Individual Frequency Components Research Articles

WHAT MAGNETAR SEISMOLOGY CAN TEACH US ABOUT MAGNETIC FIELDS

The effect of magnetic fields on the frequencies of toroidal oscillations of neutron stars is derived to lowest order. We suggest that the fine structure in the quasiperiodic oscillation power spectrum of magnetars following giant flares reported by Strohmayer & Watts is magnetic splitting of degenerate toroidal modes, and we estimate a corresponding crustal magnetic field on the order of 1015 Gauss or more. We suggest that residual m, –m symmetry following such splitting, together with nonaxisymmetric or rotational splitting of the residual symmetry, might allow beating of individual frequency components that is slow enough to be observed.

Hair bundles teaming up to tune the mammalian cochlea

The mammalian inner ear separates complex sounds into individual frequency and amplitude components with remarkable precision. The active process is a term coined to encompass the mechanisms involved in establishing both frequency selectivity and sensitivity of the living cochlea (1). The underlying molecular mechanisms that establish the active process are under debate and incorporate two distinct schools of thought. The first and more widely accepted is based on outer hair cell (OHC) somatic motility. The second theory hinges on active hair bundle motility. In this issue of PNAS, Dierkes et al. (2) create a biophysical model of outer hair cells where hair bundles are tethered to each other by the tectorial membrane, the overlying membrane in which OHC hair bundles are embedded. This association enhances both the frequency selectivity and the gain provided by the hair bundle active processes. This model is significant because it demonstrates a realistic mechanism by which hair bundle force generation can be used in tandem to make a significant contribution to the active process and because it provides a basis in which the disparate mechanisms of the active process might be unified. That is, although the model does not explicitly include outer hair cell motility or the resonant properties of the tectorial membrane, considering these additional variables in the framework presented may provide a means by which both measured frequency and sensitivity can be reproduced theoretically.

Sediment trend analysis of the hylebos waterway: Implications for liability allocations

Sediment trend analysis of the hylebos waterway: Implications for liability allocations

Experimental Research of a Mechatronical System

Systems “spindle – bearings” will inevitably have some errors and discrepancies in the dimensions and form of elements. These inaccuracies cause spindle’s run out. The run out is a complex periodic process which may include three types of frequency components: with frequencies exceeding the spindle’s rotary frequency, with frequency equal to the spindle’s rotary frequency and with frequencies lower that the spindle’s rotary frequency. Each individual frequency component may be caused by eccentricity or out-of-roundness of the inner race, out-of-roundness of the outer race, spread of ball diameters, and inaccuracy of their form. Self-adjustable pad-type bearings are sensitive to technological, service and construction perturbations. This is characteristic of vortex trajectories of the spindles. Character of these trajectories depends on the thickness of lubricant film over the pad supports and on the geometrical precision of the spindle journal and pads (segments). Geometrical precision under a high unbalance of the grinding wheel is crucial for functional quality, size and form of the orbit. Geometrical precision of trajectories and its state are subject to change depending on a number of parameters especially on the rigidity of the lubricant film and dynamic system.

Fully programmable ring-resonator-based integrated photonic circuit for phase coherent applications

A novel ring-resonator-based integrated photonic chip with ultrafine frequency resolution, providing programmable, stable, and accurate optical-phase control is demonstrated. The ability to manipulate the optical phase of the individual frequency components of a signal is a powerful tool for optical communications, signal processing, and RF photonics applications. As a demonstration of the power of these components, we report their use as programmable spectral-phase encoders (SPEs) and decoders for wavelength-division-multiplexing (WDM)-compatible optical code-division multiple access (OCDMA). Most important for the application here, the high resolution of these ring-resonator circuits makes possible the independent control of the optical phase of the individual tightly spaced frequency lines of a mode-locked laser (MLL). This unique approach allows us to limit the coded signal's spectral bandwidth, thereby allowing for high spectral efficiency (compared to other OCDMA systems) and compatibility with existing WDM systems with a rapidly reconfigurable set of codes. A four-user OCDMA system using polarization multiplexing is shown to operate at data rates of 2.5 Gb/s within a 40-GHz transparent optical window with a bit error rate (BER) better than 10/sup -9/ and a spectral efficiency of 25%.

Single-shot measurement of the full spatio-temporal field of ultrashort pulses with multi-spectral digital holography

We present a remarkably simple technique for measuring the full spatio-temporal electric field of a single ultrashort laser pulse. It involves capturing a large digital hologram containing multiple smaller holograms, each of which characterizes the spatial intensity and phase distributions of an individual frequency component of the pulse. From that single camera frame, we numerically reconstruct the complete electric field, E(x,y,t), using a direct algorithm. While holography requires a well-characterized reference pulse, this pulse can easily be generated from the pulse itself in most cases, so the technique is self-referencing. We experimentally demonstrate this technique using femtosecond pulses from a mode-locked Ti:Sapphire oscillator.

