Coherent Averaging Research Articles

Use of amplitude without phase angle to achieve pseudo-coherent processing gain

Processing gain as much as 3 dB per average doubling can be achieved by coherent temporal averaging (i.e., with phase), compared to 1.5 dB per doubling for incoherent averaging (i.e., without phase). However, it is not uncommon for signals to be coherently cancelled as if they never existed, or be severely attenuated. For this reason, coherent temporal averaging is seldom used. A method is presented that utilizes amplitudes to generate ‘‘pseudo-phase angles’’ (not real angles). Pseudo-phase angles are combined with the corresponding amplitudes to form pseudo-vectors for vector and coherent averaging. Thus, the large gains that are normally associated only with coherent processing can be achieved without using the real phase angles. This ‘‘pseudo-coherent’’ gain is about the same as coherent averaging gain, but signals are not cancelled. Furthermore, the pseudo-phase angles can be used to automatically detect signals. Results from measured data will be presented to illustrate pseudo-coherent gains in signal-to-noise ratio of 10 dB, minimum detectable level of 3 dB, resolution of 2×, and automatic signal detection. [Work supported by U.S. Army Space and Missile Defence Command.]

Evaluation of a high-speed signal-averager for sensitivity enhancement in radio frequency Fourier transform electron paramagnetic resonance imaging

A commercially available high-speed, digital signal-averager is integrated into an existing time-domain radio frequency (rf) electron paramagnetic resonance (EPR) spectrometer/imager. Sensitivity enhancement by the integrated system is estimated by coherent averaging of free induction decay signals, obtained from narrow-line EPR spin probes, and its performance is compared with that of an existing custom-built averager. For the existing custom-built “Analytek” averager, the minimum realizable trigger rate was 50 kHz, whereas for the commercial EG&G 9826 system, due the spectrometer constraints, we set the retrigger rate to 133 kHz. Very short summing and down loading times of the latter enable good temporal resolution in phantom as well as in vivo rf Fourier transform EPR images, obtained by the single point imaging (SPI) modality. For two-dimensional and three-dimensional imaging using the SPI mode, a saving of time by a factor of >2 could be achieved with the EG&G system compared with the Analytek.

Phase coherent averaging in magnetic resonance spectroscopy using interleaved navigator scans: compensation of motion artifacts and magnetic field instabilities.

The quality of spectra in (1)H magnetic resonance spectroscopy (MRS) is strongly affected by temporal signal instabilities during the acquisition. One reason for these instabilities are hardware imperfections, e.g., drifts of the main magnetic field in superconducting magnets. This is of special concern in high-field systems where the specification of the field stability is close to the spectral linewidth. A second major potential source of artifacts, particularly in clinical MRS, is patient motion. Using standard acquisition schemes of phase-cycled averaging of the individual acquisitions, long-term effects (field drifts) as well as changes on a shorter time scale (motion) can severely reduce spectral quality. The new technique for volume-selective MRS presented here is based on the additional interleaved acquisition of a navigator signal during the recovery time of the metabolite acquisition. It corrects for temporal signal instabilities by means of a deconvolution of the metabolite and the navigator signal. This leads to phase-corrected individual metabolite scans and upon summation to a phase-coherent averaging scheme. The interleaved navigator acquisition does not require any user interaction or supervision, while sequence efficiency is maintained.

Whale contribution to long time series of low-frequency oceanic ambient sound

It has long been known that baleen (mainly blue and fin) whale vocalizations are a component of oceanic ambient sound. Urick reports that the famous ‘‘20-cycle pulses’’ were observed even from the first Navy hydrophone installations in the early 1950’s. As part of the Acoustic Thermometry Ocean Climate (ATOC) and the North Pacific Acoustic Laboratory (NPAL) programs, more than 6 years of nearly continuous ambient sound data have been collected from Sound Surveillance System (SOSUS) sites in the northeast Pacific. These records now show that the average level of the ambient sound has risen by as much as 10 dB since the 1960’s. Although much of this increase is probably attributable to manmade sources, the whale call component is still prominent. The data also show that the whale signal is clearly seasonal: in coherent averages of year-long records, the whale call signal is the only feature that stands out, making strong and repeatable patterns as the whale population migrates past the hydrophone systems. This prominent and sometimes dominant component of ambient sound has perhaps not been fully appreciated in current ambient noise models. [Work supported by ONR.]

