On the Transform Method of Solution of an External Crack Problem

The breakdown of the usual method of Fourier transforms in the problem of an external line crack in a thin infinite elastic plate is discovered and the correct solution of this problem is derived using the concept of a generalised Fourier transform of a type discussed first by Golecki [1] in connection with Flamant's problem.

Evaluation of two-dimensional quantizers for Fourier transform binary holograms

Quantization formats of four digital holographic codes (Lohmann,Lee, Burckhardt and Hsueh-Sawchuk) are evaluated. A quantitative assessment is made from errors in both the Fourier transform and image domains. In general, small errors in the Fourier amplitude or phase alone do not guarantee high image fidelity. From quantization considerations, the Lee hologram is shown to be the best choice for randomly phase coded objects. When phase coding is not feasible, the Lohmann hologram is preferable as it is easier to plot.

Analysis-By-Synthesis Based Switched Transform Domain Split Vq Using Gaussian Mixture Model

Using analysis-by-synthesis (AbS) approach, we develop a soft decision based switched vector quantization (VQ) method for high quality and low complexity coding of wideband speech line spectral frequency (LSF) parameters. For each switching region, a low complexity transform domain split VQ (TrSVQ) is designed. The overall rate-distortion (R/D) performance optimality of new switched quantizer is addressed in the Gaussian mixture model (GMM) based parametric framework. In the AbS approach, the reduction of quantization complexity is achieved through the use of nearest neighbor (NN) TrSVQs and splitting the transform domain vector into higher number of subvectors. Compared to the current LSF quantization methods, the new method is shown to provide competitive or better trade-off between R/D performance and complexity.

A novel method for the age estimation of Saddletail snapper (Lutjanus malabaricus) using Fourier Transform-near infrared (FT-NIR) spectroscopy

Near infrared (NIR) spectroscopy was investigated as a potential rapid method of estimating fish age from whole otoliths of Saddletail snapper (Lutjanus malabaricus). Whole otoliths from 209 Saddletail snapper were extracted and the NIR spectral characteristics were acquired over a spectral range of 800–2780 nm. Partial least-squares models (PLS) were developed from the diffuse reflectance spectra and reference-validated age estimates (based on traditional sectioned otolith increments) to predict age for independent otolith samples. Predictive models developed for a specific season and geographical location performed poorly against a different season and geographical location. However, overall PLS regression statistics for predicting a combined population incorporating both geographic location and season variables were: coefficient of determination (R2) = 0.94, root mean square error of prediction (RMSEP) = 1.54 for age estimation, indicating that Saddletail age could be predicted within 1.5 increment counts. This level of accuracy suggests the method warrants further development for Saddletail snapper and may have potential for other fish species. A rapid method of fish age estimation could have the potential to reduce greatly both costs of time and materials in the assessment and management of commercial fisheries.

Adaptive frequency scaled wavelet packet decomposition for frog call classification

Environmental changes have put great pressure on biological systems leading to the rapid decline of biodiversity. To monitor this change and protect biodiversity, animal vocalizations have been widely explored by the aid of deploying acoustic sensors in the field. Consequently, large volumes of acoustic data are collected. However, traditional manual methods that require ecologists to physically visit sites to collect biodiversity data are both costly and time consuming. Therefore it is essential to develop new semi-automated and automated methods to identify species in automated audio recordings. In this study, a novel feature extraction method based on wavelet packet decomposition is proposed for frog call classification. After syllable segmentation, the advertisement call of each frog syllable is represented by a spectral peak track, from which track duration, dominant frequency and oscillation rate are calculated. Then, a k-means clustering algorithm is applied to the dominant frequency, and the centroids of clustering results are used to generate the frequency scale for wavelet packet decomposition (WPD). Next, a new feature set named adaptive frequency scaled wavelet packet decomposition sub-band cepstral coefficients is extracted by performing WPD on the windowed frog calls. Furthermore, the statistics of all feature vectors over each windowed signal are calculated for producing the final feature set. Finally, two well-known classifiers, a k-nearest neighbour classifier and a support vector machine classifier, are used for classification. In our experiments, we use two different datasets from Queensland, Australia (18 frog species from commercial recordings and field recordings of 8 frog species from James Cook University recordings). The weighted classification accuracy with our proposed method is 99.5% and 97.4% for 18 frog species and 8 frog species respectively, which outperforms all other comparable methods.

Inverse Problem for Fractional Brownian Motion with Discrete Data

The problem of recovering information from measurement data has already been studied for a long time. In the beginning, the methods were mostly empirical, but already towards the end of the sixties Backus and Gilbert started the development of mathematical methods for the interpretation of geophysical data. The problem of recovering information about a physical phenomenon from measurement data is an inverse problem. Throughout this work, the statistical inversion method is used to obtain a solution. Assuming that the measurement vector is a realization of fractional Brownian motion, the goal is to retrieve the amplitude and the Hurst parameter. We prove that under some conditions, the solution of the discretized problem coincides with the solution of the corresponding continuous problem as the number of observations tends to infinity. The measurement data is usually noisy, and we assume the data to be the sum of two vectors: the trend and the noise. Both vectors are supposed to be realizations of fractional Brownian motions, and the goal is to retrieve their parameters using the statistical inversion method. We prove a partial uniqueness of the solution. Moreover, with the support of numerical simulations, we show that in certain cases the solution is reliable and the reconstruction of the trend vector is quite accurate.

