Compressed sensing based cyclic feature spectrum sensing for cognitive radios

Spectrum sensing is currently one of the most challenging design problems in cognitive radio. A robust spectrum sensing technique is important in allowing implementation of a practical dynamic spectrum access in noisy and interference uncertain environments. In addition, it is desired to minimize the sensing time, while meeting the stringent cognitive radio application requirements. To cope with this challenge, cyclic spectrum sensing techniques have been proposed. However, such techniques require very high sampling rates in the wideband regime and thus are costly in hardware implementation and power consumption. In this thesis the concept of compressed sensing is applied to circumvent this problem by utilizing the sparsity of the two-dimensional cyclic spectrum. Compressive sampling is used to reduce the sampling rate and a recovery method is developed for re- constructing the sparse cyclic spectrum from the compressed samples. The reconstruction solution used, exploits the sparsity structure in the two-dimensional cyclic spectrum do-main which is different from conventional compressed sensing techniques for vector-form sparse signals. The entire wideband cyclic spectrum is reconstructed from sub-Nyquist-rate samples for simultaneous detection of multiple signal sources. After the cyclic spectrum recovery two methods are proposed to make spectral occupancy decisions from the recovered cyclic spectrum: a band-by-band multi-cycle detector which works for all modulation schemes, and a fast and simple thresholding method that works for Binary Phase Shift Keying (BPSK) signals only. In addition a method for recovering the power spectrum of stationary signals is developed as a special case. Simulation results demonstrate that the proposed spectrum sensing algorithms can significantly reduce sampling rate without sacrifcing performance. The robustness of the algorithms to the noise uncertainty of the wireless channel is also shown.

Comparison of the distributions of classical and adaptively aligned EEG power spectra

The distributions of eyes-closed resting electroencephalography (EEG) power spectra and their residuals were described and compared using classically averaged and adaptively aligned averaged spectra. Four minutes of eyes-closed resting EEG was available from 69 participants. Spectra were calculated with 0.5-Hz resolution and were analyzed at this level. It was shown that power in the individual 0.5 Hz frequency bins can be considered normally distributed when as few as three or four 2-second epochs of EEG are used in the average. A similar result holds for the residuals. Power at the peak Alpha frequency has quite different statistical behaviour to power at other frequencies and it is considered that power at peak Alpha represents a relatively individuated process that is best measured through aligned averaging. Previous analyses of contrasts in upper and lower alpha bands may be explained in terms of the variability or distribution of the peak Alpha frequency itself.

Application of higher order statistics/spectra in biomedical signals : a review

For many decades correlation and power spectrum have been primary tools for digital signal processing applications in the biomedical area. The information contained in the power spectrum is essentially that of the autocorrelation sequence; which is sufficient for complete statistical descriptions of Gaussian signals of known means. However, there are practical situations where one needs to look beyond autocorrelation of a signal to extract information regarding deviation from Gaussianity and the presence of phase relations. Higher order spectra, also known as polyspectra, are spectral representations of higher order statistics, i.e. moments and cumulants of third order and beyond. HOS (higher order statistics or higher order spectra) can detect deviations from linearity, stationarity or Gaussianity in the signal. Most of the biomedical signals are non-linear, non-stationary and non-Gaussian in nature and therefore it can be more advantageous to analyze them with HOS compared to the use of second order correlations and power spectra. In this paper we have discussed the application of HOS for different bio-signals. HOS methods of analysis are explained using a typical heart rate variability (HRV) signal and applications to other signals are reviewed.

Application of higher order spectra to identify epileptic EEG

Epilepsy is characterized by the spontaneous and seemingly unforeseeable occurrence of seizures, during which the perception or behavior of patients is disturbed. An automatic system that detects seizure onsets would allow patients or the people near them to take appropriate precautions, and could provide more insight into this phenomenon. Various methods have been proposed to predict the onset of seizures based on EEG recordings. The use of nonlinear features motivated by the higher order spectra (HOS) has been reported to be a promising approach to differentiate between normal, background (pre-ictal) and epileptic EEG signals. In this work, we made a comparative study of the performance of Gaussian mixture model (GMM) and Support Vector Machine (SVM) classifiers using the features derived from HOS and from the power spectrum. Results show that the selected HOS based features achieve 93.11% classification accuracy compared to 88.78% with features derived from the power spectrum for a GMM classifier. The SVM classifier achieves an improvement from 86.89% with features based on the power spectrum to 92.56% with features based on the bispectrum.

