Spectral Peak Frequency Research Articles

A comparison of observed and calculated directional wave spectra in the East China Sea

Directional wave spectra measured by a cloverleaf buoy in the East China Sea during AMTEX '75 have been compared with those calculated with the operational numerical MRI wave model developed at the Meteorological Research Institute of the Japan Meteorological Agency (J.M.A.). It is shown that the numerical wave model MRI can predict rather well, not only the frequency spectrum, but also the angular distribution function of the spectrum. The frequency dependence of the calculated angular distribution function is quite similar to that observed; the angular distribution is narrower for the spectral components near the peak spectral frequency but widens toward high frequencies and approaches the cos2ϑ-distribution.

Comments on 'Theory and application of calibration techniques for an NDBC directional wave measurements buoy' by K.E. Steele, et al.: nonlinear effects

For original paper see ibid., vol. OE-10, no.4, p.382-96 (1985). The authors of the above mentioned paper present an extensive set of linear calibration techniques that are applied to National Data Buoy Center wave-buoy sensor spectral output before calculating and disseminating directional wave spectra. The commentators identify and estimate the nonlinear effects that produce biases still present in the output, due both to wave nonlinearities themselves and to constraints on the buoy and mooring system to the driving forces. Simple models show that these nonlinearities can produce spectral energy biases of 5-15% at and above the spectral peak frequency, and even greater errors below it. NDBC presently records wave data from vertically stabilized and fixed accelerometers and slope sensors. Calculations show that these sensors all incur bias due to wave nonlinearities: this is greater for vertically stabilized accelerometers and least for slope sensors. Effects of the resulting inconsistencies between the different sensors are most pronounced below the spectral peak where the nonlinear terms dominate; these effects are illustrated with measured data.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Effect of low-dose atropine on heart rate fluctuations during orthostatic load: a spectral analysis

Spectral analysis was utilized in order to determine the influence of low (0.7 μg/kg)-dose atropine sulfate injections on the isolated spectral power components of heart rate fluctuations in contrast to moderate (0.02 mg/dose)-dose atropine and unmedicated states in human subjects during orthostatic load. Low-dose atropine decreased mean heart rate and increased respiration-related spectral power compared with controls in both the supine and standing posture. In supine subjects total power (0.01-0.5 Hz) was unchanged compared with controls due to a decreasing trend of low-frequency (0.01-0.05 Hz) and mid-frequency (0.05-0.15 Hz) heart rate spectral power. Standing upright, there was a distinct increase in total power with significantly higher values than in the controls resulting from an enormous activation of mid-frequency heart rate fluctuations. The peak frequency of the mid-frequency component was increased with a strong tendency compared with controls. Moderate-dose atropine increased mean heart rate and decreased total power, mid-frequency and respiration-related heart rate spectral power and peak frequency compared with controls in both positions. Our results suggest that low-dose atropine affects the interaction between sympathetic and parasympathetic limbs in the autonomic control of cardiac function in a complex manner producing a differentiated pattern of heart rate fluctuations dependent on the body posture. We suggest that low-dose atropine augments and moderate-dose atropine attenuates the vagal cardiac efferent activity in each position.

Stability of the heart rate power spectrum over time in the conscious dog.

The purpose of this experiment was to test the stability of the heart rate (HR) power spectrum over time in conscious dogs. HR was recorded for 1 h for each of six animals on 2 days. A Fast Fourier transform was used to derive the HR power spectrum for the 12 contiguous 5-min epochs comprising the 1-h recordings. Changes in frequency and amplitude of the various spectral peaks were quantitatively examined. We confirm the presence of two major concentrations of power centered around 0.02 (low frequency peak) and 0.32 Hz (high frequency peak). However, we observed variations in these spectral peaks, especially their amplitudes, both within each hour and from day 1 to day 2. The amplitudes of these two spectral peaks tended to vary reciprocally. HR power spectra based on 5 min of recorded data were also derived from an additional eight animals in both the lying and standing positions; the power spectra from these short recordings were sufficiently sensitive to detect redistributions in power due to changes in posture in all eight dogs. We conclude that: 1) data should be recorded for relatively long periods (e.g., 1 h) to characterize the HR power spectrum; 2) some variability in frequency and amplitude will persist across spectra even when based on longer data bases; 3) care should be taken to ensure that the subject's behavioral state is stable within the recording period; 4) shorter (e.g., 5 min) data bases are not suitable except for detecting relatively robust changes in the HR power spectrum.

