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Description
The concentration factor edge detection method was developed to compute the locations and values of jump discontinuities in a piecewise-analytic function from its first few Fourier series coecients. The method approximates the singular support of a piecewise smooth function using an altered Fourier conjugate partial sum. The accuracy and characteristic features of the resulting jump function approximation depends on these lters, known as concentration factors. Recent research showed that that these concentration factors could be designed using aexible iterative framework, improving upon the overall accuracy and robustness of the method, especially in the case where some Fourier data are untrustworthy or altogether missing. Hypothesis testing methods were used to determine how well the original concentration factor method could locate edges using noisy Fourier data. This thesis combines the iterative design aspect of concentration factor design and hypothesis testing by presenting a new algorithm that incorporates multiple concentration factors into one statistical test, which proves more ective at determining jump discontinuities than the previous HT methods. This thesis also examines how the quantity and location of Fourier data act the accuracy of HT methods. Numerical examples are provided.
ContributorsLubold, Shane Michael (Author) / Gelb, Anne (Thesis director) / Cochran, Doug (Committee member) / Viswanathan, Aditya (Committee member) / Economics Program in CLAS (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
The purpose of this senior thesis is to explore the abstract ideas that give rise to the well-known Fourier series and transforms. More specifically, finite group representations are used to study the structure of Hilbert spaces to determine under what conditions an element of the space can be expanded as a sum. The Peter-Weyl theorem is the result that shows why integrable functions can be expressed in terms of trigonometric functions. Although some theorems will not be proved, the results that can be derived from them will be briefly discussed. For instance, the Pontryagin Duality theorem states that there is a canonical isomorphism between a group and the second dual of the group, and it can be used to prove $Plancherel$ theorem which essentially says that the Fourier transform is itself a unitary isomorphism.
ContributorsReyna De la Torre, Luis E (Author) / Kaliszewski, Steven (Thesis director) / Rainone, Timothy (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Department of Physics (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
ContributorsEvans, Bartlett R. (Conductor) / Schildkret, David (Conductor) / Glenn, Erica (Conductor) / Concert Choir (Performer) / Chamber Singers (Performer) / ASU Library. Music Library (Publisher)
Created2018-03-16
ContributorsOwen, Ken (Conductor) / McDevitt, Mandy L. M. (Performer) / Larson, Brook (Conductor) / Wang, Lin-Yu (Performer) / Jacobs, Todd (Performer) / Morehouse, Daniel (Performer) / Magers, Kristen (Performer) / DeGrow, Gary (Performer) / DeGrow, Richard (Performer) / Women's Chorus (Performer) / Sun Devil Singers (Performer) / ASU Library. Music Library (Publisher)
Created2004-03-24
ContributorsMetz, John (Performer) / Sowers, Richard (Performer) / Collegium Musicum (Performer) / ASU Library. Music Library (Publisher)
Created1983-01-29
ContributorsEvans, Bartlett R. (Conductor) / Glenn, Erica (Conductor) / Steiner, Kieran (Conductor) / Thompson, Jason D. (Conductor) / Arizona Statesmen (Performer) / Women's Chorus (Performer) / Concert Choir (Performer) / Gospel Choir (Conductor) / ASU Library. Music Library (Publisher)
Created2019-03-15
ContributorsKillian, George W. (Performer) / Killian, Joni (Performer) / Vocal Jazz Ensemble (Performer) / ASU Library. Music Library (Publisher)
Created1992-11-05
ContributorsButler, Robb (Conductor) / McCreary, Kimilee (Conductor) / Bakko, Nicki L. (Conductor) / Schreuder, Joel (Conductor) / Larson, Matthew (Performer) / Ortman, Mory (Performer) / Graduate Chorale I (Performer) / Graduate Chorale II (Performer) / ASU Library. Music Library (Publisher)
Created1999-12-02
ContributorsGarrett, Jennifer (Conductor) / FitzPatrick, Carole (Performer) / Aspnes, Lynne (Performer) / Campbell, Andrew (Pianist) (Performer) / Ryan, Russell (Performer) / Rockmaker, Jody (Performer) / Kocour, Mike (Performer) / McLin, Katherine (Performer) / Larson, Brook Carter (Conductor) / Women's Chorus (Performer) / Men's Chorus (Performer) / ASU Library. Music Library (Publisher)
Created2009-05-04
ContributorsLarson, Brook Carter (Conductor) / Gentry, Gregory R. (Conductor) / Garrison, Ryan D. (Conductor) / Schildkret, David (Conductor) / Men's Chorus (Performer) / Symphonic Chorale (Performer) / Women's Chorus (Performer) / Chamber Singers (Performer) / Choral Union (Performer) / ASU Library. Music Library (Publisher)
Created2007-12-03