is presented, whereby use is made of an approximating function that allows for the quantities involving temperature and pressure to be factored out of the wavenumber-dependent terms. Although the approximating function is restricted to wavenumbers farther than about a line halfwidth at STP from the line center, a numerical procedure is presented for dealing with the remaining few cases. This approach results in a significant reduction in the number of arithmetic operations from the use of the exact coefficient and generally yields a transmittance with a numerical accuracy of four significant figures or better. An application is made to five Nimbus 6 center-filter frequencies in the 4.3-mum CO(2) band for H(2)O, CO(2), N(2)O, and CO in a 33-level atmosphere with average computational times reduced by a factor of over 9.

Interval estimates for signal processing: Special purpose hardware

Error estimation for the results of signal processing is traditionally based on the assumption that we know the probability distribution of the input signals. In many real-life situations, however, we only know the upper bounds for the signals error, i.e., we only know the intervals of possible values of the input signal. In such situations, we are interested in knowing the interval of possible values of the output. The corresponding computations are often very computationally intensive; in this paper, we describe a special purpose hardware which can drastically speed up the computation of interval estimates for signal processing.

Simulation and performance evaluation of a modularly configurable attached processor

A new architecture for high-performance parallel attached processors is studied in this paper. The unique features are that the attached processor can be configured to match a set of algorithms and its memory controllers can be programmed to fit the access patterns required by the algorithms. As a result, high utilization of the processing logic for given sets of algorithms can be obtained. A simulator with interactive graphic interface is designed to study the performance of the proposed architecture. An example based on matrix multiplication is used for illustration. The simulation results show that a sustained execution rate as high as 95% of the peak speed for matrices with a size of 128/spl times/128 can be achieved in the proposed attached processor architecture. If CMOS technology is chosen to implement the MCAP architecture, a sustained speed of 190 MFLOPS can be obtained for matrix multiplication with four multipliers and four adders.

The Use of Legendre Polynomial Expansions in Solving Optimal Control Problems in the Space l 2

ABSTRACT A method for solving a class of general deterministic optimal control problems is presented here. The method consists of relating the functions involved in the problem to sequences and then converting the problem to one which deals with these sequences alone. The function-sequence correspondence is defined by representing each function by its Legendre polynomial expansion and then relating the function to the sequence of coefficients in this expansion. After this is done, the problem is converted to one in l 2; by determining the equivalents in l 2; of differentiation, inner multiplication, and multiplication. The resulting problem in l 2; is a non-linear programming problem which consists of an infinite array of equations, inequalities, and expressions, each of which involves infinite polynomial expressions. To solve a problem of this type it must be approximated by a finite non-linear programming problem. After this is done various methods can bo used for solving the final problem.

CAD tools for developing modularly configured attached processors

A computer-aided design tool, the SIMARC package, is used for the fast prototyping of modularly configured attached processor (MCAP) architectures. This tool consists of a graphics-user-interface (GUI) architecture editor, a GUI assembler tool, and a GUI simulator tool. This document presents the standard set of connections and component types that form the structure of a MCAP architecture. A new architecture for the conjugate gradient algorithm is introduced.

Approximation of the product error made in calculating atmospheric band transmittances

Abstract The error was modeled for the assumption that the band transmittance at the n+1st level in a layered atmosphere is the nth level band transmittance times the band transmittance through the nth layer. A good approximation of this error was found to be a power of the band transmittance at the nth level, with the exponent being a function of the temperature, pressure, gas densities, and the layer band transmittance of the nth layer. The model was tested using six standard atmospheric profiles at five frequencies. The r.m.s. error for the entire transmittance profiles for all tests was 0.00167.