The Marple algorithm for the autoregressive spectral estimates of the SMMW fourier transform spectroscopy data

The Marple algorthm for the autoregressive spectral estimates has been applied to the SMMW Fourier transform spectrum analysis. The experimental results have shown that this method yields AR spectra with three times higher resolution than the FFT method does. The improvements obtained from the Marple algorithm over the maximum entropy algorithm include higher resolution, less bias in the spectral peak frequency estimation and absence of observed spectral line splitting. The effects of the structure of the spectral lines and the noise on the resolution are discussed.

Modeling the perception of concurrent vowels: vowels with the same fundamental frequency.

The ability of listeners to identify pairs of simultaneous synthetic vowels has been investigated in the first of a series of studies on the extraction of phonetic information from multiple-talker waveforms. Both members of the vowel pair had the same onset and offset times and a constant fundamental frequency of 100 Hz. Listeners identified both vowels with an accuracy significantly greater than chance. The pattern of correct responses and confusions was similar for vowels generated by (a) cascade formant synthesis and (b) additive harmonic synthesis that replaced each of the lowest three formants with a single pair of harmonics of equal amplitude. In order to choose an appropriate model for describing listeners' performance, four pattern-matching procedures were evaluated. Each predicted the probability that (i) any individual vowel would be selected as one of the two responses, and (ii) any pair of vowels would be selected. These probabilities were estimated from measures of the similarities of the auditory excitation patterns of the double vowels to those of single-vowel reference patterns. Up to 88% of the variance in individual responses and up to 67% of the variance in pairwise responses could be accounted for by procedures that highlighted spectral peaks and shoulders in the excitation pattern. Procedures that assigned uniform weight to all regions of the excitation pattern gave poorer predictions. These findings support the hypothesis that the auditory system pays particular attention to the frequencies of spectral peaks, and possibly also of shoulders, when identifying vowels. One virtue of this strategy is that the spectral peaks and shoulders can indicate the frequencies of formants when other aspects of spectral shape are obscured by competing sounds.

Spline function approximation for velocimeter Doppler frequency measurement

A spline function approximation approach for measuring the Doppler spectral peak frequency in a laser Doppler velocimeter system is presented. The processor is designed for signal bursts with mean Doppler shift frequencies up to 100 MHz, input turbulence up to 20%, and photon counts as low as 300. The frequency-domain processor uses a bank of digital bandpass filters for the capture of the energy spectrum of each signal burst. The average values of the filter output energies, as a function of normalized frequency, are modeled as deterministic spline functions which are linearly weighted to evaluate the spectral peak location associated with the Doppler shift. The weighting coefficients are chosen to minimize the mean square error. Performance evaluation by simulation yields average errors in estimating mean Doppler frequencies within 0.5% for poor signal-to-noise conditions associated with a low photon count of 300 photons/burst. >

Within‐subject comparisons of analog and pulsatile speech processors for cochlear implants

Analog and pulsatile speech processors for cochlear implants represent widely different strategies for coding perceptual information in speech. Between‐subject comparisons of their efficacy, however, have been confounded by large and unquantified subject differences. Two patients implanted with multiple electrode arrays have been tested both with four‐channel analog and pulsatile coding strategies. The analog processor performed bandpass filtering with syllabic compression/limiting and stimulated four bipolar electrode pairs. The pulsatile processor delivered volleys of biphasic pulses at the rate of F0 during voiced intervals of speech to four of six possible bipolar electrode pairs selected on the basis of spectral peak frequencies. Tests of auditory capabilities showed that the two coding strategies provided similar overall benefit. Analyses of consonant and vowel confusions revealed that the two strategies were not equally effective for some types of speech information. The results of these analyses can be used to identify the strengths and weaknesses of analog and pulsatile speech coding strategies for cochlear implants.

A Finite-Depth Wind-Wave Model. Part I: Model Description

Abstract A parametric windsea model for arbitrary water depths is presented. The model is derived from a conservation of energy flux formulation and includes shoaling, refraction, dissipation by bottom friction, as well as finite-depth modifications of the atmospheric input and nonlinear wave–wave interaction source terms. The importance of dissipation due to a rough ocean floor on the migration of the spectral peak frequency is discussed and compared with that caused by nonlinear energy transfer. Numerical simulations are used to systematically examine wave growth and the development of the spectral peak in a depth-limited ocean. Two idealized situations of wave growth and propagation are considered to further understand the influence of bottom friction on the spectral dynamics. The first case studies the characteristics of fetch-limited wave growth in a steady, uniform wind as function of depth and bottom roughness. The second case examines the role of bottom dissipation on a fully developed deep-water ...

