Square Of Magnitude Research Articles

Localized exciton states in π-conjugated polymers with finite torsion

We investigate localized exciton states in π-conjugated polymers with finite torsion. The localized states are associated with a perturbed transfer integral for which the magnitude of cosine of the torsion angle exceeds the magnitude of the corresponding cosine of the unperturbed system. The localized-state energy and spatial extent are calculated as a function of the ratio of the perturbed to unperturbed transfer integrals. Particular attention is paid to the optically active symmetric localized states, and the effective oscillator strength, or square of the absolute magnitude of the transition dipole moment, is calculated as a function of the energy. The relation of the theory to recent optical studies of poly(di- n-octylfluorene) (PF8) is discussed.

Comparison of different methods for combining phase-contrast images obtained with multiple coils

The ability to determine coil sensitivities implies that a method optimized in terms of maximized signal-to-noise ratio (SNR) can be applied to the combination of multiple coil images. An optimization of SNR subsequently results in a minimized variance in quantitative velocity measurements using phase-contrast imaging. When coil sensitivities are unknown, the weighted mean method, utilizing the square of the signal magnitude as weights, is suitable for combination of multiple phase images. In this study, the optimized method using estimated coil sensitivities was compared to the weighted mean method both theoretically and experimentally. It is shown that absence of noise correlation between the different coil images implies no difference between the methods regarding the variance of the phase. In the practical situation, noise correlation does exist, implying an opportunity for further reduction of phase variance using the optimized method. In vitro and in vivo studies showed, however, no significant difference between the two methods studied.

The influence of pool length on local turbulence production and energy slope: a flume experiment

AbstractThe influence of pool length on the strength of turbulence generated by vortex shedding was investigated in a 6 m long recirculating flume. The experiment utilized a 38% constriction of flow and an average channel‐bed slope of 0·007. The base geometry for the intermediate‐length pool experiment originated from a highly simplified, 0·10 scale model of a forced pool from North Saint Vrain Creek, Colorado. Discharge in the flume was 31·6 l/s, which corresponds to a discharge in the prototype channel of 10 m3/s. Three shorter and four longer pool lengths also were created with a fixed bed to determine changes in turbulence intensities and energy slope with pool elongation. Three‐dimensional velocities were measured with an acoustic Doppler velocimeter at 31–40 different 0·6‐depth and near‐bed locations downstream of the rectangular constriction. The average velocity and root mean square (RMS) of the absolute magnitude of velocity at both depths are significantly related to the distance from the constriction in most pool locations downstream of the constriction. In many locations, pool elongation results in a non‐linear change in turbulence intensities and average velocity. Based on the overall flow pattern, the strongest turbulence occurs in the center of the pool along the shear zone between the jet and recirculating eddy. The lateral location of this shear zone is sensitive to changes in pool length. Energy slope also was sensitive to pool length due to a combination of greater length of the pool and greater head loss with shorter pools. The results indicate some form of hydraulic optimization is possible with pools adjusting their length to adjust the location and strength of turbulent intensities in the center of pools, and lower their rate of energy dissipation. Copyright © 2004 John Wiley & Sons, Ltd.

16QAM symbol timing recovery in the upstream transmission of DOCSIS standard

This paper investigates the performance of the digital symbol timing recovery schemes for 16QAM upstream transmission of the DOCSIS standard. Two forms of nonlinearity are considered: the magnitude square operation and the delay multiplication operation, both of which generate the output signal that contains the symbol timing information. The detailed analysis for the magnitude square timing recovery is given in the digital domain, and consequently the symbol timing estimate can be directly obtained by the discrete Fourier transform. The simulation results show that the magnitude square timing recovery and delay multiplication timing recovery algorithms suffer from the same problem that the estimation error is reduced slowly at high signal-to-noise ratios due to the effect of self-noise. To this end, the third scheme, which is the magnitude square timing recovery with prefilter, is examined. This scheme shows a superior performance and a comparison with the results of the other two schemes is made.

Power spectrum tests of random numbers

Three nonrandomness tests having very low correlation between them and utilizing some statistical properties of the spectral estimates of the random number sequences having any shape of probability distribution function, are given. The spectral density is estimated as 1/ N times the periodogram (magnitude square of the discrete Fourier transform) of an N-term sequence of the random numbers. From M such spectral estimates, M peak values, M spacings between the ordered (sorted) frequencies of the peak values, and the peak value of the ensemble average of the estimates, are found and tested to decide if they closely fit their cumulative probability distributions as derived for random numbers. The sensibility thresholds of the tests are measured on random binary sequences artificially contaminated by substitution of periodic binary signals or substitution of random binary signals having periodic mean or shortening long runs.

