A bandlimited step function for use in discrete periodic extension
dc.contributor.author | Pathmanathan, Sureka | |
dc.date.accessioned | 2013-08-16T18:33:49Z | |
dc.date.available | 2013-08-16T18:33:49Z | |
dc.date.graduationmonth | August | en_US |
dc.date.issued | 2013-08-16 | |
dc.date.published | 2013 | en_US |
dc.description.abstract | A new methodology is introduced for use in discrete periodic extension of non-periodic functions. The methodology is based on a band-limited step function, and utilizes the computational efficiency of FC-Gram (Fourier Continuation based on orthonormal Gram polynomial basis on the extension stage) extension database. The discrete periodic extension is a technique for augmenting a set of uniformly-spaced samples of a smooth function with auxiliary values in an extension region. If a suitable extension is constructed, the interpolating trigonometric polynomial found via an FFT(Fast Fourier Transform) will accurately approximate the original function in its original interval. The discrete periodic extension is a key construction in the FC-Gram algorithm which is successfully implemented in several recent efficient and high-order PDEs solvers. This thesis focuses on a new flexible discrete periodic extension procedure that performs at least as well as the FC-Gram method, but with somewhat simpler implementation and significantly decreased setup time. | en_US |
dc.description.advisor | Nathan Albin | en_US |
dc.description.degree | Master of Science | en_US |
dc.description.department | Department of Mathematics | en_US |
dc.description.level | Masters | en_US |
dc.identifier.uri | http://hdl.handle.net/2097/16281 | |
dc.language.iso | en_US | en_US |
dc.publisher | Kansas State University | en |
dc.subject | Discrete periodic extension | en_US |
dc.subject | Bandlimited step | en_US |
dc.subject | Fourier continuation | en_US |
dc.subject | Three step process | en_US |
dc.subject.umi | Acoustics (0986) | en_US |
dc.subject.umi | Applied Mathematics (0364) | en_US |
dc.subject.umi | Engineering (0537) | en_US |
dc.subject.umi | Mathematics (0405) | en_US |
dc.title | A bandlimited step function for use in discrete periodic extension | en_US |
dc.type | Thesis | en_US |