Simultaneous suppression of tone burst-evoked otoacoustic emissions – Effect of level and presentation paradigm

There is conflict in the literature over whether individual frequency components of a transient-evoked otoacoustic emission (TEOAE) are generated within relatively independent “channels” along the basilar membrane (BM), or whether each component may be generated by widespread areas of the BM. Two previous studies on TEOAE suppression are consistent with generation within largely independent channels, but with a degree of interaction between nearby channels. However, both these studies reported significant suppression only at high stimulus levels, at which the “nonlinear” presentation paradigm was used. The present study clarifies the separate influences of stimulus level and presentation paradigm on this type of suppression. TEOAEs were recorded using stimulus tone bursts at 1, 2 and 3 kHz and a complex stimulus consisting of a digital addition of the three tone bursts, over a range of stimulus levels and both “linear” and “nonlinear” presentation paradigms. Responses to the individual tone bursts were combined offline and compared with responses to the complex stimuli. Results clearly demonstrate that TEOAE suppression under these conditions is dependent upon stimulus level, and not upon presentation paradigm. It is further argued that the data support the “local” rather than “widespread” model of TEOAE generation, subject to nonlinear interactions between nearby generation channels.

Assessment of the seismic resistance of a ventilation stack on a reactor building

The paper analyzes the seismic resistance of a ventilation stack on a reactor building, including the possible reserves of increasing the resistance. Structures of this type are highly sensitive to seismic loads, as the tuning of the stack (the spectrum of its lowest natural frequencies) corresponds with the frequency spectrum of excitation due to seismic effects. The purpose of the paper is to present an example of an actual structure to show the character of the response of the structure, and the participation of the individual frequency components of the response in the overall stress and strain state of a structure of this type. The methodology for a numerical analysis of the structure is also given. The load of the stack proper is modified by the transfer characteristics of the building. In engineering practice, the system is usually divided into two subsystems: the building with the sub-base, and the stack proper. The level of justification for the application of this simplification depends on the distance of the natural frequencies of the stack from the natural frequencies of the building. Finally, the paper deals with possible errors in determining the actual seismic resistance of the stack structure.

Spectral analysis of digital quasiperiodic signals

The spectrum calculation results are used for its estimation in a band of frequencies and for determining the parameters of individual frequency components. It is shown that the discrete Fourier transformation and the parametric method should be employed only for rough estimation of the spectrum. In spectral analysis of digital quasiperiodic signals, it is expedient to apply methods based on approximation of a sequence of data samples by the first-order trigonometric polynomial with variable frequency of its harmonic functions.

Decomposition of incident and reflected higher harmonic waves using four wave gauges

This study proposes a new technique to separate incident and reflected higher harmonic waves using four or more spatially separated probes. Both the free and locked modes in the higher harmonics of the regular waves can be isolated. The complex waves are decomposed into individual frequency components using the Fourier transform. The least squares method is applied to minimize the error caused by possible signal noise and to obtain the equations for solving the unknown parameters related to the wave amplitudes. Probe spacing condition for preventing singularity in the calculation is provided. The accuracy of this method is verified by applying it to resolve artificial waves with arbitrarily selected amplitudes. The sensitivity of this method to the noise inevitably associated with the experiments is also tested. The free surface elevation data collected from probes located upstream and downstream of a submerged breakwater in a numerical wave tank are analyzed to demonstrate the applicability of this method. The results are compared with those obtained using the methods of Goda and Suzuki [Goda, Y., Suzuki, Y., 1976. Estimation of incident and reflected waves in random wave experiments. Proc. 15th Costal Eng. Conf., ASCE, pp. 828–845] and Mansard and Funke [Mansard, E.P.D., Funke, E.R., 1980. The measurement of incident and reflected spectra using a least squares method. Proc. 17th Costal Eng. Conf., ASCE, pp. 154–172]. The comparison indicated that this method gives exactly the same first harmonic incident and reflected wave amplitudes as the other two methods. The full modes in the higher harmonics can be determined using this method, while the higher harmonics are presumed to be free waves in the other two methods.

Virtual pitch integration for asynchronous harmonics.