Bispectral and trispectral characterization of transition to chaos in the Duffing oscillator

Higher-order spectral (bispectral and trispectral) analyses of numerical solutions of the Duffing equation with a cubic stiffness are used to isolate the coupling between the triads and quartets, respectively, of nonlinearly interacting Fourier components of the system. The Duffing oscillator follows a period-doubling intermittency catastrophic route to chaos. For period-doubled limit cycles, higher-order spectra indicate that both quadratic and cubic nonlinear interactions are important to the dynamics. However, when the Duffing oscillator becomes chaotic, global behavior of the cubic nonlinearity becomes dominant and quadratic nonlinear interactions are weak, while cubic interactions remain strong. As the nonlinearity of the system is increased, the number of excited Fourier components increases, eventually leading to broad-band power spectra for chaos. The corresponding higher-order spectra indicate that although some individual nonlinear interactions weaken as nonlinearity increases, the number of nonlinearly interacting Fourier modes increases. Trispectra indicate that the cubic interactions gradually evolve from encompassing a few quartets of Fourier components for period-1 motion to encompassing many quartets for chaos. For chaos, all the components within the energetic part of the power spectrum are cubically (but not quadratically) coupled to each other.

The unfinished landscape fractal geometry and the aesthetics of ecological design

During the late 20th century it was proposed that a design aesthetic reflecting current ecological concerns was required within the overall domain of the built environment and specifically within landscape design. To address this, some authors suggested various theoretical frameworks upon which such an aesthetic could be based. Within these frameworks there was an underlying theme that the patterns and processes of Nature may have the potential to form this aesthetic — an aesthetic based on fractal rather than Euclidean geometry. In order to understand how fractal geometry, described as the geometry of Nature, could become the referent for a design aesthetic, this research examines the mathematical concepts of fractal Geometry, and the underlying philosophical concepts behind the terms ‘Nature’ and ‘aesthetics’. The findings of this initial research meant that a new definition of Nature was required in order to overcome the barrier presented by the western philosophical Nature¯culture duality. This new definition of Nature is based on the type and use of energy. Similarly, it became clear that current usage of the term aesthetics has more in common with the term ‘style’ than with its correct philosophical meaning. The aesthetic philosophy of both art and the environment recognises different aesthetic criteria related to either the subject or the object, such as: aesthetic experience; aesthetic attitude; aesthetic value; aesthetic object; and aesthetic properties. Given these criteria, and the fact that the concept of aesthetics is still an active and ongoing philosophical discussion, this work focuses on the criteria of aesthetic properties and the aesthetic experience or response they engender. The examination of fractal geometry revealed that it is a geometry based on scale rather than on the location of a point within a three-dimensional space. This enables fractal geometry to describe the complex forms and patterns created through the processes of Wild Nature. Although fractal geometry has been used to analyse the patterns of built environments from a plan perspective, it became clear from the initial review of the literature that there was a total knowledge vacuum about the fractal properties of environments experienced every day by people as they move through them. To overcome this, 21 different landscapes that ranged from highly developed city centres to relatively untouched landscapes of Wild Nature have been analysed. Although this work shows that the fractal dimension can be used to differentiate between overall landscape forms, it also shows that by itself it cannot differentiate between all images analysed. To overcome this two further parameters based on the underlying structural geometry embedded within the landscape are discussed. These parameters are the Power Spectrum Median Amplitude and the Level of Isotropy within the Fourier Power Spectrum. Based on the detailed analysis of these parameters a greater understanding of the structural properties of landscapes has been gained. With this understanding, this research has moved the field of landscape design a step close to being able to articulate a new aesthetic for ecological design.

The effect of exercise repetition on the frequency characteristics of motor output force : Implications for Achilles tendinopathy rehabilitation

Objectives: To investigate the frequency characteristics of the ground reaction force (GRF) recorded throughout the eccentric Achilles tendon rehabilitation programme described by Alfredson. Design: Controlled laboratory study, longitudinal. Methods: Nine healthy adult males performed six sets (15 repetitions per set) of eccentric ankle exercise. Ground reaction force was recorded throughout the exercise protocol. For each exercise repetition the frequency power spectrum of the resultant ground reaction force was calculated and normalised to total power. The magnitude of peak relative power within the 8-12 Hz bandwidth and the frequency at which this peak occurred was determined. Results: The magnitude of peak relative power within the 8-12 Hz bandwidth increased with each successive exercise set and following the 4th set (60 repetitions) of exercise the frequency at which peak relative power occurred shifted from 9 to 10 Hz. Conclusions: The increase in magnitude and frequency of ground reaction force vibrations with an increasing number of exercise repetitions is likely connected to changes in muscle activation with fatigue and tendon conditioning. This research illustrates the potential for the number of exercise repetitions performed to influence the tendons' mechanical environment, with implications for tendon remodelling and the clinical efficacy of eccentric rehabilitation programmes for Achilles tendinopathy.