Resonance of a fluid‐driven crack: Radiation properties and implications for the source of long‐period events and harmonic tremor

A dynamic source model is presented, in which a three‐dimensional crack containing a viscous compressible fluid is excited into resonance by an impulsive pressure transient applied over a small area ΔS of the crack surface. The crack excitation depends critically on two dimensionless parameters called the crack stiffness, C = (b/μ)(L/d), and viscous damping loss, F = (12ηL)/(ρƒd2α), where b is the bulk modulus, η is the viscosity, ρƒ is the density of the fluid, μ is the rigidity, α is the compressional velocity of the solid, L is the crack length, and d is the crack thickness. The first parameter characterizes the ability of the crack to vibrate and shapes the spectral signature of the source, and the second quantifies the effect of fluid viscosity on the duration of resonance. Resonance is sustained by a very slow wave trapped in the fluid‐filled crack. This guided wave, called the crack wave, is similar to the tube wave propagating in a fluid‐filled borehole; it is inversely dispersive, showing a phase velocity that decreases with increasing wavelength, and its wave speed is always lower than the acoustic velocity of the fluid, decreasing rapidly as the crack stiffness increases. The source spectrum shows many sharp peaks characterizing the individual modes of vibration of the crack; the variation of spectral shape, both in the number and width of peaks, is surprisingly complex, reflecting the interference between the lateral and longitudinal modes of resonance, as well as nodes for these modes. The far‐field spectrum is marked by narrow‐band dominant and subdominant peaks that reflect the interaction of the various source modes. The frequency of the dominant spectral peak radiated by the source is independent of the radiation direction. The frequency, bandwidth, and spacing of the resonant peaks are strongly dependent on the crack stiffness, larger values of the stiffness factor shifting these peaks to lower frequencies and decreasing their bandwidth. The excitation of a particular mode depends on the position of the trigger and on the extent of the crack surface affected by the pressure transient. Fluid viscosity decreases the amplitudes of the main spectral peaks, smears out the finer structure of the spectrum, and greatly reduces the duration of the radiated signal. The energy loss by radiation is stronger for high frequencies, producing a seismic signature that is marked by a high‐frequency content near the onset of the signal and dominated by a longer‐period component of much longer duration in the signal coda. Such signature is in harmony with those displayed by long‐period events observed on active volcanoes and in hydrofracture experiments. The very low velocity which is possible in a crack with high stiffness (C ≥ 100) also provides an attractive explanation for very long period tremor, such as type 2 tremor at Aso volcano, Japan, without the requirement of an unrealistically large magma container. The standing wave pattern set up on the crack surface by the sustained resonance in the fluid is observable in the near field of the crack, suggesting that the location and extent of the source may be estimated from the mapping of the pattern of nodes and antinodes seen in its vicinity. According to the model, the long‐period event and harmonic tremor share the same source but differ in the boundary conditions for fluid flow and in the triggering mechanism setting up the resonance of the source, the former being viewed as the impulse response of the tremor generating system and the latter representing the excitation due to more complex forcing functions.

Power spectra of inspiratory nerve activity with lung inflations in cats.

To investigate the effect of lung inflations on the high-frequency synchrony (70-122 Hz) observed in the inspiratory activity of respiratory motor nerves of decerebrate cats, I applied a step increase in lung inflation pressure at fixed delays into the inspiratory phase and computed power spectra of phrenic neurograms before and during inflation. In 25 decerebrate paralyzed cats the frequency of the high spectral peak was 92.3 +/- 11.1 Hz before and 105.3 +/- 12.1 Hz during the step in inflation pressure, shifting upward by 13.0 +/- 6.0 Hz. For 8 of the 25 cats, the recurrent laryngeal and phrenic neurograms were recorded simultaneously. The high spectral peak was present during inspiration in the recurrent laryngeal power spectra and coherent with the high peak in the phrenic power spectra. In response to lung inflation, the high peak disappeared from the power spectra of the recurrent laryngeal nerve as the inspiratory activity was inhibited; a shift upward in frequency was not detectable. Comparing inspiratory times (TI, based on the phrenic neurograms) for breaths with no lung inflations to those for breaths with lung inflations, I found that lung inflations early in inspiration caused a decrease in TI, lung inflations at intermediates times had no effect on TI, and lung inflations late in inspiration caused an increase in TI. Despite lung inflation decreasing, not affecting, or increasing inspiratory duration and amplitude of the phrenic neurogram, lung inflation always caused a shift upward in the high-frequency peak of the phrenic power density. The fact that lung inflation, a powerful respiratory stimulus, affected the frequency of the high peak in a consistent manner suggests that the high-frequency synchrony is an important and robust feature of the central respiratory pattern generator.

