Revisiting the Fourier transform on the Heisenberg group

A recent theorem of S. Alesker, S. Artstein-Avidan and V. Milman characterises the Fourier transform on R-n as essentially the only transform on the space of tempered distributions which interchanges convolutions and pointwise products. In this note we study the image of the Schwartz space on the Heisenberg group under the Fourier transform and obtain a similar characterisation for the Fourier transform on the Heisenberg group.

End point estimates for Radon transform of radial functions on non-Euclidean spaces

We prove end point estimate for Radon transform of radial functions on affine Grasamannian and real hyperbolic space. We also discuss analogs of these results on the sphere.

Precoding-Based Network Alignment Using Transform Approach for Acyclic Networks With Delay

The algebraic formulation for linear network coding in acyclic networks with the links having integer delay is well known. Based on this formulation, for a given set of connections over an arbitrary acyclic network with integer delay assumed for the links, the output symbols at the sink nodes, at any given time instant, is a F(p)m-linear combination of the input symbols across different generations, where F(p)m denotes the field over which the network operates (p is prime and m is a positive integer). We use finite-field discrete Fourier transform to convert the output symbols at the sink nodes, at any given time instant, into a F(p)m-linear combination of the input symbols generated during the same generation without making use of memory at the intermediate nodes. We call this as transforming the acyclic network with delay into n-instantaneous networks (n is sufficiently large). We show that under certain conditions, there exists a network code satisfying sink demands in the usual (nontransform) approach if and only if there exists a network code satisfying sink demands in the transform approach. When the zero-interference conditions are not satisfied, we propose three precoding-based network alignment (PBNA) schemes for three-source three-destination multiple unicast network with delays (3-S 3-D MUN-D) termed as PBNA using transform approach and time-invariant local encoding coefficients (LECs), PBNA using time-varying LECs, and PBNA using transform approach and block time-varying LECs. We derive sets of necessary and sufficient conditions under which throughputs close to n' + 1/2n' + 1, n'/2n' + 1, and n'/2n' + 1 are achieved for the three source-destination pairs in a 3-S 3-D MUN-D employing PBNA using transform approach and time-invariant LECs, and PBNA using transform approach and block time-varying LECs, where n' is a positive integer. For PBNA using time-varying LECs, we obtain a sufficient condition under which a throughput demand of n(1)/n, n(2)/n, and n(3)/n can be met for the three source-destination pairs in a 3-S 3-D MUN-D, where n(1), n(2), and n(3) are positive integers less than or equal to the positive integer n. This condition is also necessary when n(1) + n(3) = n(1) + n(2) = n where n(1) >= n(2) >= n(3).

MULTI-PITCH TRACKING USING GAUSSIAN MIXTURE MODEL WITH TIME VARYING PARAMETERS AND GRATING COMPRESSION TRANSFORM

Grating Compression Transform (GCT) is a two-dimensional analysis of speech signal which has been shown to be effective in multi-pitch tracking in speech mixtures. Multi-pitch tracking methods using GCT apply Kalman filter framework to obtain pitch tracks which requires training of the filter parameters using true pitch tracks. We propose an unsupervised method for obtaining multiple pitch tracks. In the proposed method, multiple pitch tracks are modeled using time-varying means of a Gaussian mixture model (GMM), referred to as TVGMM. The TVGMM parameters are estimated using multiple pitch values at each frame in a given utterance obtained from different patches of the spectrogram using GCT. We evaluate the performance of the proposed method on all voiced speech mixtures as well as random speech mixtures having well separated and close pitch tracks. TVGMM achieves multi-pitch tracking with 51% and 53% multi-pitch estimates having error <= 20% for random mixtures and all-voiced mixtures respectively. TVGMM also results in lower root mean squared error in pitch track estimation compared to that by Kalman filtering.

