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Learning algorithms based on the Fourier transform attempt to learn functions by approximating the largest coefficients of their Fourier representations. Nearly all previous work in Fourier-based learning has been in the theoretical realm, where properties of the transform have made it possible to prove many interesting learnability results. The real-world usefulness of Fourier-based methods, however, has not been thoroughly explored. This thesis explores methods for the practical application of Fourier-based learning. The primary contribution of this thesis is a new search algorithm for finding the largest coefficients of a function's Fourier representation. Although the search space is exponentially large, empirical results demonstrate that only a small fraction of the space needs to be explored to find the largest coefficients. Furthermore, the algorithm is applicable to a much wider range of learning scenarios than previous approaches. Results of learning real-world problems with algorithms based on this search technique are also presented. The accuracies of the Fourier-based learning methods are not particularly impressive, however, and analysis and empirical results suggest why the Fourier representation may be a poor choice for typical real-world learning problems. Finally, this thesis shows that the search algorithm can be generalized to explore any basis of functions. Furthermore, it can search multiple bases simultaneously. This greatly enhances the learning techniques, and empirical results demonstrate significantly improved accuracy over the Fourier-based approach.

Hammed Hammid Mohammed, universitetsadjunkt vid KTH i Flemingsberg gav uppdragetatt utveckla en mobil kontaktlös andningsbevakare för spädbarn och äldre i form av en mobilapplikationsom använder sig av kameran för att detektera fel i andningen. Denna skullefungera som ett billigare och enklare alternativ till konventionella andningsbevakningsinstrument.Uppgiften utfördes genom att först genomföra en litteraturstudie för att finna olikaalgoritmer och matematiska modeller att implementera och testa. Andra steget var att testade mest lämpade algoritmerna och matematiska modellerna i en datorprototyp gjord i Matlabför att se ifall dessa fungerade som det var tänkt. Tredje steget var att föra över datorprototypensalgoritmer så fullständigt som möjligt till en mobilapplikation.Arbetet resulterade i en algoritm, implementerbar i mobiltelefon, som kan ingå som indikationpå att andning pågår. Detta föregicks av tester av olika parametrar såsom belysning, kontraster,avstånd, position och vinklar mellan mobilkameran och försökspersonen. Testernavisade att stark ljussättning, goda kontraster mellan försöksperson och bakgrund samt rättavstånd och position mellan kamera och försöksperson gav goda resultat.Resultatet i sin helhet gav insikten att användandet av den matematiska algoritmen FFT (FastFourier Transform) kan ingå som indikator på att det är andning som detekteras.

A digital program has been developed to Fourier analyse the data obtained in experiments to study the de Haas-van Alphen effect. A physical account of the origin of this effect is given and the problem of analysing the data is explained. An account is given of the development of the program together with a consideration of the mathematical properties of the Fourier transform. General questions concerning the resolving power and accuracy of this method of analysis are discussed. The program was tested using artificial synthetic data of known analytic form and later applied to the analysis of data from a single crystal of mercury. / Thesis / Master of Science (MSc)

No / In this work, we discuss two new multicarrier modulating kernels that can be adopted for multicarrier signaling. These multicarrier transforms are the fractional Forurier transform (FrFT) and discrete wavelet transforms (DWT). At first, we relate the transforms in terms of mathematical relationships, and then using numerical and simulation comparisons we show their performances in terms of bit error ratio (BER) for Multiple Input Multiple Output (MIMO) applications. Numerical results using BPSK and QPSK support that both can be applied for multicarrier signaling, however, it can be resource effective to drive the DWT as the baseband multicarrier kernel at the expense of the FrFT

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