IRREGULAR WAVE LOADING ON A CONICAL STRUCTURE

The horizontal forces, vertical forces and overturning moments exerted by waves on a fixed model of a 45" conical structure are presented. Irregular wave loading tests were conducted for a range of conditions described by base diameter on peak period wave length D/Lp from 0.31 to 1.76, water depth on peak period wave length h/Lp from 0.11 to 0.63, and significant wave height on peak period wave length Hm./Lp up to 0.07. Time series records, spectral densities and transfer functions for the irregular wave loading tests are used to illustrate the nonlinear nature of the measured wave loads. In most cases, similar trends in wave loading were observed for irregular and regular wave tests. For deep-water waves, the irregular and regular force measurements showed spectral peaks at the second harmonic of the wave frequency even though the waves themselves had relatively small second-order components. However, unlike the regular wave loading results, the fundamental spectral peak frequency for the irregular wave forces occurred at a frequency considerably lower than the peak frequency of the waves. Although linear diffraction theory provided a reasonable estimate of the wave forces for waves of low steepness, larger deviations were often present for higher wave steepness results. Comparison of theory and experiment for overturning moments was generally very poor for most wave conditions.

Near‐inertial current oscillations in the vicinity of the Bering Sea marginal ice zone

Near‐inertial current oscillations with 10–20‐cm/s amplitudes were prevalent over the Bering Sea shelf during November 1982 and again in March and April 1983 and also evident at reduced amplitudes during the intervening winter. Spectral peak frequencies were consistently within ∼1% of the local inertial frequency ƒ, in contrast to the more superinertial (∼5% aboveƒ) frequencies commonly reported elsewhere. A superinertial secondary energy peak at 1.038ƒ was evident, corresponding to the first‐mode wave. Amplitudes decreased with distance shoreward from the shelf break, consistent with the effects of decreasing bottom depth and increasing mixed layer depth. The oscillations were highly coherent over ∼100 km distances, similar to observations reported by Thomson and Huggett (1981) for the British Columbia coast, whereas near‐inertial oscillations have been commonly reported to be uncoupled over much shorter (∼10 km) distances in other regions. Vigorous near‐inertial “ringing” was associated with rapidly passing weather systems. The decline in near‐inertial oscillation amplitudes during winter was partially due to a significant reduction in both cyclone frequency and occurrence of wind events causing clockwise wind shifts. The decline was enhanced by reduction in the vertical stratification needed to support inertio‐gravity internal waves, as the shelf waters apparently became mixed from top to bottom. The loose, mobile sea ice in the winter marginal ice zone (MIZ) did not appear to inhibit wind generation of the inertial oscillations. The presence of sea ice appears, in fact, to have contributed to the spring increase of near‐inertial current amplitudes through restratification of the water column caused by melting ice. Our observations, particularly the spatial coherency and spectral properties, were generally consistent with Kundu and Thomson's (1985) model for inertio‐gravity waves generated in the wake of a translating weather front. The half wavelength typical of these waves forced by transiting weather fronts on the Bering shelf appears to be ∼150 km, or approximately the width of the winter MIZ. The associated near‐inertial currents are 180° out of phase with those a half wavelength away in the direction of phase propagation. Thus a storm passing perpendicular to the ice edge can excite waves at near‐inertial frequencies which compress, deform, and dilate the ice pack by up to a few percent of the MIZ width. We suggest that this mechanism, in conjunction with near‐inertial interfacial shear which can increase upward heat flux, influences the width scale of the MIZ.

Mating behaviour and male mating success in the green treefrog

Green treefrogs, Hyla cinerea, at a study site in eastern Georgia behaved as prolonged breeders: there were many more males present each night than females, the arrival of which was unpredictable. Individual males were usually consistent in their behaviour during a single night, and were most often observed calling. There was a weak, negative correlation between male size (snout-vent length, unless otherwise stated) and the frequency of satellite behaviour, defined as a non-calling male's being situated near a calling male. In 2 of 3 years, the mean size of males observed as satellites was less than that of the calling males with which they were associated on a given night; however, many satellites were the same size or larger than calling males. The distributions of matings per male during three seasons were not significantly different than Poisson distributions with the same means. Individual mating success was best predicted by attendance at the breeding site; mating success was negatively related to the frequency of satellite behaviour in some analyses, but very little of the variance was explained. An exhaustive series of analyses failed to show any pattern of size-dependent mating, including weight-assortative mating, even when males that were frequently satellites were excluded. The relative sizes of males and females in amplexus had little effect on fertilization success. On a seasonal basis, males were clumped in their spatial distribution, and matings tended to occur where male density was highest. Individual males were highly variable in their patterns of movement, which were not correlated with size or mating success. Mating success was also unrelated to the frequency (Hz) of the low-frequency spectral peak in the advertisement call of the male; male size and weight were negatively correlated with the frequency of the low-frequency peak.