Signal de‐noising in magnetic resonance spectroscopy using wavelet transforms

AbstractComputer signal processing is used for quantitative data analysis (QDA) in magnetic resonance spectroscopy (MRS). The main difficulty in QDA is that MRS signals appear to be contaminated with random noise. Noise reduction can be achieved by coherent averaging, but it is not always possible to average many MRS waveforms. Wavelet shrinkage de‐noising (WSD) is a technique that can be employed in this case. The potentialities of WSD in MRS, alone and combined with the Cadzow algorithm, are analyzed through computer simulations. The results can facilitate an appropriate application of WSD, as well as a deeper understanding of this technique. © 2002 Wiley Periodicals, Inc. Concepts Magn Reson 14: 388–401, 2002

Rough boundary effects on shallow water propagation: Some comparisons between GRAB and PE

The Gaussian Ray Bundle (GRAB) computer code is an accepted Navy Standard for calculating propagation. GRAB uses an effective reflection loss to approximate the effect of ocean surface roughness. Results for GRAB and rough surface PE are compared for a shallow water waveguide (50 m depth with a sand bottom) for several wind speeds and for ranges up to 5 km. A special case examined is a 3.2 kHz source at mid depth with a 10° beamwidth and 10° grazing angle. The GRAB results use the Bechmann-Spezzichino reflection coefficient module. The PE results are calculated using 50 realizations of a Pierson–Moskowitz surface and either coherent or incoherent averaging. GRAB with Bechmann–Spezzichino is most appropriately compared to the PE coherent averages. This comparison shows differences on the order of 3 dB in the intensity averaged across water depth at 5 km and a wind speed of 5 m/s. The general implications of these differences as well as differences seen in the intensity as a function of depth at discussed. Work supported by the ONR.

Focused synthetic aperture radar processing of ice-sounder data collected over the Greenland ice sheet

The authors developed a synthetic aperture radar (SAR) processing algorithm for airborne/spaceborne ice-sounding radar systems and applied it to data collected in Greenland. By using focused SAR (phase-corrected coherent averaging), they improved along-track resolution by a factor of four and provided a 6-dB processing gain over unfocused SAR (coherent averaging without phase correction) based on a point-target analysis for a Greenland ice-sounding data set. Also, They demonstrated that the focused-SAR processing reduced clutter and enabled them to identify bedrock-interface returns buried in clutter. Using focused-SAR technique, they processed data collected over a key 360-km-long portion of the 2000-m contour line of southwest Greenland. To the best of their knowledge, these are the first high-quality radar ice thickness measurements over this key location. Moreover, these ice-thickness measurements have been used for improving mass-balance estimates of the Greenland ice sheet.

Toeplitz and Hankel kernels for estimating time-varying spectra of discrete-time random processes

For a nonstationary random process, the dual-time correlation function and the dual frequency Loeve spectrum are complete theoretical descriptions of second-order behavior. That is, each may be used to synthesize the random process itself, according to the Cramer-Loeve spectral representation. When suitably transformed on one of its two variables, each of these descriptions produces a time-varying spectrum. This spectrum is, in fact, the expected value of the Rihaczek distribution. In this paper, we derive two large families of estimators for this spectrum: one based on a diagonal-Toeplitz-diagonal (dTd) factorization of smoothing kernels and the other based on a diagonal-Hankel-diagonal (dHd) factorization. The dTd factorization produces noncoherent averages of the time-varying spectrogram, and the dHd factorization produces coherent averages. Some of the dTd estimators may be called time-varying power spectrum estimators, and some of the dHd estimators may be called time-varying Wigner-Ville (WV) estimators. The former may always be implemented as multiwindow spectrum estimators, and in some casts, they are true time variations on the Blackman-Tukey-Rosenblatt-Grenander (BTGR) spectrogram. The latter are variations on the Stankovic class of WV estimators.

Quantum codes for controlling coherent evolution

Control over spin dynamics has been obtained in nuclear magnetic resonance (NMR) via coherent averaging, which modifies the effective internal Hamiltonian, and via quantum codes, which can protect against decoherent evolution. Here, we discuss the design and implementation of quantum codes that enable modification of the internal Hamiltonian. A detailed example is given of a quantum code for protecting two data spins from evolution under a weak coupling term in the Hamiltonian, using an “isolated” ancilla that does not evolve on the experimental time scale. The code is realized in a three-spin system by liquid-state NMR spectroscopy on 13C-labeled alanine, and tested for two initial states. It is also shown that with internal interactions and isolated ancillae, codes exist that do not require the ancillae to initially be in a (pseudo-) pure state. Finally, it is shown that even with nonisolated ancillae, quantum codes exist which can protect against evolution under weak coupling. An example is presented for a six-qubit code that protects two data spins to first order.

