Parallel vector processing of multidimensional orthogonal transforms for digital signal processing applications

The performance of the parallel vector implementation of the 1D and 2D orthogonal transforms is evaluated. The orthogonal transforms are computed using actual or modified fast Fourier transform kernels. The factors considered in comparing the speed-up of these vectorized digital signal processing algorithms are discussed and it is shown that the traditional way of comparing the execution speed of digital signal processing algorithms by the ratios of the number of multiplications and additions is no longer effective for vector implementation; the structure of the algorithm must also be considered as a factor when comparing the execution speed of vectorized digital signal processing algorithms. Simulation results on the Cray X/MP with the following orthogonal transforms are presented: discrete Fourier transform, discrete cosine transform, discrete sine transform, discrete Hartley transform, discrete Walsh transform and discrete Hadamard transform. A comparison between the discrete Hartley transform and the fast Hartley transform is also included