How much is enough? The effect of exercise repetition on the force frequency characteristics of eccentric exercise used for tendinopathy rehabilitation

Introduction: Eccentric exercise (EE) is a commonly used treatment for Achilles tendinopathy. While vibrations in the 8–12 Hz frequency range generated during eccentric muscle actions have been put forward as a potential mechanism for the beneficial effect of EE, optimal loading parameters required to expedite recovery are currently unknown. Alfredson's original protocol employed 90 repetitions of eccentric loading, however abbreviated protocols consisting of fewer repetitions (typically 45) have been developed, albeit with less beneficial effect. Given that 8–12 Hz vibrations generated during isometric muscle actions have been previously shown to increase with fatigue, this research evaluated the effect of exercise repetition on motor output vibrations generated during EE by investigating the frequency characteristics of ground reaction force (GRF) recorded throughout the 90 repetitions of Alfredson's protocol. Methods: Nine healthy adult males performed six sets (15 repetitions per set) of eccentric ankle exercise. GRF was recorded at a frequency of 1000 Hz throughout the exercise protocol. The frequency power spectrum of the resultant GRF was calculated and normalized to total power. Relative spectral power was summed over 1 Hz widows within the frequency rage 7.5–11.5 Hz. The effect of each additional exercise set (15 repetitions) on the relative power within each widow was investigated using a general linear modelling approach. Results: The magnitude of peak relative power within the 7.5–11.5 Hz bandwidth increased across the six exercise sets from 0.03 in exercise set one to 0.12 in exercise set six (P < 0.05). Following the 4th set of exercise the frequency at which peak relative power occurred shifted from 9 to 10 Hz. Discussion: This study has demonstrated that successive repetitions of eccentric loading over six exercise sets results in an increase in the amplitude of motor output vibrations in the 7.5–11.5 Hz bandwidth, with an increase in the frequency of these vibrations occurring after the 4th set (60th repetition). These findings are consistent with findings from previous studies of muscle fatigue. Assuming that the magnitude and frequency of these vibrations represent important stimuli for tendon remodelling as hypothesized within the literature, the findings of this study question the role of abbreviated EE protocols and raise the question; can EE protocols for tendinopathy be optimized by performing eccentric loading to fatigue?

Achilles tendinopathy modulates force frequency characteristics of eccentric exercise

Introduction Previous research has demonstrated that ground reaction force (GRF) recorded during eccentric ankle exercise is characterised by greater power in the 8-12Hz bandwidth when compared to that recorded during concentric ankle exercise. Subsequently, it was suggested that vibrations in this bandwidth may underpin the beneficial effect of eccentric loading in tendon repair. However, this observation has been made only in individuals without Achilles tendinopathy. This research compared the force frequency characteristics of eccentric and concentric exercises in individuals with and without Achilles tendinopathy., Methods Eleven male adults with unilateral mid-portion Achilles tendinopathy and nine control male adults without tendinopathy participated in the research. Kinematics and GRF were recorded while the participants performed a common eccentric rehabilitation exercise protocol and a concentric equivalent. Ankle joint kinematics and the frequency power spectrum of the resultant GRF were calculated. Results Eccentric exercise was characterised by a significantly greater proportion of spectral power between 4.5 and 11.5Hz when compared to concentric exercise. There were no significant differences between limbs in the force frequency characteristics of concentric exercise. Eccentric exercise, in contrast, was defined by a shift in the power spectrum of the symptomatic limb, resulting in a second spectral peak at 9Hz, rather than 10Hz in the control limb. Conclusions Compared to healthy tendon, Achilles tendinopathy was characterised by lower frequency vibrations during eccentric rehabilitation exercises. This finding may be associated with changes in neuromuscular activation and tendon stiffness which have been shown to occur with tendinopathy and provides a possible rationale for the previous observation of a different biochemical response to eccentric exercise in healthy and injured Achilles tendons., (C)2012The American College of Sports Medicine

Spatially varying ground motion effects on seismic response of adjacent structures considering soil-structure interaction

Spatial variation of seismic ground motions is caused by incoherence effect, wave passage, and local site conditions. This study focuses on the effects of spatial variation of earthquake ground motion on the responses of adjacent reinforced concrete (RC) frame structures. The adjacent buildings are modeled considering soil-structure interaction (SSI) so that the buildings can be interacted with each other under uniform and non-uniform ground motions. Three different site classes are used to model the soil layers of SSI system. Based on fast Fourier transformation (FFT), spatially correlated non-uniform ground motions are generated compatible with known power spectrum density function (PSDF) at different locations. Numerical analyses are carried out to investigate the displacement responses and the absolute maximum base shear forces of adjacent structures subjected to spatially varying ground motions. The results are presented in terms of related parameters affecting the structural response using three different types of soil site classes. The responses of adjacent structures have changed remarkably due to spatial variation of ground motions. The effect can be significant on rock site rather than clay site.