Meteor observations with a modern digital ionosonde

A modern low-power digital ionosonde was easily adapted to meteor observations. To achieve usable meteor rates it was necessary to improve performance, mainly by significantly increasing the pulse repetition frequency and using coherent averaging. Measurements were made at 9.3 MHz. Our maximum hourly meteor rates were ∼35 in early morning, the majority of the echoes being of the overdense/underdense transitional type. The height distribution of the meteors maximized at 93km, and the typical echo was seen at a zenith angle of 30° towards north. Diffusion coefficients and winds were measured.

Amplitude modulation and relaxation due to diffusion in NMR experiments with a rotating sample

The simultaneous effects of diffusion and coherent averaging by magic angle sample spinning (MASS) are investigated both theoretically and experimentally for spins diffusing in a spatially varying susceptibility field. The diffusion introduces a periodic modulation and a relaxation of the magnetization amplitude. The attenuation exponent for the nth echo at an early time is given by D 0 γ 2 g 2 πn/(4 ω r 3), where ω r is the rotor frequency, D 0 the diffusion coefficient, γ is the gyromagnetic factor, and a factor g 2 which is related to, but different from, the volume average of the gradient squared.

Processing of Abdominal Fetal Electrocardiogram—A Review

The fetal heart signal is useful in the management of the birth process as well as in assessing fetal development including congenital defects. The fetal electrocardiogram can be recorded noninvasively by placing the electrodes on the mother's abdomen. The abdominal fetal signal consists of a weak fetal signal, a relatively strong maternal heart signal and considerable noise contributed by electrical potential from the maternal abdominal muscles and random electrical noise. Several techniques have been developed to improve the quality of fetal signals. These techniques include coherent time averaging, correlation techniques, spatial filtering techniques, estimation techniques, adaptive filtering techniques and so on. In this paper various techniques proposed for improving the signal-to-noise ratio of abdominal fetal electrocardiogram are studied and their performances are compared.

The development of a software program for analyzing spontaneous and externally elicited skin conductance changes in infants and adults

Objectives: Changes in palmar and plantar skin conductance (SC) are due to outgoing bursts in the postganglionic efferent sympathetic cholinergic fibres, which responds to changes in central arousal state. The purpose of this study was designed to develop a software program for analyzing spontaneous and external elicited SC changes for infants and adults.Methods: The program was designed to calculate the number and mean amplitude of the waves as well as the mean basal level in a given period. Different pre-set values for the minimum amplitude, maximum slope and minimum width of the spontaneous waves were used in the analysis program, and the results were compared with manually counted waves. The program was also used to perform coherent averaging of repeated elicited SC changes. For the mean elicited skin conductance responses, the latency time, response amplitude and recovery time were calculated. The habituation pattern could be calculated semi-automatically by analyzing each response.Results: For SC waves, the minimum amplitude and the maximum slope should be, respectively, 0.02 microsiemens (μS) and 2 μS/s for infants and adults, and the width of the waves should be at least 1 s for adults, and unlimited for infants. The coherent average method was found to be a satisfactory method for revealing whether a subject responded to stimuli, and is recommended, especially for infants.Conclusions: Spontaneous and stimulated skin conductance are easily analyzed by this software program.

Dynamic cerebral autoregulation in sick newborn infants.

The sick newborn infant is vulnerable to brain injury and impaired cerebral autoregulation is thought to contribute to this. Coherent averaging is a method of measuring the dynamic cerebral autoregulatory response that is particularly suitable for neonates. We used this method in combination with a measure of the gradient of the cerebral blood flow velocity (CBFV) response following transient blood pressure (BP) peaks to study dynamic autoregulation in infants undergoing intensive care. Term and preterm infants at high risk of neurologic injury were compared with a control group of infants, also undergoing intensive care. Simultaneous video-EEG, CBFV (using transcranial Doppler), and arterial blood pressure measurements were obtained intermittently during a study period of at least 2 h. Cerebral autoregulatory response curves were constructed for high risk and control groups. Intact cerebral autoregulation produces a characteristic response consisting of a brief period when CBFV follows arterial blood pressure but quickly returns to baseline value. An impaired autoregulatory response shows CBFV mirroring the arterial blood pressure curve closely. Thirteen high-risk infants, who also had seizures (10 term and 3 preterm) and 12 control infants (6 term and 6 preterm) were studied. Autoregulation was absent in high-risk term and preterm infants. It was also absent in preterm control infants. Term, neurologically healthy infants undergoing intensive care have an intact autoregulatory response. The constant passive response seen in high-risk infants may reflect the severity of the underlying neurologic disease.

