Connecting spatial and frequency domains for the quaternion Fourier transform

The quaternion Fourier transform (qFT) is an important tool in multi-dimensional data analysis, in particular for the study of color images. An important problem when applying the qFT is the mismatch between the spatial and frequency domains: the convolution of two quaternion signals does not map to the pointwise product of their qFT images. The recently defined ‘Mustard’ convolution behaves nicely in the frequency domain, but complicates the corresponding spatial domain analysis. The present paper analyses in detail the correspondence between classical convolution and the new Mustard convolution. In particular, an expression is derived that allows one to write classical convolution as a finite linear combination of suitable Mustard convolutions. This result is expected to play a major role in the further development of quaternion image processing, as it yields a formula for the qFT spectrum of the classical convolution

A silent speech system based on permanent magnet articulography and direct synthesis

In this paper we present a silent speech interface (SSI) system aimed at restoring speech communication for individuals who have lost their voice due to laryngectomy or diseases affecting the vocal folds. In the proposed system, articulatory data captured from the lips and tongue using permanent magnet articulography (PMA) are converted into audible speech using a speaker-dependent transformation learned from simultaneous recordings of PMA and audio signals acquired before laryngectomy. The transformation is represented using a mixture of factor analysers, which is a generative model that allows us to efficiently model non-linear behaviour and perform dimensionality reduction at the same time. The learned transformation is then deployed during normal usage of the SSI to restore the acoustic speech signal associated with the captured PMA data. The proposed system is evaluated using objective quality measures and listening tests on two databases containing PMA and audio recordings for normal speakers. Results show that it is possible to reconstruct speech from articulator movements captured by an unobtrusive technique without an intermediate recognition step. The SSI is capable of producing speech of sufficient intelligibility and naturalness that the speaker is clearly identifiable, but problems remain in scaling up the process to function consistently for phonetically rich vocabularies

Integrating user-centred design in the development of a silent speech interface based on permanent magnetic articulography

Abstract: A new wearable silent speech interface (SSI) based on Permanent Magnetic Articulography (PMA) was developed with the involvement of end users in the design process. Hence, desirable features such as appearance, port-ability, ease of use and light weight were integrated into the prototype. The aim of this paper is to address the challenges faced and the design considerations addressed during the development. Evaluation on both hardware and speech recognition performances are presented here. The new prototype shows a com-parable performance with its predecessor in terms of speech recognition accuracy (i.e. ~95% of word accuracy and ~75% of sequence accuracy), but significantly improved appearance, portability and hardware features in terms of min-iaturization and cost

Fundamental representations and algebraic properties of biquaternions or complexified quaternions

The fundamental properties of biquaternions (complexified quaternions) are presented including several different representations, some of them new, and definitions of fundamental operations such as the scalar and vector parts, conjugates, semi-norms, polar forms, and inner and outer products. The notation is consistent throughout, even between representations, providing a clear account of the many ways in which the component parts of a biquaternion may be manipulated algebraically

Ultrafast pump-probe dynamics in ZnSe-based semiconductor quantum-wells

Pump-probe experiments are used as a controllable way to investigate the properties of photoexcited semiconductors, in particular, the absorption saturation. We present an experiment-theory comparison for ZnSe quantum wells, investigating the energy renormalization and bleaching of the excitonic resonances. Experiments were performed with spin-selective excitation and above-bandgap pumping. The model, based on the semiconductor Bloch equations in the screened Hartree-Fock approximation, takes various scattering processes into account phenomenologically. Comparing numerical results with available experimental data, we explain the experimental results and find that the electron spin-flip occurs on a time scale of 30 ps.Comment: 10 pages, 9 figures. Key words: nonlinear and ultrafast optics, modeling of femtosecond pump-probe experiments, electron spin-flip tim

Some results on the lattice parameters of quaternionic Gabor frames

Gabor frames play a vital role not only modern harmonic analysis but also in several fields of applied mathematics, for instances, detection of chirps, or image processing. In this work we present a non-trivial generalization of Gabor frames to the quaternionic case and give new density results. The key tool is the two-sided windowed quaternionic Fourier transform (WQFT). As in the complex case, we want to write the WQFT as an inner product between a quaternion-valued signal and shifts and modulates of a real-valued window function. We demonstrate a Heisenberg uncertainty principle and for the results regarding the density, we employ the quaternionic Zak transform to obtain necessary and sufficient conditions to ensure that a quaternionic Gabor system is a quaternionic Gabor frame. We conclude with a proof that the Gabor conjecture do not hold true in the quaternionic case

Influence of Coulomb and Phonon Interaction on the Exciton Formation Dynamics in Semiconductor Heterostructures

A microscopic theory is developed to analyze the dynamics of exciton formation out of incoherent carriers in semiconductor heterostructures. The carrier Coulomb and phonon interaction is included consistently. A cluster expansion method is used to systematically truncate the hierarchy problem. By including all correlations up to the four-point (i.e. two-particle) level, the fundamental fermionic substructure of excitons is fully included. The analysis shows that the exciton formation is an intricate process where Coulomb correlations rapidly build up on a picosecond time scale while phonon dynamics leads to true exciton formation on a slow nanosecond time scale.Comment: 18 pages, 7 figure

Quantum Maxwell-Bloch equations for spatially inhomogeneous semiconductor lasers

We present quantum Maxwell-Bloch equations (QMBE) for spatially inhomogeneous semiconductor laser devices. The QMBE are derived from fully quantum mechanical operator dynamics describing the interaction of the light field with the quantum states of the electrons and the holes near the band gap. By taking into account field-field correlations and field-dipole correlations, the QMBE include quantum noise effects which cause spontaneous emission and amplified spontaneous emission. In particular, the source of spontaneous emission is obtained by factorizing the dipole-dipole correlations into a product of electron and hole densities. The QMBE are formulated for general devices, for edge emitting lasers and for vertical cavity surface emitting lasers, providing a starting point for the detailed analysis of spatial coherence in the near field and far field patterns of such laser diodes. Analytical expressions are given for the spectra of gain and spontaneous emission described by the QMBE. These results are applied to the case of a broad area laser, for which the frequency and carrier density dependent spontaneous emission factor beta and the evolution of the far field pattern near threshold are derived.Comment: 22 pages RevTex and 7 figures, submitted to Phys.Rev.A, revisions in abstract and in the discussion of temporal coherenc