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.

Numerical Computation of a Certain Dirichlet Series Attached to Siegel Modular Forms of Degree Two

The Rankin convolution type Dirichlet series D-F,D-G(s) of Siegel modular forms F and G of degree two, which was introduced by Kohnen and the second author, is computed numerically for various F and G. In particular, we prove that the series D-F,D-G(s), which shares the same functional equation and analytic behavior with the spinor L-functions of eigenforms of the same weight are not linear combinations of those. In order to conduct these experiments a numerical method to compute the Petersson scalar products of Jacobi Forms is developed and discussed in detail.

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 ( )

Computation of discrete cosine transform using Clenshaw's recurence formula

Clenshaw’s recurrenee formula is used to derive recursive algorithms for the discrete cosine transform @CT) and the inverse discrete cosine transform (IDCT). The recursive DCT algorithm presented here requires one fewer delay element per coefficient and one fewer multiply operation per coeflident compared with two recently proposed methods. Clenshaw’s recurrence formula provides a unified development for the recursive DCT and IDCT algorithms. The M v e al gorithms apply to arbitrary lengtb algorithms and are appropriate for VLSI implementation.

Unexpected Polymorphism and Unique Particle Morphologies from Monodisperse Droplet Evaporation

The particle sizes, morphologies, and structures are presented for succinic acid particles formed from the evaporation of uniform droplets created with a vibrating orifice aerosol generator. Particle sizes are monodisperse, and solvent choice is found to be the dominant factor in determining the final morphology and structure. The external particle morphologies range from round to cap shaped, while the surface roughness ranges from fairly smooth to extremely rough and pitted. Internally, the particles have significant void space and noticeable crystals. X-ray diffraction confirms that the particles are crystalline. Thus, the morphologies of the particles take on a crystal filled structure that is unique in comparison to previous particles formed through droplet evaporation. The structure of the particles contains β succinic acid; however, the particles formed from water also contain α succinic acid. α Succinic acid has not previously been able to be formed from solution at near atmospheric conditions. The unique morphologies and ability to identify unexpected polymorphs provide for a potential tool to not only enhance particle engineering but also to identify metastable polymorphs.

Dads, Daughters, And Disney: The Historical Trajectory Of Fairy Tale Fathers And Daughters

In my thesis I use a historical approach to close readings of fairy tale texts and movies to study the evolution of fathers, daughters, and marriage within three landmark tales: ¿Cinderella,¿ ¿Sleeping Beauty,¿ and ¿Snow White.¿ Using the works of Giambattista Basile, Charles Perrault, Jacob and Wilhelm Grimm, and Walt Disney and his cohort of animators, I trace the historical trajectory of these three elements, analyzing both the ways they change and develop as history progresses as well as the ways they remain consistent. Through close and comparative readings of primary sources and films, I demonstrate the power structures and familial dynamics evident through the interactions of fathers and daughters. Specifically, I show that through the weakness and ineptitude of fairy tale fathers, fairy tale daughters are able to gain power, authority, and autonomy by using magic and marriage to navigate patriarchal systems. The work I have done is important because it explores how each tale is a product of the story before it and thus that in order for these tales to continue to survive the test of time, we must not only recognize the validity of the academic merit of the Disney stories, but also remember them and others as we forge new paths in the stories we use to teach both children and parents. Specifically, this work is important because it explores the historical trend evident in the evolving relationships between fathers and daughters. This relationship ultimately it reveals the deep underlying need for family within all of us.