ON THE ROLE OF THE HILBERT TRANSFORM IN BOOSTING THE PERFORMANCE OF THE ANNIHILATING FILTER

We consider the problem of parameter estimation from real-valued multi-tone signals. Such problems arise frequently in spectral estimation. More recently, they have gained new importance in finite-rate-of-innovation signal sampling and reconstruction. The annihilating filter is a key tool for parameter estimation in these problems. The standard annihilating filter design has to be modified to result in accurate estimation when dealing with real sinusoids, particularly because the real-valued nature of the sinusoids must be factored into the annihilating filter design. We show that the constraint on the annihilating filter can be relaxed by making use of the Hilbert transform. We refer to this approach as the Hilbert annihilating filter approach. We show that accurate parameter estimation is possible by this approach. In the single-tone case, the mean-square error performance increases by 6 dB for signal-to-noise ratio (SNR) greater than 0 dB. We also present experimental results in the multi-tone case, which show that a significant improvement (about 6 dB) is obtained when the parameters are close to 0 or pi. In the mid-frequency range, the improvement is about 2 to 3 dB.

Multi-transform based spectral element to include first order shear deformation in plates

For obtaining dynamic response of structure to high frequency shock excitation spectral elements have several advantages over conventional methods. At higher frequencies transverse shear and rotary inertia have a predominant role. These are represented by the First order Shear Deformation Theory (FSDT). But not much work is reported on spectral elements with FSDT. This work presents a new spectral element based on the FSDT/Mindlin Plate Theory which is essential for wave propagation analysis of sandwich plates. Multi-transformation method is used to solve the coupled partial differential equations, i.e., Laplace transforms for temporal approximation and wavelet transforms for spatial approximation. The formulation takes into account the axial-flexure and shear coupling. The ability of the element to represent different modes of wave motion is demonstrated. Impact on the derived wave motion characteristics in the absence of the developed spectral element is discussed. The transient response using the formulated element is validated by the results obtained using Finite Element Method (FEM) which needs significant computational effort. Experimental results are provided which confirms the need to having the developed spectral element for the high frequency response of structures. (C) 2015 Elsevier Ltd. All rights reserved.

Voice source characterization using pitch synchronous discrete cosine transform for speaker identification

A characterization of the voice source (VS) signal by the pitch synchronous (PS) discrete cosine transform (DCT) is proposed. With the integrated linear prediction residual (ILPR) as the VS estimate, the PS DCT of the ILPR is evaluated as a feature vector for speaker identification (SID). On TIMIT and YOHO databases, using a Gaussian mixture model (GMM)-based classifier, it performs on par with existing VS-based features. On the NIST 2003 database, fusion with a GMM-based classifier using MFCC features improves the identification accuracy by 12% in absolute terms, proving that the proposed characterization has good promise as a feature for SID studies. (C) 2015 Acoustical Society of America

Demodulation of Narrowband Speech Spectrograms Using the Riesz Transform

We propose a two-dimensional (2-D) multicomponent amplitude-modulation, frequency-modulation (AM-FM) model for a spectrogram patch corresponding to voiced speech, and develop a new demodulation algorithm to effectively separate the AM, which is related to the vocal tract response, and the carrier, which is related to the excitation. The demodulation algorithm is based on the Riesz transform and is developed along the lines of Hilbert-transform-based demodulation for 1-D AM-FM signals. We compare the performance of the Riesz transform technique with that of the sinusoidal demodulation technique on real speech data. Experimental results show that the Riesz-transform-based demodulation technique represents spectrogram patches accurately. The spectrograms reconstructed from the demodulated AM and carrier are inverted and the corresponding speech signal is synthesized. The signal-to-noise ratio (SNR) of the reconstructed speech signal, with respect to clean speech, was found to be 2 to 4 dB higher in case of the Riesz transform technique than the sinusoidal demodulation technique.

