Fast directional correlation on the sphere with steerable filters

A fast algorithm is developed for the directional correlation of scalar band-limited signals and band-limited steerable filters on the sphere. The asymptotic complexity associated to it through simple quadrature is of order O(L^5), where 2L stands for the square-root of the number of sampling points on the sphere, also setting a band limit L for the signals and filters considered. The filter steerability allows to compute the directional correlation uniquely in terms of direct and inverse scalar spherical harmonics transforms, which drive the overall asymptotic complexity. The separation of variables technique for the scalar spherical harmonics transform produces an O(L^3) algorithm independently of the pixelization. On equi-angular pixelizations, a sampling theorem introduced by Driscoll and Healy implies the exactness of the algorithm. The equi-angular and HEALPix implementations are compared in terms of memory requirements, computation times, and numerical stability. The computation times for the scalar transform, and hence for the directional correlation, of maps of several megapixels on the sphere (L~10^3) are reduced from years to tens of seconds in both implementations on a single standard computer. These generic results for the scale-space signal processing on the sphere are specifically developed in the perspective of the wavelet analysis of the cosmic microwave background (CMB) temperature (T) and polarization (E and B) maps of the WMAP and Planck experiments. As an illustration, we consider the computation of the wavelet coefficients of a simulated temperature map of several megapixels with the second Gaussian derivative wavelet.Comment: Version accepted in APJ. 14 pages, 2 figures, Revtex4 (emulateapj). Changes include (a) a presentation of the algorithm as directly built on blocks of standard spherical harmonics transforms, (b) a comparison between the HEALPix and equi-angular implementation

Efficient performance simulation of class D amplifier output stages

Straightforward simulation of amplifier distortion involves transient simulation of operation on a sine wave input signal, and a subsequent FFT of the output voltage. This approach is very slow on class D amplifiers, since the switching behavior forces simulation time steps that are many orders of magnitude smaller than the duration of one period of an audio sine wave. This work presents a method of simulating the amplifier transfer characteristic using a minimum amount of simulation time, and then deriving THD from the results

Algorithm for the evaluation of reduced Wigner matrices

Algorithms for the fast and exact computation of Wigner matrices are described and their application to a fast and massively parallel 4pi convolution code between a beam and a sky is also presented.Comment: 8 pages, 3 figure

PENERAPAN PEMBELAJARAN KOOPERATIF PDEODE DENGAN BANTUAN SIMULASI KOMPUTER UNTUK MENGURANGI MISKONSEPSI SISWA SMA PADA MATERI LISTRIK DINAMIS

Berdasarkan studi literatur, cukup banyak siswa yang mengalami miskonsepsi. Miskonsepsi merupakan pemahaman suatu konsep yang diyakini secara kuat namun konsep yang diyakini tidak sesuai dengan konsep-konsep ilmiah para ahli. Miskonsepsi apabila tidak diperbaiki akan memahami salah konsep selamanya. Sehingga, miskonsepsi dipandang penting untuk diubah agar siswa memiliki pemahaman konsep yang benar. Untuk mengatasi miskonsepsi diperlukan pembelajaran yang mampu membuat siswa menggali konsep sendiri, dalam hal ini peneliti menggunakan pembelajaran kooperatif PDEODE menggunakan simulasi komputer . Tujuan penelitian ini adalah untuk melihat penerapan pembelajaran PDEODE dengan bantuan simulasi komputer dapat mengurangi miskonsepsi siswa pada materi listrik dinamis. Penelitian ini menggunakan metode quasi experiment jenis Pre test and Post test Group Design dengan sampel 27 siswa pada salah satu SMA Boarding di Kabupaten Bandung Barat secara purposive sample. Hasil penelitian mengungkapkan bahwa pembelajaran kooperatif PDEODE dapat menurunkan miskonsepsi siswa.;---Based on study of some literature, there are students who have misconceptions. The misconception is understanding a concept that is believed to be strong but inconsistent with the concepts of scientis. If it’s not corrected, student wouldn’t be understand on concept forever. Therefore, misconceptions is essential to be changed until they have true concepts. Cooperative learning PDEODE with computer simulations was used to overcome misconceptions required learning that makes the students explore own concept. The purpose of this study is to look at the application of cooperative learning PDEODE with the support of computer simulations can reduce misconceptions students on the dynamic electricity. This study uses quasi experimental test types Pre and Post Test Group Design with a sample of 27 students at one high school in West Bandung. Results of the study revealed that cooperative learning PDEODE can reduce misconceptions students