Fast evaluation of squared-Hankel transforms of order-1 by linear digital filtering (subprogram SQJ1)

1982 ◽  
Author(s):  
W.L. Anderson
Keyword(s):  
Digital Filtering ◽  
Fast Evaluation ◽  
Hankel Transforms

Numerical integration of related Hankel transforms of orders 0 and 1 by adaptive digital filtering

Geophysics ◽  
1979 ◽  
Vol 44 (7) ◽  
pp. 1287-1305 ◽  
Author(s):  
Walter L. Anderson
Keyword(s):  
Large Range ◽  
Digital Filtering ◽  
Hankel Transform ◽  
Kernel Functions ◽  
General Nature ◽  
Earth Model ◽  
Hankel Transforms ◽  
Quadrature Methods ◽  
Test Driver ◽  
Different Order

A linear digital filtering algorithm is presented for rapid and accurate numerical evaluation of Hankel transform integrals of orders 0 and 1 containing related complex kernel functions. The kernel for Hankel transforms is defined as the non‐Bessel function factor of the integrand. Related transforms are defined as transforms, of either order 0 or 1, whose kernel functions are related to one another by simple algebraic relationships. Previously saved kernel evaluations are used in the algorithm to obtain rapidly either order transform following an initial convolution operation. Each order filter is designed with identical abscissas over a large range so that an adaptive convolution procedure can be applied to a large class of kernels. Different order Hankel transforms with related kernels are often found in electromagnetic (EM) applications. Because of the general nature of this algorithm, the need to design new filters should not be necessary for most applications. Accuracy of the filters is comparable to that of single‐precision numerical quadrature methods, provided well‐behaved kernels and moderate values of the transform argument are used. Filtering errors of less than 0.005 percent are demonstrated numerically using known analytical Hankel transform pairs. The digital filter accuracy is also illustrated by comparison with other published filters for computing the apparent resistivity for a Schlumberger array over a horizontally layered earth model. The algorithm is written in Fortran IV and is listed in the Appendix along with a test driver program. Detailed comments are included to define sufficiently all calling parameter requirements.

To: “Numerical integration of related Hankel transforms of orders 0 and 1 by adaptive digital filtering” (Walter L. Anderson, GEOPHYSICS, July 1979, p. 1287–1305)

Geophysics ◽  
1979 ◽  
Vol 44 (10) ◽  
pp. 1769-1769
Keyword(s):  
Computer Program ◽  
Numerical Integration ◽  
Digital Filtering ◽  
Hankel Transforms ◽  
Recent Computer

The author of the recent computer program, “Numerical integration of related Hankel transforms of orders 0 and 1 by adaptive digital filtering” (Walter L. Anderson, Geophysics, July 1979 p. 1287–1305) wishes to correct the following errors. On p. 1290, under FUN =, the use of brackets is incorrect as appearing in: FUN = CMPLX[F1(G), 0.0] and FUN = CMPLX[F1(G),F2(G)].The correct Fortran notation should use parentheses as: FUN = CMPLX(F1(G),0.0) and FUN = CMPLX(F1(G),F2(G)). On p. 1291, the DO statement appears incorrectly as: Do 1 I-1, NSAVE Insert code to modify FSAVE in COMMON for a related kernel; for example, if ZF2(G) = G*ZF1(G), use the code; if 1 FSAVE (I) = GSAVE(I)*FSAVE(I) The correct DO statement should be: DO 1 I = 1,NSAVE Insert code to modify FSAVE in COMMON for a related kernel; for example, if ZF2(G( = G*ZF1(G), then use the following code, 1 FSAVE(I) = GSAVE(I)*FSAVE(I)

A Comparative Study of Digital Filtering Techniques in Ultrasound and Carotid Bifurcation Atherosclerosis

2018 ◽  
Vol 1 (1) ◽  
pp. 5-12
Author(s):  
Adriana Milășan ◽  
◽  
Cristian Molder ◽  
Silviu Dumitrescu ◽  
◽  
...  
Keyword(s):  
Comparative Study ◽  
Digital Filtering ◽  
Carotid Bifurcation ◽  
Filtering Techniques

Urban Railway Bridge Fast Evaluation Based on Cloud Computing

2011 ◽  
Vol 71-78 ◽  
pp. 4501-4505
Author(s):  
Ming Chen ◽  
Wan Zhou
Keyword(s):  
Neural Networks ◽  
Cloud Computing ◽  
Model Updating ◽  
Condition Assessment ◽  
Fe Model ◽  
Railway Bridge ◽  
Fast Evaluation ◽  
Railway Bridges ◽  
Computing Model ◽  
Bridge Condition Assessment

Although modern bridge are carefully designed and well constructed, damage may occur in them due to unexpected causes. Currently, many different techniques have been proposed and investigated in bridge condition assessment. However, evaluation efficiency of condition assessment has not been paid much attention by the researchers. A fast evaluation of the urban railway bridge condition based on the cloud computing is presented. In this paper dynamic FE model and Artificial neural networks technique is applied to model updating. The cloud computing model provides the basis for fast analyses. It was found that when applied to the actually railway bridges, the proposed method provided results similar to those obtained by experts, but can improve efficiency of bridge

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