α=(1,2) Inverse Control of Speed and Flux in Voltage-Fed Induction Motor

The α=(1,2) inverse model from the electrical torque and square of rotor flux magnitude to the stator voltages in a stator fixed reference frame has been applied to design a controller for tracking the desired rotor speed and flux magnitude for a voltage-fed induction motor. A robustness of the controller with respect to variations of the rotor resistance has been investigated from an online learning the inverse model perspectives

Quadratic Gabor filters for object detection

We present a new class of quadratic filters that are capable of creating spherical, elliptical, hyperbolic and linear decision surfaces which result in better detection and classification capabilities than the linear decision surfaces obtained from correlation filters. Each filter comprises of a number of separately designed linear basis filters. These filters are linearly combined into several macro filters; the output from these macro filters are passed through a magnitude square operation and are then linearly combined using real weights to achieve the quadratic decision surface. For detection, the creation of macro filters (linear combinations of multiple single filters) allows for a substantial computational saving by reducing the number of correlation operations required. In this work, we consider the use of Gabor basis filters; the Gabor filter parameters are separately optimized. The fusion parameters to combine the Gabor filter outputs are optimized using an extended piecewise quadratic neural network (E-PQNN). We demonstrate methods for selecting the number of macro Gabor filters, the filter parameters and the linear and nonlinear combination coefficients. We present preliminary results obtained for an infrared (IR) vehicle detection problem.

Causal and unique reconstruction of nonminimum reflection phase for a class of submerged structures

An approach is presented for uniquely determining the phase of an acoustic reflection from an object whose impedance magnitude approximates the acoustic impedance of the surrounding medium. This approximation defines a semiannular region in the complex impedance plane that lies between the rigid and pressure-release limits. When this region is mapped onto the complex reflection coefficient plane, the approximation allows for a wide range of reflection coefficients. A Taylor series expansion for the square of the reflection coefficient magnitude is used to estimate the phase of the reflecting impedance. The causality condition is invoked to recover the magnitude of the impedance from its phase. Once the magnitude and phase of the impedance is known, the complex-valued reflection coefficient algebraically follows regardless of whether or not the reflection coefficient is minimum phase. The approach is useful in experimental situations that only allow the accurate measurement of reflection magnitude and not phase. As an example, the approach is demonstrated on one-dimensional numerical simulations that simulate uncertainty in target location and ambient noise. [Work supported by ONR.]

Two-dimensional, highly directive currents on large circular loops

Properties of idealized, two-dimensional current distributions on circular loops are investigated analytically via the solution of a constrained optimization problem. The directivity in the far field is maximized under a fixed C=N/T, where N is the integral of the square of the current magnitude and T is the total radiated power. C enters the ensuing Fourier series for the current implicitly through a Lagrange multiplier α. For non-negative α and large electrical radius ka, the directivity and the current are evaluated approximately via combined use of the Poisson summation formula and the Mellin transform technique. As a result, a geometrical-ray representation for the current is derived for the case of directivities that are slightly larger than that of the uniform distribution. The analysis indicates certain advantages of large radiating structures for moderate values of the constraint C. In the limit C→∞ of Oseen’s “Einstein needle radiation,” an asymptotic formula for the directivity is obtained. Possible extensions of these results to classes of smooth convex loops are briefly discussed.

On a higher order analysis of laminated composite strips with extension-twist coupling

A finite displacement analysis for extension-twist coupling in pretwisted laminated composite strips is presented. A new formulation of the kinematics is constructed by neglecting the terms of order of the square of the maximum strain magnitude in the strain–displacement relations. The closed-form extension-twist relationships are derived and the influence of out-of-plane shear strains on the results is estimated. The accuracy of the model is assessed through comparison with test data and analytical predictions.

Comments on "On induction motors control"

In the above paper (Rachid, 1997), the author claims that by using the square of the flux magnitude, he is able to develop a nonsingular controller which requires less computation than the standard field-oriented controller. The purpose of this paper is point out that these claims are incorrect.

