A Wavelet based Teager Energy Operator for Spike Detection in Microelectrode Array Recordings

Spike detection in neural recordings is the initial step in the creation of brain machine interfaces. The Teager energy operator (TEO) treats a spike as an increase in the `local' energy and detects this increase. The performance of TEO in detecting action potential spikes suffers due to its sensitivity to the frequency of spikes in the presence of noise which is present in microelectrode array (MEA) recordings. The multiresolution TEO (mTEO) method overcomes this shortcoming of the TEO by tuning the parameter k to an optimal value m so as to match to frequency of the spike. In this paper, we present an algorithm for the mTEO using the multiresolution structure of wavelets along with inbuilt lowpass filtering of the subband signals. The algorithm is efficient and can be implemented for real-time processing of neural signals for spike detection. The performance of the algorithm is tested on a simulated neural signal with 10 spike templates obtained from [14]. The background noise is modeled as a colored Gaussian random process. Using the noise standard deviation and autocorrelation functions obtained from recorded data, background noise was simulated by an autoregressive (AR(5)) filter. The simulations show a spike detection accuracy of 90%and above with less than 5% false positives at an SNR of 2.35 dB as compared to 80% accuracy and 10% false positives reported [6] on simulated neural signals.

Deformation and failure of a film/substrate system subjected to spherical indentation: Part 1. Experimental validation of stresses and strains derived using Hankel transform technique in an elastic film/substrate system

Our concern here is to rationalize experimental observations of failure modes brought about by indentation of hard thin ceramic films deposited on metallic substrates. By undertaking this exercise, we would like to evolve an analytical framework that can be used for designs of coatings. In Part I of the paper we develop an algorithm and test it for a model system. Using this analytical framework we address the issue of failure of columnar TiN films in Part II [J. Mater. Res. 21, 783 (2006)] of the paper. In this part, we used a previously derived Hankel transform procedure to derive stress and strain in a birefringent polymer film glued to a strong substrate and subjected to spherical indentation. We measure surface radial strains using strain gauges and bulk film stresses using photo elastic technique (stress freezing). For a boundary condition based on Hertzian traction with no film interface constraint and assuming the substrate constraint to be a function of the imposed strain, the theory describes the stress distributions well. The variation in peak stresses also demonstrates the usefulness of depositing even a soft film to protect an underlying substrate.

Wave propagation analysis in carbon nanotube embedded composite using wavelet based spectral finite elements

In this paper, elastic wave propagation is studied in a nanocomposite reinforced with multiwall carbon nanotubes (CNTs). Analysis is performed on a representative volume element of square cross section. The frequency content of the exciting signal is at the terahertz level. Here, the composite is modeled as a higher order shear deformable beam using layerwise theory, to account for partial shear stress transfer between the CNTs and the matrix. The walls of the multiwall CNTs are considered to be connected throughout their length by distributed springs, whose stiffness is governed by the van der Waals force acting between the walls of nanotubes. The analyses in both the frequency and time domains are done using the wavelet-based spectral finite element method (WSFEM). The method uses the Daubechies wavelet basis approximation in time to reduce the governing PDE to a set of ODEs. These transformed ODEs are solved using a finite element (FE) technique by deriving an exact interpolating function in the transformed domain to obtain the exact dynamic stiffness matrix. Numerical analyses are performed to study the spectrum and dispersion relations for different matrix materials and also for different beam models. The effects of partial shear stress transfer between CNTs and matrix on the frequency response function (FRF) and the time response due to broadband impulse loading are investigated for different matrix materials. The simultaneous existence of four coupled propagating modes in a double-walled CNT-composite is also captured using modulated sinusoidal excitation.

Segal-Bargmann transform and Paley-Wiener theorems on M(2)

We study the Segal-Bargmann transform on M(2). The range of this transform is characterized as a weighted Bergman space. In a similar fashion Poisson integrals are investigated. Using a Gutzmer's type formula we characterize the range as a class of functions extending holomorphically to an appropriate domain in the complexification of M(2). We also prove a Paley-Wiener theorem for the inverse Fourier transform.

Interior Medial Axis Transform computation of 3D objects bound by free-form surfaces

This paper presents an algorithm for generating the Interior Medial Axis Transform (iMAT) of 3D objects with free-form boundaries. The algorithm proposed uses the exact representation of the part and generates an approximate rational spline description of the iMAT. The algorithm generates the iMAT by a tracing technique that marches along the object's boundary. The level of approximation is controlled by the choice of the step size in the tracing procedure. Criteria based on distance and local curvature of boundary entities are used to identify the junction points and the search for these junction points is done in an efficient way. The algorithm works for multiply-connected objects as well. Results of the implementation are provided. (C) 2010 Elsevier Ltd. All rights reserved.

