Parallel recusive algorithms for inverse discrete Legendre transform and inverse discrete Laguerre transform

This paper presents parallel recursive algorithms for the computation of the inverse discrete Legendre transform (DPT) and the inverse discrete Laguerre transform (IDLT). These recursive algorithms are derived using Clenshaw's recurrence formula, and they are implemented with a set of parallel digital filters with time-varying coefficients.

Parallel-recusive filter structures for the computation of discrete transforms

A general approach is presented for implementing discrete transforms as a set of first-order or second-order recursive digital filters. Clenshaw's recurrence formulae are used to formulate the second-order filters. The resulting structure is suitable for efficient implementation of discrete transforms in VLSI or FPGA circuits. The general approach is applied to the discrete Legendre transform as an illustration.

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

The performance of the parallel vector implementation of the one- and two-dimensional orthogonal transforms is evaluated. The orthogonal transforms are computed using actual or modified fast Fourier transform (FFT) 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 th 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 (DFT), discrete cosine transform (DCT), discrete sine transform (DST), discrete Hartley transform (DHT), discrete Walsh transform (DWHT), and discrete Hadamard transform (DHDT). A comparison between the DHT and the fast Hartley transform is also included.(34 refs)

Further Evidence for Hemisity Sorting During Career Specialization

Hemisity refers to binary thinking and behavioral style differences between right and left brain-oriented individuals. The inevitability of hemisity became clear when it was discovered by magnetic resonance imaging (MRI) that an anatomical element of the executive system was unilaterally embedded in either the right or the left side of the ventral gyrus of the anterior cingulate cortex in an idiosyncratic manner that was congruent with an individual's inherent hemisity subtype. Based upon the MRI-calibrated hemisity of many individuals, a set of earlier biophysical and questionnaire hemisity assays was calibrated for accuracy and found appropriate for use in the investigation of the hemisity of individuals and groups. It had been reported that a partial sorting of individuals into hemisity right and left brain-oriented subgroups occurred during the process of higher education and professional development. Here, these results were extended by comparison of the hemisity of a putative unsorted population of 1,049 high school upper classmen, with that of 228 university freshmen. These hemisity outcomes were further compared with that of 15 university librarians, here found to be predominantly left brain-oriented, and 91 academically trained musicians, including 47 professional pianists, here found to be mostly right brainers. The results further supported the existence of substantial hemisity selection occurring during the process of higher education and in professional development.