This experiment examined the generation of virtual pitch for harmonically related tones that do not overlap in time. The interval between successive tones was systematically varied in order to gauge the integration period for virtual pitch. A pitch discrimination task was employed, and both harmonic and nonharmonic tone series were tested. The results confirmed that a virtual pitch can be generated by a series of brief, harmonically related tones that are separated in time. Robust virtual pitch information can be derived for intervals between successive 40-ms tones of up to about 45 ms, consistent with a minimum estimate of integration period of about 210 ms. Beyond intertone intervals of 45 ms, performance becomes more variable and approaches an upper limit where discrimination of tone sequences can be undertaken on the basis of the individual frequency components. The individual differences observed in this experiment suggest that the ability to derive a salient virtual pitch varies across listeners.

An evaluation of linear instability waves as sources of sound in a supersonic turbulent jet

Mach wave radiation from supersonic jets is revisited to better quantify the extent to which linearized equations represent the details of the actual mechanism. To this end, we solve the linearized Navier–Stokes equations (LNS) with precisely the same mean flow and inflow disturbances as a previous direct numerical simulation (DNS) of a perfectly expanded turbulent M=1.92 jet [Freund et al., AIAA J. 38, 2023 (2000)]. We restrict our attention to the first two azimuthal modes, n=0 and n=1, which constitute most of the acoustic field. The direction of peak radiation and the peak Strouhal number matches the DNS reasonably well, which is in accord with previous experimental justification of the linear theory. However, it is found that the sound pressure level predicted by LNS is significantly lower than that from DNS. In order to investigate the discrepancy, individual frequency components of the solution are examined. These confirm that near the peak Strouhal number, particularly for the first helical mode n=1, the amplification of disturbances in the LNS closely matches the DNS. However, away from the peak frequency (and generally for the azimuthal mode n=0), modes in the LNS are damped while those in the DNS grow at rates comparable to those at the peak Strouhal number.

Extraction of acoustic normal mode depth functions using vertical line array data.

A method for extracting the normal modes of acoustic propagation in the shallow ocean from sound recorded on a vertical line array (VLA) of hydrophones as a source travels nearby is presented. The mode extraction is accomplished by performing a singular value decomposition (SVD) of individual frequency components of the signal's temporally averaged, spatial cross-spectral density matrix. The SVD produces a matrix containing a mutually orthogonal set of basis functions, which are proportional to the depth-dependent normal modes, and a diagonal matrix containing the singular values, which are proportional to the modal source excitations and mode eigenvalues. The conditions under which the method is expected to work are found to be (1) sufficient depth sampling of the propagating modes by the VLA receivers; (2) sufficient source-VLA range sampling, and (3) sufficient range interval traversed by the source. The mode extraction method is applied to data from the Area Characterization Test II, conducted in September 1993 in the Hudson Canyon Area off the New Jersey coast. Modes are successfully extracted from cw tones recorded while (1) the source traveled along a range-independent track with constant bathymetry and (2) the source traveled up-slope with gradual changes in bathymetry. In addition, modes are successfully extracted at multiple frequencies from ambient noise.

Enhanced frequency analysis using wavelets

An enhanced frequency analysis method is introduced, using a phase shift wavelet representation, to analyse individual frequency components and to reveal features of a given signal. The frequency representation provides details at each time location without the loss, caused by local orthogonality between the wavelet basis functions and the given signal, which occurs when a normal wavelet decomposition is employed. Movement of the local orthogonality locations, corresponding to the phase shift of the wavelet basis functions, are studied and it is shown that these movements are important and can be used to reveal features of the signal in the frequency domain, such as continuities, smoothness, and trends. Several examples are presented to illustrate the method and an application to a permanent magnet synchronous drive system is provided to demonstrate the approach.

A mathematical theory of comodulation

Amplitude comodulation is the phenomenon that for many types of sound sources, all of the individual frequency components emitted will be amplitude modulated in a related manner, i.e., they will all start/stop and rise/fall together. It is known from various psychophysical studies that comodulation plays an important role in perceptual grouping of sound components. In this work, amplitude comodulation is examined for possible use as a basis for auditory source separation. A derivation is presented of the equations governing a comodulated system for the case of constant frequency sources. A theorem is proved giving necessary and sufficient conditions for uniquely decomposing a sound mixture into its constituent sources. A by-product of these conditions is an understanding of the importance of common onsets and offsets in source separation. An algorithm is presented for computing the unique solution in those cases where one exists. Finally, possible future extensions to the case of frequency varying sources are discussed. [Work supported by NIH Training Grant No. 5T32 DC00038.]