Segal-Bargmann Transform and Paley-Wiener Theorems on Motion Groups

We study the Segal-Bargmann transform on a motion group R-n v K, where K is a compact subgroup of SO(n) A characterization of the Poisson integrals associated to the Laplacian on R-n x K is given We also establish a Paley-Wiener type theorem using complexified representations

Performance of a pipelined ring algorithm for Fast Fourier Transform on transputer arrays

In this paper a pipelined ring algorithm is presented for efficient computation of one and two dimensional Fast Fourier Transform (FFT) on a message passing multiprocessor. The algorithm has been implemented on a transputer based system and experiments reveal that the algorithm is very efficient. A model for analysing the performance of the algorithm is developed from its computation-communication characteristics. Expressions for execution time, speedup and efficiency are obtained and these expressions are validated with experimental results obtained on a four transputer system. The analytical model is then used to estimate the performance of the algorithm for different number of processors, and for different sizes of the input data.

Predictive uncertainty of chaotic daily streamflow using ensemble wavelet networks approach

Perfect or even mediocre weather predictions over a long period are almost impossible because of the ultimate growth of a small initial error into a significant one. Even though the sensitivity of initial conditions limits the predictability in chaotic systems, an ensemble of prediction from different possible initial conditions and also a prediction algorithm capable of resolving the fine structure of the chaotic attractor can reduce the prediction uncertainty to some extent. All of the traditional chaotic prediction methods in hydrology are based on single optimum initial condition local models which can model the sudden divergence of the trajectories with different local functions. Conceptually, global models are ineffective in modeling the highly unstable structure of the chaotic attractor. This paper focuses on an ensemble prediction approach by reconstructing the phase space using different combinations of chaotic parameters, i.e., embedding dimension and delay time to quantify the uncertainty in initial conditions. The ensemble approach is implemented through a local learning wavelet network model with a global feed-forward neural network structure for the phase space prediction of chaotic streamflow series. Quantification of uncertainties in future predictions are done by creating an ensemble of predictions with wavelet network using a range of plausible embedding dimensions and delay times. The ensemble approach is proved to be 50% more efficient than the single prediction for both local approximation and wavelet network approaches. The wavelet network approach has proved to be 30%-50% more superior to the local approximation approach. Compared to the traditional local approximation approach with single initial condition, the total predictive uncertainty in the streamflow is reduced when modeled with ensemble wavelet networks for different lead times. Localization property of wavelets, utilizing different dilation and translation parameters, helps in capturing most of the statistical properties of the observed data. The need for taking into account all plausible initial conditions and also bringing together the characteristics of both local and global approaches to model the unstable yet ordered chaotic attractor of a hydrologic series is clearly demonstrated.

Wavelet based compression and denoising of optical tomography data

Two methods based on wavelet/wavelet packet expansion to denoise and compress optical tomography data containing scattered noise are presented, In the first, the wavelet expansion coefficients of noisy data are shrunk using a soft threshold. In the second, the data are expanded into a wavelet packet tree upon which a best basis search is done. The resulting coefficients are truncated on the basis of energy content. It can be seen that the first method results in efficient denoising of experimental data when scattering particle density in the medium surrounding the object was up to 12.0 x 10(6) per cm(3). This method achieves a compression ratio of approximate to 8:1. The wavelet packet based method resulted in a compression of up to 11:1 and also exhibited reasonable noise reduction capability. Tomographic reconstructions obtained from denoised data are presented. (C) 1999 Published by Elsevier Science B.V. All rights reserved,

GMM basedbayesian approach to speech enhancement in signal/transform domain

Considering a general linear model of signal degradation, by modeling the probability density function (PDF) of the clean signal using a Gaussian mixture model (GMM) and additive noise by a Gaussian PDF, we derive the minimum mean square error (MMSE) estimator.The derived MMSE estimator is non-linear and the linear MMSE estimator is shown to be a special case. For speech signal corrupted by independent additive noise, by modeling the joint PDF of time-domain speech samples of a speech frame using a GMM, we propose a speech enhancement method based on the derived MMSE estimator. We also show that the same estimator can be used for transform-domain speech enhancement.

An optimal transform Architecture for H.264/AVC

This paper presents the design of the area optimized integer two dimensional discrete cosine transform (2-D DCT) used in H.264/AVC codecs. The 2-D DCT calculation is performed by utilizing the separability property, in such a way that 2-D DCT is divided into two 1-D DCT calculation that are joined through a common memory. Due to its area optimized approach, the design will find application in mobile devices. Verilog hardware description language (HDL) in cadence environment has been used for design, compilation, simulation and synthesis of transform block in 0.18 mu TSMC technology.

V-Transform: “An Enhanced Polynomial Coefficient Based DC Test for Non-linear Analog Circuits

Abstract—DC testing of parametric faults in non-linear analog circuits based on a new transformation, entitled, V-Transform acting on polynomial coefficient expansion of the circuit function is presented. V-Transform serves the dual purpose of monotonizing polynomial coefficients of circuit function expansion and increasing the sensitivity of these coefficients to circuit parameters. The sensitivity of V-Transform Coefficients (VTC) to circuit parameters is up to 3x-5x more than sensitivity of polynomial coefficients. As a case study, we consider a benchmark elliptic filter to validate our method. The technique is shown to uncover hitherto untestable parametric faults whose sizes are smaller than 10 % of the nominal values. I.