Spectrophotometric and potentiometric investigations of copper (II)-Ethanolamine complexes - Part III. diethanolamine (Gaussian analysis of electronic spectra in mono and diethanolamine systems)

Spectrophotometric and potentiometric investigations have been carried out on copper-diethanolamine system. Job plots at 900, 900 and 580 mμ have indicated the formation of CuD++, CuD2++ and CuD3++. The n- pA curves obtained indicate the formation of CuD++, CuD2++, CuD3++, CuDOH+, CuD2OH+ and CuD3OH+. The n- pA curves have been analyzed to obtain the stability constants of these complexes. Absorption curves of pure complexes have been computed by a graphical method. Gaussian analysis of the absorption curves of pure and hydroxy complexes show the presence of a second band, indicating that the structure is that of a distorted octahedron.

Estimation of signals in colored non gaussian noise based on Gaussian Mixture models

Non-Gaussianity of signals/noise often results in significant performance degradation for systems, which are designed using the Gaussian assumption. So non-Gaussian signals/noise require a different modelling and processing approach. In this paper, we discuss a new Bayesian estimation technique for non-Gaussian signals corrupted by colored non Gaussian noise. The method is based on using zero mean finite Gaussian Mixture Models (GMMs) for signal and noise. The estimation is done using an adaptive non-causal nonlinear filtering technique. The method involves deriving an estimator in terms of the GMM parameters, which are in turn estimated using the EM algorithm. The proposed filter is of finite length and offers computational feasibility. The simulations show that the proposed method gives a significant improvement compared to the linear filter for a wide variety of noise conditions, including impulsive noise. We also claim that the estimation of signal using the correlation with past and future samples leads to reduced mean squared error as compared to signal estimation based on past samples only.

Coding for Two-User Gaussian MAC with PSK and PAM Signal Sets

Constellation Constrained (CC) capacity regions of a two-user Gaussian Multiple Access Channel(GMAC) have been recently reported. For such a channel, code pairs based on trellis coded modulation are proposed in this paper with MPSK and M-PAM alphabet pairs, for arbitrary values of M,toachieve sum rates close to the CC sum capacity of the GMAC. In particular, the structure of the sum alphabets of M-PSK and M-PAMmalphabet pairs are exploited to prove that, for certain angles of rotation between the alphabets, Ungerboeck labelling on the trellis of each user maximizes the guaranteed squared Euclidean distance of the sum trellis. Hence, such a labelling scheme can be used systematically,to construct trellis code pairs to achieve sum rates close to the CC sum capacity. More importantly, it is shown for the first time that ML decoding complexity at the destination is significantly reduced when M-PAM alphabet pairs are employed with almost no loss in the sum capacity.

Study of the random vibration of nonlinear systems by the Gaussian closure technique

A technique is developed to study random vibration of nonlinear systems. The method is based on the assumption that the joint probability density function of the response variables and input variables is Gaussian. It is shown that this method is more general than the statistical linearization technique in that it can handle non-Gaussian excitations and amplitude-limited responses. As an example a bilinear hysteretic system under white noise excitation is analyzed. The prediction of various response statistics by this technique is in good agreement with other available results.

Semi-Supervised Classification Using Sparse Gaussian Process Regression

Gaussian Processes (GPs) are promising Bayesian methods for classification and regression problems. They have also been used for semi-supervised learning tasks. In this paper, we propose a new algorithm for solving semi-supervised binary classification problem using sparse GP regression (GPR) models. It is closely related to semi-supervised learning based on support vector regression (SVR) and maximum margin clustering. The proposed algorithm is simple and easy to implement. It gives a sparse solution directly unlike the SVR based algorithm. Also, the hyperparameters are estimated easily without resorting to expensive cross-validation technique. Use of sparse GPR model helps in making the proposed algorithm scalable. Preliminary results on synthetic and real-world data sets demonstrate the efficacy of the new algorithm.

On Two-User Gaussian Multiple Access Channels With Finite Input Constellations

Constellation Constrained (CC) capacity regions of two-user Single-Input Single-Output (SISO) Gaussian Multiple Access Channels (GMAC) are computed for several Non-Orthogonal Multiple Access schemes (NO-MA) and Orthogonal Multiple Access schemes (O-MA). For NO-MA schemes, a metric is proposed to compute the angle(s) of rotation between the input constellations such that the CC capacity regions are maximally enlarged. Further, code pairs based on Trellis Coded Modulation (TCM) are designed with PSK constellation pairs and PAM constellation pairs such that any rate pair within the CC capacity region can be approached. Such a NO-MA scheme which employs CC capacity approaching trellis codes is referred to as Trellis Coded Multiple Access (TCMA). Then, CC capacity regions of O-MA schemes such as Frequency Division Multiple Access (FDMA) and Time Division Multiple Access (TDMA) are also computed and it is shown that, unlike the Gaussian distributed continuous constellations case, the CC capacity regions with FDMA are strictly contained inside the CC capacity regions with TCMA. Hence, for finite constellations, a NO-MA scheme such as TCMA is better than FDMA and TDMA which makes NO-MA schemes worth pursuing in practice for two-user GMAC. Then, the idea of introducing rotations between the input constellations is used to construct Space-Time Block Code (STBC) pairs for two-user Multiple-Input Single-Output (MISO) fading MAC. The proposed STBCs are shown to have reduced Maximum Likelihood (ML) decoding complexity and information-losslessness property. Finally, STBC pairs with reduced sphere decoding complexity are proposed for two-user Multiple-Input Multiple-Output (MIMO) fading MAC.