On the effect of Reynolds number for flow past three side-by-side square cylinders for unequal gap spacings

Flow patterns and aerodynamic characteristics behind three side-by-side square cylinders has been found depending upon the unequal gap spacing (g1 = s1/d and g2 = s2/d) between the three cylinders and the Reynolds number (Re) using the Lattice Boltzmann method. The effect of Reynolds numbers on the flow behind three cylinders are numerically studied for 75 ≤ Re ≤ 175 and chosen unequal gap spacings such as (g1, g2) = (1.5, 1), (3, 4) and (7, 6). We also investigate the effect of g2 while keeping g1 fixed for Re = 150. It is found that a Reynolds number have a strong effect on the flow at small unequal gap spacing (g1, g2) = (1.5, 1.0). It is also found that the secondary cylinder interaction frequency significantly contributes for unequal gap spacing for all chosen Reynolds numbers. It is observed that at intermediate unequal gap spacing (g1, g2) = (3, 4) the primary vortex shedding frequency plays a major role and the effect of secondary cylinder interaction frequencies almost disappear. Some vortices merge near the exit and as a result small modulation found in drag and lift coefficients. This means that with the increase in the Reynolds numbers and unequal gap spacing shows weakens wakes interaction between the cylinders. At large unequal gap spacing (g1, g2) = (7, 6) the flow is fully periodic and no small modulation found in drag and lift coefficients signals. It is found that the jet flows for unequal gap spacing strongly influenced the wake interaction by varying the Reynolds number. These unequal gap spacing separate wake patterns for different Reynolds numbers: flip-flopping, in-phase and anti-phase modulation synchronized, in-phase and anti-phase synchronized. It is also observed that in case of equal gap spacing between the cylinders the effect of gap spacing is stronger than the Reynolds number. On the other hand, in case of unequal gap spacing between the cylinders the wake patterns strongly depends on both unequal gap spacing and Reynolds number. The vorticity contour visualization, time history analysis of drag and lift coefficients, power spectrum analysis of lift coefficient and force statistics are systematically discussed for all chosen unequal gap spacings and Reynolds numbers to fully understand this valuable and practical problem.

Spectral analysis of pair-correlation bandwidth: Application to cell biology images

Images from cell biology experiments often indicate the presence of cell clustering, which can provide insight into the mechanisms driving the collective cell behaviour. Pair-correlation functions provide quantitative information about the presence, or absence, of clustering in a spatial distribution of cells. This is because the pair-correlation function describes the ratio of the abundance of pairs of cells, separated by a particular distance, relative to a randomly distributed reference population. Pair-correlation functions are often presented as a kernel density estimate where the frequency of pairs of objects are grouped using a particular bandwidth (or bin width), Δ>0. The choice of bandwidth has a dramatic impact: choosing Δ too large produces a pair-correlation function that contains insufficient information, whereas choosing Δ too small produces a pair-correlation signal dominated by fluctuations. Presently, there is little guidance available regarding how to make an objective choice of Δ. We present a new technique to choose Δ by analysing the power spectrum of the discrete Fourier transform of the pair-correlation function. Using synthetic simulation data, we confirm that our approach allows us to objectively choose Δ such that the appropriately binned pair-correlation function captures known features in uniform and clustered synthetic images. We also apply our technique to images from two different cell biology assays. The first assay corresponds to an approximately uniform distribution of cells, while the second assay involves a time series of images of a cell population which forms aggregates over time. The appropriately binned pair-correlation function allows us to make quantitative inferences about the average aggregate size, as well as quantifying how the average aggregate size changes with time.

Short-window spectral analysis using AMVAR and multitaper methods: a comparison

We compare two popular methods for estimating the power spectrum from short data windows, namely the adaptive multivariate autoregressive (AMVAR) method and the multitaper method. By analyzing a simulated signal (embedded in a background Ornstein-Uhlenbeck noise process) we demonstrate that the AMVAR method performs better at detecting short bursts of oscillations compared to the multitaper method. However, both methods are immune to jitter in the temporal location of the signal. We also show that coherence can still be detected in noisy bivariate time series data by the AMVAR method even if the individual power spectra fail to show any peaks. Finally, using data from two monkeys performing a visuomotor pattern discrimination task, we demonstrate that the AMVAR method is better able to determine the termination of the beta oscillations when compared to the multitaper method.

Quantum diffusion in thin disordered wires

Quantum Ohmic residual resistance of a thin disordered wire, approximated as a one-dimensional multichannel conductor, is known to scale exponentially with length. This nonadditivity is shown to imply (i) a low-frequency noise-power spectrum proportional to -ln(Ω)/Ω, and (ii) a dispersive capacitative impedance proportional to tanh(√iΩ )/ √iΩ. A deep connection to the quantum Brownian motion with linear dynamical frictional coupling to a harmonic-oscillator bath is pointed out and interpreted in physical terms.