Molecular profiling of sepsis in mice using Fourier Transform Infrared Microspectroscopy

Sepsis is a life threatening condition resulting from a high burden of infection. It is a major health care problem and associated with inflammation, organ dysfunction and significant mortality. However, proper understanding and delineating the changes that occur during this complex condition remains a challenge. A comparative study involving intra-peritoneal injection of BALB/c mice with Salmonella Typhimurium (infection), lipopolysaccharide (endotoxic shock) or thioglycollate (sterile peritonitis) was performed. The changes in organs and sera were profiled using immunological assays and Fourier Transform Infrared (FTIR) micro-spectroscopy. There is a rapid rise in inflammatory cytokines accompanied with lowering of temperature, respiratory rate and glucose amounts in mice injected with S. Typhimurium or lipopolysaccharide. FTIR identifies distinct changes in liver and sera: decrease in glycogen and protein/lipid ratio and increase in DNA and cholesteryl esters. These changes were distinct from the pattern observed in mice treated with thioglycollate and the differences in the data obtained between the three models are discussed. The combination of FTIR spectroscopy and other biomarkers will be valuable in monitoring molecular changes during sepsis. GRAPHICS] Intra-peritoneal infection with high dose of Salmonella Typhimurium leads to rapid increase in inflammatory cytokines, e.g. Tnf alpha (A). FTIR analysis of liver (B) and sera (C) identifies several metabolic changes: glycogen, protein/lipid, cholesteryl esters and DNA.

Surface chemical studies of Thiobacillus ferrooxidans with reference to copper tolerance

A strain of Thiobacillus ferrooxidans was adapted to grow at higher concentrations of copper by single step culturing in the presence of 20 g/L (0.314 mol/L) cupric ions added to 9K medium. Exposure to copper results in change in the surface chemistry of the microorganism. The isoelectric point of the adapted strain (pI=4.7) was observed to be at a higher pH than that of the wild unadapted strain(pI=2.0). Compared to the wild strain, the copper adapted strain was found to be more hydrophobic and showed enhanced attachment efficiency to the pyrite mineral. The copper adsorption ability of the adapted strain was also found to be higher than that of the wild strain. Fourier transform infrared spectroscopy of adapted cells suggested that a proteinaceous new cell surface component is synthesized by the adapted strain. Treatment of adapted cells with proteinase-K, resulted in complete loss of tolerance to copper, reduction in copper adsorption and hydrophobicity of the adapted cells. These observations strongly suggest a role played by cell surface modifications of Thiobacillus ferrooxidans in imparting the copper tolerance to the cells and bioleaching of sulphide minerals.

Increasing ionic conductivity and mechanical strength of a plastic electrolyte by inclusion of a polymer

in this contribution we present a soft matter solid electrolyte which was obtained by inclusion of a polymer (polyacrylonitrile, PAN) in LiClO4/LiTFSI-succinonitrile (SN), a semi-solid organic plastic electrolyte. Addition of the polymer resulted in considerable enhancement in ionic conductivity as well as mechanical strength of LiX-SN (X=ClO4, TFSI) plastic electrolyte. Ionic conductivity of 92.5%-[1 M LiClO4-SN]:7.5%-PAN (PAN amount as per SN weight) composite at 25 degrees C recorded a remarkably high value of 7 x 10(-3) Omega(-1) cm(-1), higher by few tens of order in magnitude compared to 1 M LiClO4-SN. Composite conductivity at sub-ambient temperature is also quite high. At -20 degrees C, the ionic conductivity of (100 -x)%-[1 M LiClO4-SN]:x%-PAN composites are in the range 3 x 10(-5)-4.5 x 10(-4) Omega(-1) cm(-1), approximately one to two orders of magnitude higher with respect to 1 M LiClO4-SN electrolyte conductivity. Addition of PAN resulted in an increase of the Young's modulus (Y) from Y -> 0 for LiClO4-SN to a maximum of 0.4MPa for the composites. Microstructural studies based on X-ray diffraction, differential scanning calorimetry and Fourier transform infrared spectroscopy suggest that enhancement in composite ionic conductivity is a combined effect of decrease in crystallinity and enhanced trans conformer concentration. (c) 2008 Elsevier Ltd. All rights reserved.

The effect of surface tension in porous wave maker problems

Using a mixed-type Fourier transform of a general form in the case of water of infinite depth and the method of eigenfunction expansion in the case of water of finite depth, several boundary-value problems involving the propagation and scattering of time harmonic surface water waves by vertical porous walls have been fully investigated, taking into account the effect of surface tension also. Known results are recovered either directly or as particular cases of the general problems under consideration.

