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.

Efficient computation of discrete polynomial transforms

This letter presents a new recursive method for computing discrete polynomial transforms. The method is shown for forward and inverse transforms of the Hermite, binomial, and Laguerre transforms. The recursive flow diagrams require only 2 additions, 2( +1) memory units, and +1multipliers for the +1-point Hermite and binomial transforms. The recursive flow diagram for the +1-point Laguerre transform requires 2 additions, 2( +1) memory units, and 2( +1) multipliers. The transform computation time for all of these transforms is ( )

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)

New Results Concerning Probability Distributions with Increasing Generalized Failure Rates

The generalized failure rate of a continuous random variable has demonstrable importance in operations management. If the valuation distribution of a product has an increasing generalized failure rate (that is, the distribution is IGFR), then the associated revenue function is unimodal, and when the generalized failure rate is strictly increasing, the global maximum is uniquely specified. The assumption that the distribution is IGFR is thus useful and frequently held in recent pricing, revenue, and supply chain management literature. This note contributes to the IGFR literature in several ways. First, it investigates the prevalence of the IGFR property for the left and right truncations of valuation distributions. Second, we extend the IGFR notion to discrete distributions and contrast it with the continuous distribution case. The note also addresses two errors in the previous IGFR literature. Finally, for future reference, we analyze all common (continuous and discrete) distributions for the prevalence of the IGFR property, and derive and tabulate their generalized failure rates.

Synchrotron X-ray interlaced microbeams suppress paroxysmal oscillations in neuronal networks initiating generalized epilepsy

Radiotherapy has shown some efficacy for epilepsies but the insufficient confinement of the radiation dose to the pathological target reduces its indications. Synchrotron-generated X-rays overcome this limitation and allow the delivery of focalized radiation doses to discrete brain volumes via interlaced arrays of microbeams (IntMRT). Here, we used IntMRT to target brain structures involved in seizure generation in a rat model of absence epilepsy (GAERS). We addressed the issue of whether and how synchrotron radiotherapeutic treatment suppresses epileptic activities in neuronal networks. IntMRT was used to target the somatosensory cortex (S1Cx), a region involved in seizure generation in the GAERS. The antiepileptic mechanisms were investigated by recording multisite local-field potentials and the intracellular activity of irradiated S1Cx pyramidal neurons in vivo. MRI and histopathological images displayed precise and sharp dose deposition and revealed no impairment of surrounding tissues. Local-field potentials from behaving animals demonstrated a quasi-total abolition of epileptiform activities within the target. The irradiated S1Cx was unable to initiate seizures, whereas neighboring non-irradiated cortical and thalamic regions could still produce pathological oscillations. In vivo intracellular recordings showed that irradiated pyramidal neurons were strongly hyperpolarized and displayed a decreased excitability and a reduction of spontaneous synaptic activities. These functional alterations explain the suppression of large-scale synchronization within irradiated cortical networks. Our work provides the first post-irradiation electrophysiological recordings of individual neurons. Altogether, our data are a critical step towards understanding how X-ray radiation impacts neuronal physiology and epileptogenic processes.