Real-time sliding-mode observer and control of an induction motor

This paper deals with the control and observation of an induction motor using a sliding-mode technique. The authors' aim is to regulate the speed and the square of the rotor flux magnitude to specified references. Assuming that all the states are measured, sliding surfaces are proposed within a sliding-mode control framework. Then, the stator voltages are derived such that the sliding surfaces are asymptotically attractive since, in practice, the rotor fluxes are not usually measurable, a sliding-mode observer is derived to estimate the rotor fluxes. Furthermore, it is shown that their observer is robust against modeling uncertainties and measurement noise. To illustrate their purpose, they present experimental results for a 0.37-kW induction motor obtained on a digital-signal-processor-based system (TMS 320C31/40 MHz). The experimental results show that the proposed control system is robust against rotor resistance variations.

EFFECT OF MAGNITUDE OF VERTICAL WHOLE-BODY VIBRATION ON ABSORBED POWER FOR THE SEATED HUMAN BODY

The power absorbed by 12 male subjects during exposure to vertical whole-body vibration at six magnitudes of random vibration (0·25, 0·5, 1·0, 1·5, 2·0 and 2·5 ms−2r.m.s.) has been measured in the laboratory. All subjects showed greatest absorbed power at about 5 Hz, but the frequency of this peak in the absorbed power reduced with increasing vibration magnitude. The total absorbed power increased approximately in proportion to the square of the acceleration magnitude: normalizing the absorbed power to the square of the r.m.s. vibration magnitude removed most of the differences, although the changes in resonance frequency were still evident. The frequency dependence of absorbed power at a constant magnitude of acceleration was approximated by a simple weighting having slopes of ±6 dB/octave either side of 5 Hz. Comparing the characteristics of this absorbed power weighting to standard frequency weightings showed substantial differences, especially at high frequencies. It is concluded that the differences from currently accepted frequency weightings are so great that the absorbed power is unlikely to yield good general predictions of the discomfort or risks of injury from whole-body vertical vibration.

Group delay based magnitude square coherence estimation by an ARMA model

In this paper, a new method of estimation of the magnitude square coherence function (MSC) by an ARMA model is proposed. The estimation is achieved by modeling the periodogram estimate of the MSC and the ARMA model has been realized by the pole-zero decomposition property of the group delay function (GDF). Its performance has been found to be superior to that of the periodogram MSC estimate in terms of normalized sum of the sample mean square error (NSSMSE) and maximum sample root mean square error (RMSE). Further, its performance is comparable with those of the existing ARMA based estimation methods and requires less computations. The proposed ARMA-MSC estimation is simple and does not involve any explicit solution of a system of equations.

On computation of certain discrete Fourier transforms using binary calculus

Completely multiplyless algorithms are proposed to approximately compute Discrete Fourier Transform (DFT). The computational complexity of the proposed algorithms for a transform of size N, is O( N 2 ) addition and shift operations. In these algorithms, the DFT can be computed sequentially, with a single adder in O( N 2 ) addition times. Parallel versions of the algorithms can be executed in O( N) addition times, with O( N) number of adders. The accuracy of the trigonometric approximations used, is bounded by O( N −1). For more elaborate algorithms, the accuracy of the trigonometric approximations is bounded by O( N −2). The degree of approximation in the transformation can be characterized by the ratio of the average magnitude squared error in the transformed sequence, and the average magnitude square of the transformed sequence. This ratio is very low for higher values of the transform length, N. For smaller values of the transform length, this value is generally low. A stipulation is made, that the size of the transform be a Ramanujan number. These Ramanujan numbers are related to Π and integers which are powers of 2. It is assumed in this paper that it is more expensive to perform a multiplication than a shift operation.

Quadratic detectors for energy estimation

The estimation of signal energy is an important part of physics and signal processing. A commonly used energy estimate in signal processing is instantaneous energy that is defined by the square of the signal magnitude at time t, i.e.,.

Spatial coherence and rough bottom scattering in shallow water

Shallow-water acoustic data collected off Mallorca in March 1993 are analyzed for spatial coherence, and their relation to rough bottom scattering is investigated. Bistatic reverberation data were collected by a horizontal receiver array with equispaced hydrophones suspended 1 m above the bottom. A flextentional transducer towed behind the ship was used as a source, generating a 209-dB source level at center frequency of 400 Hz, with 5-ms signal length, and 10-s interval. The ship made a hexagonal run with the horizontal receiver array inside the track. A theoretical source model has been designed to approximate the actual source pulse, and is used to match-filter the data. The modal arrivals are clearly identified in the resulting impulse responses, allowing for mode-by-mode analysis. The total field is decomposed into a mean field (coherent field) and scattered field (incoherent field) by a stacking procedure. The spatial coherence is then calculated using a correlation and a coherence function. The magnitude square of the complex coherence function (MSC) of the total field was 0.9 while the MSC of the scattered field was 0.1, which suggested that the bottom roughness was very small, allowing for modeling by perturbation theory.

