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Paper: Radially-symmetric Fourier Transforms
Volume: 61, Astronomical Data Analysis Software and Systems III
Page: 249
Authors: Birkinshaw, Mark
Abstract: A frequent need in data-analysis is to perform convolutions of a model with a response function, and for many purposes these functions are radially-symmetric or may be approximated as being radially symmetric. If this is the case, then the 2-D Fourier transforms and convolution may conveniently be performed using 1-D J(0) Bessel function transforms. The relationship between 2-D Fourier transforms and the 1-D Bessel transform for radially symmetric functions will be discussed, and an implementation of the code will be displayed. The resolution of the Fourier transform that is produced will be discussed, and the accuracy of the transform and the convolution product will be described. This method has been used in modelling the ROSAT PSPC and HRI responses to Beta-model atmospheres of galaxies, where the angular extents of the models are comparable with the FWHMs of the PRFs. Examples of the use of the method in practice will be shown.
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