No description available.

Inaug.-Diss.--Uppsala. / Extra t.p., with thesis note, inserted. Includes bibliographical references (p. [61]-64).

Thesis (M.S.)--University of Wisconsin--Madison, 1967. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--Drexel University, 2007. / Includes abstract and vita. Includes bibliographical references (leaves [111]-116).

[From Introduction, p. 2] The first chapter of this thesis deals with an analysis of F2 critical frequency data first for SANAE and then for eleven other Antarctic and sub-Antarctic stations covering the period 1957 to 1969. This shows certain aspects of the F2 behaviour. Some of the results of this chapter have been reported in a paper by Gledhill and Williams. The two most important mechanisms thought to be responsible for the Antarctic f₀F2 behaviour are incoming corpuscular radiation and horizontal neutral winds. These two mechanisms together with two others (the temperature theory of Torr and Torr and the semi-annual variation of neutral atmospheric density) are discussed in detail in part 2 (Chapters 2 to 4) with a view to discovering which aspects of the f₀F2 behaviour over Antarctica can be explained by each theory. An attempt is made in Part 3 (Chapters 5 and 6) to explain the observed behaviour by solving the continuity equation of the ionosphere for high-latitude stations. Finally, besides the critical frequency, another parameter of importance in explaining the behaviour in the F2 region is the height at which the F2 maximum occurs. This quantity cannot be read directly from an ionogram and it is not an easy quantity to determine. In fact the way in which it is usually obtained is by "scaling" the ionogram in question and converting the virtual heights obtained into real heights. In Part 4 (Chapter 7 and 8) an outline is given of the two computer programs which were written to perform this conversion.

Ph.D. / Harmonic time series are often used to describe the periodic nature of a time series, for example the periodic nature of a variable star’s observed light curve. Statistical methods for determining the number of harmonic components to include in harmonic time series are limited. In this thesis a stepwise bootstrap procedure based on a F-type statistic is suggested. The performance of the stepwise procedure is compared to that of Schwartz’s Bayesian Criterion (SBC) and a procedure based on a statistic described by Siegel (1980). Harmonic series with correlated noise terms and irregularly spaced observations are also considered. Tests to detect changes in harmonic parameters are also derived in this thesis. A cumulative sum statistic to test for constant amplitude is derived. It is shown that testing for constant amplitude is equivalent to testing for constant slope in simple linear regression. We also derive a likelihood ratio statistic to test for constant amplitude. It is shown that the latter likelihood ratio statistic is asymptotically equivalent to the cumulative sum statistic. These statistics are compared to a quadratic form statistic used by Koen (2009). Likelihood ratio tests are also derived for detecting changes in the frequency or phase of harmonic time series. Graphical devices to aid in diagnostic checking are suggested.

We investigate tiling properties of spectra of measures, i.e., sets Λ in R such that {e 2πiλx : λ ∈ Λ} forms an orthogonal basis in L 2 (µ), where µ is some finite Borel measure on R. Such measures include Lebesgue measure on bounded Borel subsets, finite atomic measures and some fractal Hausdorff measures. We show that various classes of such spectra of measures have translational tiling properties. This lead to some surprizing tiling properties for spectra of fractal measures, the existence of complementing sets and spectra for finite sets with the Coven-Meyerowitz property, the existence of complementing Hadamard pairs in the case of Hadamard pairs of size 2,3,4 or 5. In the context of the Fuglede conjecture, we prove that any spectral set is a tile, if the period of the spectrum is 2,3,4 or 5

No description available.

by See Kai-hung. / Title in Chinese: / Includes bibliographical references / Thesis (M.Ph.)--Chinese University of Hong Kong, 1986

This thesis explores the automatic extraction of musical information from live performances - with the intention of using that information to create novel, responsive and adaptive performance tools for musicians. We focus specifically on two forms of musical analysis - harmonic analysis and beat tracking. We present two harmonic analysis algorithms - specifically we present a novel chroma vector analysis technique which we later use as the input for a chord recognition algorithm. We also present a real-time beat tracker, based upon an extension of state of the art non-causal models, that is computationally efficient and capable of strong performance compared to other models. Furthermore, through a modular study of several beat tracking algorithms we attempt to establish methods to improve beat tracking and apply these lessons to our model. Building upon this work, we show that these analyses can be combined to create a beat-synchronous musical representation, with harmonic information segmented at the level of the beat. We present a number of ways of calculating these representations and discuss their relative merits. We proceed by introducing a technique, which we call Performance Following, for recognising repeated patterns in live musical performances. Through examining the real-time beat-synchronous musical representation, this technique makes predictions of future harmonic content in musical performances with no prior knowledge in the form of a score. Finally, we present a number of potential applications for live performances that incorporate the real-time musical analysis techniques outlined previously. The applications presented include audio effects informed by beat tracking, a technique for synchronising video to a live performance, the use of harmonic information to control visual displays and an automatic accompaniment system based upon our performance following technique.