R U there yet? using virtual classrooms to transform teaching practice

Access to quality higher education is challenging for many Western Australians that live outside the metropolitan area. In 2010, the School of Education moved to flexible delivery of a fully online Bachelor of Education degree for their non -metropolitan students. The new model of delivery allows access for students from any location provided they have a computer and an internet connection. A number of academic staff had previously used an asynchronous environment to deliver learning modules housed within a learning management system (LMS) but had not used synchronous software with their students. To enhance the learning environment and to provide high quality learning experiences to students learning at a distance, the adoption of synchronous software (Elluminate Live) was introduced. This software is a real-time virtual classroom environment that allows for communication through Voice over Internet Protocol (VoIP) and videoconferencing, along with a large number of collaboration tools to engage learners. This research paper reports on the integration of a live e-learning solution into the current LMS environment. Qualitative data were collected from academic staff through informal interviews and participant observation. The findings discuss (i) perceived level of support; (ii) identification of strategies used to create an effective online teacher presence; (iii) the perceived impact on the students' learning outcomes; and (iv) guidelines for professional development to enhance pedagogy within the live e-learning environment.

Fourier transform of the collagen triple-helical structure and its significance

The Fourier transforms of the collagen molecular structure have been calculated taking into consideration various side chain atoms, as well as the presence of bound water molecules. There is no significant change in the calculated intensity distribution on including the side chain atoms of non-imino-acid residues. Taking into account the presence of about two bound water molecules per tripeptide unit, the agreement with the observed x-ray pattern is slightly improved. Fourier transforms have also been calculated for the detailed molecular geometries proposed from other laboratories. It is found that there are no major differences between them, as compared to our structure, either in the positions of peak intensity or in the intensity distribution. Hence it is not possible to judge the relative merits of the various molecular geometries for the collagen triple helix from a comparison of the calculated transforms with the meagre data available from its x-ray fibre pattern. It is also concluded that the collagen molecular structure should be regarded as a somewhat flexible chain structure, capable of adapting itself to the requirements of the different side groups which occur in each local region.

Two Stage Transform Vector Quantization of LSFs for Wideband Speech Coding

We investigate the use of a two stage transform vector quantizer (TSTVQ) for coding of line spectral frequency (LSF) parameters in wideband speech coding. The first stage quantizer of TSTVQ, provides better matching of source distribution and the second stage quantizer provides additional coding gain through using an individual cluster specific decorrelating transform and variance normalization. Further coding gain is shown to be achieved by exploiting the slow time-varying nature of speech spectra and thus using inter-frame cluster continuity (ICC) property in the first stage of TSTVQ method. The proposed method saves 3-4 bits and reduces the computational complexity by 58-66%, compared to the traditional split vector quantizer (SVQ), but at the expense of 1.5-2.5 times of memory.

New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation

In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations.

Application of Laplace transform technique to the solution of certain third-order non-linear systems

A number of papers have appeared on the application of operational methods and in particular the Laplace transform to problems concerning non-linear systems of one kind or other. This, however, has met with only partial success in solving a class of non-linear problems as each approach has some limitations and drawbacks. In this study the approach of Baycura has been extended to certain third-order non-linear systems subjected to non-periodic excitations, as this approximate method combines the advantages of engineering accuracy with ease of application to such problems. Under non-periodic excitations the method provides a procedure for estimating quickly the maximum response amplitude, which is important from the point of view of a designer. Limitations of such a procedure are brought out and the method is illustrated by an example taken from a physical situation.

Scattering theory and the discrete linear optimal control problem

This paper deals with the interpretation of the discrete-time optimal control problem as a scattering process in a discrete medium. We treat the discrete optimal linear regulator, constrained end-point and servo and tracking problems, providing a unified approach to these problems. This approach results in an easy derivation of the desired results as well as several new ones.

Contribution from unresolved discrete sources to the extragalactic gamma-ray background (EGRB)

The origin of the extragalactic gamma-ray background (EGRB) is still an open question, even nearly forty years after its discovery. The emission could originate either from truly diffuse processes or from unresolved point sources. Although the majority of the 271 point sources detected by EGRET (Energetic Gamma Ray Experiment Telescope) are unidentified, of the identified sources, blazars are the dominant candidates. Therefore, unresolved blazars may be considered the main contributor to the EGRB, and many studies have been carried out to understand their distribution, evolution and contribution to the EGRB. Considering that gamma-ray emission comes mostly from jets of blazars and that the jet emission decreases rapidly with increasing jet to line-of-sight angle, it is not surprising that EGRET was not able to detect many large inclination angle active galactic nuclei (AGNs). Though Fermi could only detect a few large inclination angle AGNs during the first three months of its survey, it is expected to detect many such sources in the near future. Since non-blazar AGNs are expected to have higher density as compared to blazars, these could also contribute significantly to the EGRB. In this paper, we discuss contributions from unresolved discrete sources including normal galaxies, starburst galaxies, blazars and off-axis AGNs to the EGRB.

A Joint Source-Channel Coding Scheme for Transmission of Correlated Discrete Sources over a Gaussian Multiple Access Channel

We consider the problem of transmission of correlated discrete alphabet sources over a Gaussian Multiple Access Channel (GMAC). A distributed bit-to-Gaussian mapping is proposed which yields jointly Gaussian codewords. This can guarantee lossless transmission or lossy transmission with given distortions, if possible. The technique can be extended to the system with side information at the encoders and decoder.

Holomorphic Sobolev spaces, Hermite and special Hermite semigroups and a Paley-Wiener theorem for the windowed Fourier transform

The images of Hermite and Laguerre-Sobolev spaces under the Hermite and special Hermite semigroups (respectively) are characterized. These are used to characterize the image of Schwartz class of rapidly decreasing functions f on R-n and C-n under these semigroups. The image of the space of tempered distributions is also considered and a Paley-Wiener theorem for the windowed (short-time) Fourier transform is proved.