Dynamics of a dilute sheared inelastic fluid. I. Hydrodynamic modes and velocity correlation functions

The hydrodynamic modes and the velocity autocorrelation functions for a dilute sheared inelastic fluid are analyzed using an expansion in the parameter epsilon=(1-e)(1/2), where e is the coefficient of restitution. It is shown that the hydrodynamic modes for a sheared inelastic fluid are very different from those for an elastic fluid in the long-wave limit, since energy is not a conserved variable when the wavelength of perturbations is larger than the ``conduction length.'' In an inelastic fluid under shear, there are three coupled modes, the mass and the momenta in the plane of shear, which have a decay rate proportional to k(2/3) in the limit k -> 0, if the wave vector has a component along the flow direction. When the wave vector is aligned along the gradient-vorticity plane, we find that the scaling of the growth rate is similar to that for an elastic fluid. The Fourier transforms of the velocity autocorrelation functions are calculated for a steady shear flow correct to leading order in an expansion in epsilon. The time dependence of the autocorrelation function in the long-time limit is obtained by estimating the integral of the Fourier transform over wave number space. It is found that the autocorrelation functions for the velocity in the flow and gradient directions decay proportional to t(-5/2) in two dimensions and t(-15/4) in three dimensions. In the vorticity direction, the decay of the autocorrelation function is proportional to t(-3) in two dimensions and t(-7/2) in three dimensions.

On the sensitivity of elastic waves due to structural damages:Time-frequency based indexing method

Time-frequency analysis of various simulated and experimental signals due to elastic wave scattering from damage are performed using wavelet transform (WT) and Hilbert-Huang transform (HHT) and their performances are compared in context of quantifying the damages. Spectral finite element method is employed for numerical simulation of wave scattering. An analytical study is carried out to study the effects of higher-order damage parameters on the reflected wave from a damage. Based on this study, error bounds are computed for the signals in the spectral and also on the time-frequency domains. It is shown how such an error bound can provide all estimate of error in the modelling of wave propagation in structure with damage. Measures of damage based on WT and HHT is derived to quantify the damage information hidden in the signal. The aim of this study is to obtain detailed insights into the problem of (1) identifying localised damages (2) dispersion of multifrequency non-stationary signals after they interact with various types of damage and (3) quantifying the damages. Sensitivity analysis of the signal due to scattered wave based on time-frequency representation helps to correlate the variation of damage index measures with respect to the damage parameters like damage size and material degradation factors.

Growing length and time scales in glass-forming liquids

The glass transition, whereby liquids transform into amorphous solids at low temperatures, is a subject of intense research despite decades of investigation. Explaining the enormous increase in relaxation times of a liquid upon supercooling is essential for understanding the glass transition. Although many theories, such as the Adam-Gibbs theory, have sought to relate growing relaxation times to length scales associated with spatial correlations in liquid structure or motion of molecules, the role of length scales in glassy dynamics is not well established. Recent studies of spatially correlated rearrangements of molecules leading to structural relaxation, termed ``spatially heterogeneous dynamics,'' provide fresh impetus in this direction. A powerful approach to extract length scales in critical phenomena is finite-size scaling, wherein a system is studied for sizes traversing the length scales of interest. We perform finite-size scaling for a realistic glass-former, using computer simulations, to evaluate the length scale associated with spatially heterogeneous dynamics, which grows as temperature decreases. However, relaxation times that also grow with decreasing temperature do not exhibit standard finite-size scaling with this length. We show that relaxation times are instead determined, for all studied system sizes and temperatures, by configurational entropy, in accordance with the Adam-Gibbs relation, but in disagreement with theoretical expectations based on spin-glass models that configurational entropy is not relevant at temperatures substantially above the critical temperature of mode-coupling theory. Our results provide new insights into the dynamics of glass-forming liquids and pose serious challenges to existing theoretical descriptions.