Coherent-mode decomposition of general anisotropic Gaussian Schell-model beams

We present a complete solution to the problem of coherent-mode decomposition of the most general anisotropic Gaussian Schell-model (AGSM) beams, which constitute a ten-parameter family. Our approach is based on symmetry considerations. Concepts and techniques familiar from the context of quantum mechanics in the two-dimensional plane are used to exploit the Sp(4, R) dynamical symmetry underlying the AGSM problem. We take advantage of the fact that the symplectic group of first-order optical system acts unitarily through the metaplectic operators on the Hilbert space of wave amplitudes over the transverse plane, and, using the Iwasawa decomposition for the metaplectic operator and the classic theorem of Williamson on the normal forms of positive definite symmetric matrices under linear canonical transformations, we demonstrate the unitary equivalence of the AGSM problem to a separable problem earlier studied by Li and Wolf [Opt. Lett. 7, 256 (1982)] and Gori and Guattari [Opt. Commun. 48, 7 (1983)]. This conn ction enables one to write down, almost by inspection, the coherent-mode decomposition of the general AGSM beam. A universal feature of the eigenvalue spectrum of the AGSM family is noted.

The Gaussian Toeplitz matrix

An analytical expression for the LL(T) decomposition for the Gaussian Toeplitz matrix with elements T(ij) = [1/(2-pi)1/2-sigma] exp[-(i - j)2/2-sigma-2] is derived. An exact expression for the determinant and bounds on the eigenvalues follows. An analytical expression for the inverse T-1 is also derived.

Residence time distribution for a class of Gaussian Markov processes

We study the distribution of residence time or equivalently that of "mean magnetization" for a family of Gaussian Markov processes indexed by a positive parameter alpha. The persistence exponent for these processes is simply given by theta=alpha but the residence time distribution is nontrivial. The shape of this distribution undergoes a qualitative change as theta increases, indicating a sharp change in the ergodic properties of the process. We develop two alternate methods to calculate exactly but recursively the moments of the distribution for arbitrary alpha. For some special values of alpha, we obtain closed form expressions of the distribution function. [S1063-651X(99)03306-1].

Subspace Based Speech Enhancement Using Gaussian Mixture Model

Traditional subspace based speech enhancement (SSE)methods use linear minimum mean square error (LMMSE) estimation that is optimal if the Karhunen Loeve transform (KLT) coefficients of speech and noise are Gaussian distributed. In this paper, we investigate the use of Gaussian mixture (GM) density for modeling the non-Gaussian statistics of the clean speech KLT coefficients. Using Gaussian mixture model (GMM), the optimum minimum mean square error (MMSE) estimator is found to be nonlinear and the traditional LMMSE estimator is shown to be a special case. Experimental results show that the proposed method provides better enhancement performance than the traditional subspace based methods.Index Terms: Subspace based speech enhancement, Gaussian mixture density, MMSE estimation.

Low Complexity Wideband LSFQuantization Using GMM of Uncorrelated Gaussian Mixtures

We develop a Gaussian mixture model (GMM) based vector quantization (VQ) method for coding wideband speech line spectrum frequency (LSF) parameters at low complexity. The PDF of LSF source vector is modeled using the Gaussian mixture (GM) density with higher number of uncorrelated Gaussian mixtures and an optimum scalar quantizer (SQ) is designed for each Gaussian mixture. The reduction of quantization complexity is achieved using the relevant subset of available optimum SQs. For an input vector, the subset of quantizers is chosen using nearest neighbor criteria. The developed method is compared with the recent VQ methods and shown to provide high quality rate-distortion (R/D) performance at lower complexity. In addition, the developed method also provides the advantages of bitrate scalability and rate-independent complexity.

Finite Signal-set Capacity of Two-user Gaussian Multiple Access Channel

The capacity region of a two-user Gaussian Multiple Access Channel (GMAC) with complex finite input alphabets and continuous output alphabet is studied. When both the users are equipped with the same code alphabet, it is shown that, rotation of one of the user’s alphabets by an appropriate angle can make the new pair of alphabets not only uniquely decodable, but will result in enlargement of the capacity region. For this set-up, we identify the primary problem to be finding appropriate angle(s) of rotation between the alphabets such that the capacity region is maximally enlarged. It is shown that the angle of rotation which provides maximum enlargement of the capacity region also minimizes the union bound on the probability of error of the sumalphabet and vice-verse. The optimum angle(s) of rotation varies with the SNR. Through simulations, optimal angle(s) of rotation that gives maximum enlargement of the capacity region of GMAC with some well known alphabets such as M-QAM and M-PSK for some M are presented for several values of SNR. It is shown that for large number of points in the alphabets, capacity gains due to rotations progressively reduce. As the number of points N tends to infinity, our results match the results in the literature wherein the capacity region of the Gaussian code alphabet doesn’t change with rotation for any SNR.

Source-channel coding for Gaussian sources over a Gaussian multiple access channel

We consider the problem of distributed joint source-channel coding of correlated Gaussian sources over a Gaussian Multiple Access Channel (MAC). There may be side information at the encoders and/or at the decoder. First we specialize a general result in [16] to obtain sufficient conditions for reliable transmission over a Gaussian MAC. This system does not satisfy the source channel separation. Thus, next we study and compare three joint source channel coding schemes available in literature.