High-resolution and signal-averaged electrocardiography to separate post-myocardial infarction patients with and without ventricular tachycardia.

High-resolution and signal-averaged ECG, 24 h Holter recording and ejection fraction were used to separate post-myocardial infarction patients with and without ventricular tachycardia (VT) among 150 individuals: 26 patients with an old myocardial infarction and documented sustained VT, 104 patients with an acute myocardial infarction without sustained VT, who were followed-up for 2 years, and 20 healthy volunteers. Bipolar orthogonal XYZ leads were recorded, high-pass filtered at cut-off frequencies of 25, 40, 60, 80 and 100 Hz, and combined to vector magnitude square root of X2 + Y2 + Z2. The filtered QRS duration, the root-mean-square voltages of different time intervals and the durations of low amplitude signals under different thresholds, both from the initial and terminal QRS, were calculated. The sensitivity and specificity of each parameter alone and in every combination of two, three and four parameters (17 million different combinations) were computed both from non-averaged and averaged data. The best separation was achieved by 12 combinations all including four signal-averaged ECG parameters, with a sensitivity of 81% and a specificity of 79%. The parameters represented most were: filtered QRS duration at 25 Hz, RMS voltage of the last 50 ms at 25 Hz, terminal LAS duration at 80 Hz, and RMS voltage of the last 20 ms at 80 Hz. Parameters of the initial QRS complex did not improve either the sensitivity or the specificity of the method. In logistic regression analysis, the best combinations of four signal-averaged ECG parameters separated VT patients better (P < 0.001) than non-sustained ventricular tachycardia at Holter (P = 0.001); left ventricular ejection fraction (P = 0.01); or age (P = 0.006). Parameters calculated from averaged data gave better results than parameters calculated from non-averaged data.

Tuned phasic and tonic motile responses of isolated outer hair cells to direct mechanical stimulation of the cell body

Guinea pig outer hair cells (OHCs) isolated from the two apical turns of the cochlea and firmly attached to a suction pipette, were subjected to the stimulus of the near-field (particle) displacements of a calibrated oscillating fluid jet aimed at the lateral cell walls. The longitudinal length changes of the OHCs in response to stimulation, in a direction orthogonal to that of the fluid jet, were recorded by a photodiode array. The response had two components; a phasic length change which followed the frequency of the particle displacement of the jet cycle by cycle, and a tonic length change which took several milliseconds to develop depending on the magnitude of the mechanical stimulus. When the hair cell changed length the lateral walls of the OHC moved in antiphase, moving apart during shortening and together during lengthening. With increased stimulus level the phasic response grew in proportion to the stimulus magnitude and began to saturate at the highest stimulus levels, while the tonic response grew in proportion to the square of the stimulus magnitude. Both the direction of the tonic length change and the phase of the phasic component could alter with the level of stimulation. Isolevel and isoresponse -frequency functions of both the tonic and phasic length changes revealed that both response types were tuned to similar resonant frequencies (RF) between 150 and 2500 Hz. The phase of the phasic length change began to lag at frequencies just below the RF, lagged by about 90° at the RF and lagged by a further 90° at frequencies above RF. The frequency response properties of the OHCs closely corresponded to those of a damped, forced, mechanical resonance. The tonic response disappeared and the phasic response was reduced at low-levels as a consequence of intense mechanical stimulation and with time.

A weighted normalized frequency domain LMS adaptive algorithm

A general filtering scheme is presented for obtaining an input power estimate for setting the convergence parameter mu separately in each frequency bin of a frequency-domain LMS adaptive filter (FDAF) algorithm. A linear filtering operation is performed on the magnitude square of the input data and incorporated directly into the algorithm as a data-dependent time-varying stochastic mu (n). The mean performance of the weighted normalized frequency domain LMS algorithm (WNFDAF) is analyzed using independent and identically distributed Gaussian data, and the results are validated by the Monte Carlo simulations of the algorithm. The simulations are also used to study the weight transient behavior. The simulations suggest that sort smoothing times are sufficient for rapid weight convergence without large fluctuations in the power estimates significantly affecting transient weight behavior.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>