CPF transforms and convolution



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The CPF transform is faster and potentially more accurate than the FFT in computing 2D convolution. Procedures for computing the CPF and the in verse CPF transform are listed in clear, concise steps, so that users can easily understand the flow of the CPF computation. CPF transforms are shown to be the same as FFT transforms except for a permutation. This similarity enables 2D convolution to be computed using CPF transforms in the same way that the FFT is used. Further, the theoretical proofs involve only simple knowledge of matrix algebra and complex variables. A CPU time comparison of the CPF and FFT program shows that the CPF transform is 10 to 25 percent faster than the FFT in computing convolution (see section 7.2). CPF FORTRAN programs and numerical examples are also included.



Fourier transformations, Convolutions (Mathematics)