Abstract-This paper presents a method of detecting periodicities in data that exploits a series of projections onto "periodic subspaces." The algorithm finds its own set of nonorthogonal basis elements (based on the data), rather than assuming a fixed predetermined basis as in the Fourier, Gabor, and wavelet transforms. A major strength of the approach is that it is linearin-period rather than linear-in-frequency or linear-in-scale. The algorithm is derived and analyzed, and its output is compared to that of the Fourier transform in a number of examples. One application is the finding and grouping of rhythms in a musical score, another is the separation of periodic waveforms with overlapping spectra, and a third is the finding of patterns in astronomical data. Examples demonstrate both the strengths and weaknesses of the method.

Surface roughening of (100) InP films grown by metalorganic molecular beam epitaxy was observed by scanning force microscopy. The roughening process gives rise to periodic elongated terraces aligned in the [OTl] direction; kinetic control by surface diflfusion activation is indicated by the dependence on group III and V fluxes, and growth temperature. Below a given temperature for each set of growth parameters the surface roughness shows two distinct power law regimes dependent on the film thickness. This result supports growth models using ballistic aggregation and surface diffusion.PACS numbers: 68.55. Bd, 61.16.Ch, 68.35.Bs To achieve abrupt and planar interfaces in semiconductor structures grown by molecular beam epitaxy (MBE) techniques, it is important to examine the growth morphology and correlate it to the growth mechanism. This mechanism usually depends on surface diffusion of atoms to kink sites, which are energetically more favorable to nucleation. The morphology of the epitaxial film is then influenced by deposition rate, which controls the adatom population on the surface, and substrate temperature, which affects the surface diffusion rate of the species. There are thus different forms of kinetic roughening, depending on the relative magnitude of these variables. In particular, at low temperatures, the reduced surface mobility can lead to three-dimensional growth, where islands nucleate on incomplete monolayers. Recently, there has been considerable theoretical interest in surface roughness and growing interfaces. In particular, scaling behavior of the interface width-or surface roughness, W = [<(/z -(A>)^>] *^^, where h is the film thickness-is observed in these models. The scaling is expected to be of the form lPr(L,/)-Ly(//L°/^),where f{x)--x^ for x«Cl and /(jc)^ const for x^l, for a system with size L and time t [1,2]. Different models of growing interfaces have been proposed [2-4] and, although the values for a and p agree for spatial dimension rf = 2 (substrate dimension rf-1), for d>l this is not true [1]. Until now, power law scaling of surface roughness in MBE has been observed experimentally only in the case of iron films grown by this technique [5].Several experiments have been performed to understand the processes controlling semiconductor MBE growth. Scanning tunneling microscopy of submonolayer growth of Si on Si (100) has shown that surface diffusion is highly anisotropic [6,7]. The existence of a limiting thickness beyond which the film is not epitaxial, with a growth-rate-dependent activation energy, was observed by transmission electron microscopy (TEM) of Si MBE on Si(100) [8]. From the theoretical point of view, simu-lations based on the solid-on-solid model [9] showed that the thermally activated nature of surface diffusion determines the limiting thickness and its strong temperature dependence. W was postulated to build gradually with film thickness up to a saturation value, implying a continuous transition from smooth to rough surfaces. A different model, proposed by Kessle...

This paper presents a psychoacoustically based method of data reduction motivated by the desire to analyze the rhythm of musical performances. The resulting information is then analyzed by the "Periodicity Transform" (which is based on a projection onto "periodic subspaces") to locate periodicities in the resulting data. These periodicities represent the rhythm at several levels, including the "pulse", the "measure", and larger structures such as musical "phrases." The implications (and limitations ) of such automated grouping of rhythmic features is discussed. The method is applied to a number of musical examples, its output is compared to that of the Fourier Transform, and both are compared to a more traditional "musical" analysis of the rhythm. Unlike many methods of rhythm analysis, the techniques can be applied directly to the digitized performance (i.e., a soundfile) and do not require a musical score or a MIDI transcription. Several examples are presented that highlight both the strengths and weaknesses of the approach.

A statistical method has been developed for the simulation, optimization and analysis of double-crystal X-ray rocking curves for epitaxial thin films in the Bragg case. This method is based on the approach of Bartels, Hornstra & Lobeek [Acta Co, st. (1986) ratio. The use of these parameters leads to a set of constraints on the fitting process, thus permitting the procedure to be automated. Convergence to a solution is determined by examination of a statistical criterion for goodness of fit; factors that contribute to the net error between the calculated and experimental rocking curves have been identified and have been incorporated into the method. The noise associated with an experimental rocking curve has been found to be very important to the fitting process, and a method is described for explicitly including noise in the procedure presented here. Statistically significant fits to a variety of experimental rocking curves (obtained by fully automated fitting with minimal user interventions) have demonstrated good agreement with experimental data.

Using scanning force microscopy we have studied the growth rate enhancement at the edge of InP and lattice matched InGaAs layers grown into openings on SiO2-masked InP substrates by selective area epitaxy. The growth method was metalorganic molecular beam epitaxy. The growth rates were measured at the center and at the edge of the openings using a scanning force microscope. We have found that the growth rate enhancement can be minimized by using lower metalorganic and hydride flows, and that diffusion is the dominant process at work in the formation of the edge. The migration length of the species depends on the arrival rate of the precursor molecules to the substrate, determined by the absolute group III and V flows, and not on the nominal V/III ratio used for the growth.