Nonuniform fast cosine transform and the Chebyshev PSTD algorithm

Fast cosine transform (FCT) has many applications in signal processing and computational electromagnetics. Many efforts have been made in developing the efficient FCT algorithm. However, to use the regular FCT algorithm, the input data have to be uniformly distributed. This is a major limitation of the Chebyshev pseudospectral time domain (PSTD) method. We developed two different fast algorithms for forward nonuniform discrete cosine transform (NUFCT) by using the regular Fourier matrices. These algorithms have the complexity of O(Nlog/sub 2/N) where N is the number of data points. Unlike the uniform fast cosine transform which is identical to its inverse, the inverse nonuniform FCT cannot share the same algorithm. We use the conjugate-gradient fast Fourier transform (CG-FFT) methods for the fast inverse cosine transform (NU-IFCT).