Photon Number Squeezing due to Two-Photon Absorption in Internal and External Fields of a Microcavity

The amplitude and phase noise spectra of the internal and external field of a microcavity are calculated using the quantum mechanical Langevin equations. We assume that two-photon absorber works inside a cavity, which brings photon-number squeezing in the internal field as well as the external field. The individual frequency components of the output field have strong squeezing at cavity resonance due to the interference between the input and the cavity field, which is similar to the quadrature squeezing in a parametric oscillator and the photon number squeezing in a saturated laser oscillator. However, the degree of the squeezing is not perfect becuase the material fluctuation remains.

Detection of quadratic phase coupling between EEG signal components by nonparamatric and parametric methods of bispectral analysis

Recently the assumption of the independence of individual frequency components in a signal has been rejected, for example, for the EEG during defined physiological states such as sleep or sedation [9, 10]. Thus, the use of higher-order spectral analysis capable of detecting interrelations between individual signal components has proved useful. The aim of the present study was to investigate the quality of various non-parametric and parametric estimation algorithms using simulated as well as true physiological data. We employed standard algorithms available for the MATLAB. The results clearly show that parametric bispectral estimation is superior to non-parametric estimation in terms of the quality of peak localisation and the discrimination from other peaks.

Ballistic transport in a two-subband two-dimensional electron system

We report a quantitative study of ballistic transport, via measurements of commensurability oscillations (CO's), in a two-dimensional electron system confined to a wide square quantum well with two electric subbands occupied. The Fourier power spectrum of the CO's shows two clear-frequency components that correspond to ballistic transport in the upper and lower subbands. Through inverse Fourier transformation of each individual frequency component, we reconstruct the CO's of ballistic electrons in different subbands and extract their scattering times.

Auditory grouping

Although our subjective experience of the world is one of discrete sound sources, the individual frequency components that make up these separate sources are spread across the frequency spectrum. Listeners. use various simple cues, including common onset time and harmonicity, to help them achieve this perceptual separation. Our ability to use harmonicity to segregate two simultaneous sound sources is constrained by the frequency resolution of the auditory system, and is much more effective for low-numbered, resolved harmonics than for higher-numbered, unresolved ones. Our ability to use interaural time-differences (ITDs) in perceptual segregation poses a paradox. Although ITDs are the dominant cue for the localization of complex sounds, listeners cannot use ITDs alone to segregate the speech of a single talker from similar simultaneous sounds. Listeners are, however, very good at using ITD to track a particular sound source across time. This difference might reflect two different levels of auditory processing, indicating that listeners attend to grouped auditory objects rather than to those frequencies that share a common ITD.

Overview of frequency-time (spectro-temporal) analysis of signal-averaged electrocardiograms

A N EXTENSION of time-domain analysis of the signal-averaged electrocardiogram (SAECG) is the use of frequency analysis techniques. Standard time-domain methods are useful for identifying clinical subsets of patients likely to suffer arrhythmic events but also suffer from certain limitations. Time-domain methods lose sensitivity and specificity when conduction defects (eg, left bundle branch block) are present.’ In addition, time-domain methods are less valuable in patients with anterior versus inferior infarctions.“J Signal-averaging techniques have been extended to the evaluation of patients with nonsustained ventricular tachycardia (VT), ischemia, and orthotopic cardiac transplantation rejection.4,5 The desire to apply signalaveraging techniques to other patient populations for a variety of clinical purposes has led to a demand for improvement in the techniques. This has led several investigators to initiate work in frequency-domain methods of analysis of the SAECG.6-9 Researchers have become more interested in the Fourier analysis of SAECG due to its ability to separate a complex signal into its individual frequency components while providing their relative intensities.l” Using the Fourier transform, time-domain signals may be transferred into the frequency domain allowing analysis of their frequency components. A common method used for this analysis is the fast Fourier transform (FFT), a computationally efficient algorithm that lends itself to relatively easy application on computer systems. This allows a plot of frequency versus power function. The FFT algorithm has three theoretica drawbacks. The first of these is a trade-off between frequency resolution and time resolution (frequency resolution in Hertz is related to the reciprocal of the time interval in seconds). The second drawback is “leakage,” whereby energy from the main frequency area “leaks” into sidelobes (bordering frequencies) and thus distorts or obscures their measurement. Leakage results because the FFT presumes the signal to be infinitely long when in fact only a ‘*window” of time (ie, a portion of the QRS) is actually examined. And finally, the FFT presumes that the frequency components are stationary (ie, they remain relatively constant). FFT analysis of the SAECG was first performed by Cain and coinvestigators.6 He plotted frequency versus power function of the SAECG of the terminal QRS and ST segment and examined area ratios of highversus lowfrequency components and found this method to be very accurate in identifying the VT patient.