# Fast sine/cosine transform for periodic functions with reflection symmetry

## Description

Abstract A modified fast cosine transform (FCT) algorithm is presented featuring the following three properties: (1) the entire calculation is performed using arrays half the size of what would be required using a common fast Fourier transform (FFT); (2) the result of the FCT is identical to that which would be obtained using an FFT and an array double the size; (3) the FCT is its own inverse. The algorithm requires a minor modification to the FCT algorithm in Numerical Recipes by W.H. Press et al., w... Title of program: ROFT/REFT/COFT/CEFT Catalogue Id: ABTX_v1_0 Nature of problem In many physical applications one is interested in obtaining a Fourier transform of a function having a particular reflection symmetry using only half of the grid points, thus saving both computation time and space without any loss of information. Versions of this program held in the CPC repository in Mendeley Data ABTX_v1_0; ROFT/REFT/COFT/CEFT; 10.1016/0010-4655(91)90276-Q This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)