Vowel and consonant recognition of cochlear implant patients using formant-estimating speech processors.

Vowel and consonant confusion matrices were collected in the hearing alone (H), lipreading alone (L), and hearing plus lipreading (HL) conditions for 28 patients participating in the clinical trial of the multiple-channel cochlear implant. All patients were profound-to-totally deaf and "hearing" refers to the presentation of auditory information via the implant. The average scores were 49% for vowels and 37% for consonants in the H condition and the HL scores were significantly higher than the L scores. Information transmission and multidimensional scaling analyses showed that different speech features were conveyed at different levels in the H and L conditions. In the HL condition, the visual and auditory signals provided independent information sources for each feature. For vowels, the auditory signal was the major source of duration information, while the visual signal was the major source of first and second formant frequency information. The implant provided information about the amplitude envelope of the speech and the estimated frequency of the main spectral peak between 800 and 4000 Hz, which was useful for consonant recognition. A speech processor that coded the estimated frequency and amplitude of an additional peak between 300 and 1000 Hz was shown to increase the vowel and consonant recognition in the H condition by improving the transmission of first formant and voicing information.

Raman study of glassy aqueous solutions of magnesium salts: MgCl2, Mg(NO3)2, MgSO4 and Mg(ClO4)2

AbstractRaman spectra were obtained for aqueous solutions of MgCl2, Mg(NO3)2, MgSO4 and Mg(ClO4)2 in both liquid and glassy states. Spectral changes associated with the transition from the liquid to the glassy state were studied for the Raman OH stretching spectra, and the restricted translational Raman bands of the low‐frequency Raman spectra of the glassy solutions were characterized. It is shown that the spectral features and peak frequencies are greatly dependent on the chemical natures of the anions.

Similarity of the wind wave spectrum in finite depth water part 2: Statistical relations between shape and growth stage parameters

This paper continues the description of surface waves on finite depth water started in Bouws et al. [1985]. We present relationships between the parameters of the wind wave spectra similar to the correlation found in deep water between total energy and spectral peak frequency. In contrast to deep water the peak frequency is not the most convenient parameter to describe spectral development. The wave number of the spectral peak, however, is connected with other spectral parameters by relations that are independent of water depth or site.

Performance of a Discrete Spectral Peak Frequency Estimator for Doppler Wind Velocity Measurements

A frequency estimator formed from the peak of a discrete power spectrum is examined. Expressions to compute the performance of the estimator as a function of input signal bandwidth and signal-to-noise ratio are developed and used to study the estimator's capability to measure signal mean frequencies for remote Doppler measurement of atmospheric winds. Performance comparisons with the widely used complex-covariance estimator, based on simulations, show that frequency estimates formed from the spectral peak tend to have larger variance, except in the case of narrow-band input signals where the estimate standard deviation approaches that of the complex-covariance estimator.

Is it valid to use the linear gravity-wave dispersion relation when interpreting HF radar measurements?

Wave-tank measurements show that some wind waves travel at a speed that corresponds more closely to the spectral peak frequency than to the linear dispersion relation. However, Bragg echoes sampled and averaged in space and time by HF radars tend to obey the linear dispersion relation. Resolution of the dilemma will require new measurements with incisive attention to their meaning.

The role of the gravity-wave dispersion relation in HF radar measurements of the sea surface

Recent experimental and theoretical findings raise interesting questions about the applicability of the normal gravity-wave dispersion relation at wave frequencies that exceed the spectral peak frequency. The use of the dispersion relation in analysis of HF radar Doppler sea echo is examined in this paper. Drawing on the results of perturbation theory for wave-wave nonlinear interactions, we show that this relation, so essential to echo interpretation in terms of current and wave information, can be employed with no degradation in accuracy for current measurement when the dominant wave frequency is considerably less (by as much as 10) than the radar Bragg resonance frequency. This finding is supported by comparisons of currents measured by HF radar with surface truth; the first-order echo must only be identifiable in order to be used accurately. Wave-height directional spectral information can be extracted from the second-order echo at a given radar frequency up to the point (in wave height) where the perturbation solution employed in the inversion process fails; then a lower radar frequency must be used. On the other hand, most conventional wave measuring instruments should not use the dispersion relation for interpretation of data well beyond the spectral peak, because they do not observe wave height as a function of both space and time independently, as does HF radar.