High-resolution proton solid-state NMR spectroscopy by phase-modulated Lee–Goldburg experiment

In this Letter, we present a pulse scheme for coherent averaging of spin–spin interactions called phase-modulated Lee–Goldburg (PMLG) which is aimed at achieving high-resolution proton NMR spectra in the solid state. Our objective is mainly to discuss the design and execution of this experiment and to show some preliminary experimental results as evidence of the far-reaching potentials of this technique.

An acoustic model of a laminar sand bed

It was postulated that a laminar sand bed may be modeled as an ensemble of randomly layered Biot media. The thickness of each layer was approximately half a grain diameter. The porosity variations in the vertical direction were matched to the mean and standard deviation of that of a structure of packed spherical grains. The effect of large-scale lateral variations in porosity was simulated by performing a coherent ensemble average of the acoustic output from several realizations of the randomly layered medium. The medium parameters were chosen to represent water-saturated sand. Specifically, the sand bed was modeled as bounded by a homogeneous water halfspace above, and a homogeneous poroelastic halfspace of equal average porosity below. Reflected and transmitted signals were computed. Coherent and random components of the reflected signal were calculated. The coherent parts were directly related to the reflected and the transmitted waves. Results showed significant differences between the modeled sand bed and an equivalent uniform Biot medium. In the modeled sand bed, the fast wave attenuation was found to be anisotropic, and a propagating slow wave was excited at most incident angles, except at normal incidence, which may explain the apparent failure to detect the slow wave of certain experiments.

A method of assessing ventilatory responses to chemoreceptor stimulation in infants

Various methods of assessing infant chemoreceptor responses have been reported in the literature. However, equipment dead space, trigeminal stimulation and inherent respiratory variability may have affected the results. A method is presented which attempts to reduce the effect of these factors and thereby isolate the chemoreceptor response. Inspiratory gas was delivered into a lightweight face mask with a pliable rim, minimal dead space and a connected pneumotachograph. Ventilatory data were computed breath by breath. Computer‐controlled electromagnetic valves allowed instantaneous switching between air and different gas mixtures, repeated in a randomized sequence. In 18 healthy term neonates, the mask increased ventilation by 12% (95% confidence interval 6—18%), measured by calibrated strain‐gauge bands. The effect on respiratory frequency and tidal volume differed significantly between sleep states. Neonates were challenged with short‐lasting hyperoxia, mild hypoxia, rebreathing and mild hypercapnia. Coherent averaging of several ventilatory responses from each sleep state reduced the variability while maintaining a high time‐resolution. □Chemoreceptors, infant, respiration, respiratory dead space

Cerebrovascular Response to Dynamic Changes in pCO2

Fifty-six subjects with carotid artery disease were assessed by measuring the cerebral blood flow velocity (CBFV) change in response to inhalation of 5% CO₂ in air whilst continuously monitoring the blood pressure (BP). Coherent averaging of the data characterised differences in CBFV, BP, resistance area product and critical closing pressure during changes in end-tidal CO₂ (ETCO₂). The results primarily demonstrate that the augmentation of ETCO₂ increases the CBFV and BP, causing a pressure autoregulatory response, and allows the processes of pressure autoregulation and cerebral vascular reserve to be differentiated.

A method of assessing ventilatory responses to chemoreceptor stimulation in infants.

Various methods of assessing infant chemoreceptor responses have been reported in the literature. However, equipment dead space, trigeminal stimulation and inherent respiratory variability may have affected the results. A method is presented which attempts to reduce the effect of these factors and thereby isolate the chemoreceptor response. Inspiratory gas was delivered into a lightweight face mask with a pliable rim, minimal dead space and a connected pneumotachograph. Ventilatory data were computed breath by breath. Computer-controlled electromagnetic valves allowed instantaneous switching between air and different gas mixtures, repeated in a randomized sequence. In 18 healthy term neonates, the mask increased ventilation by 12% (95% confidence interval 6-18%), measured by calibrated strain-gauge bands. The effect on respiratory frequency and tidal volume differed significantly between sleep states. Neonates were challenged with short-lasting hyperoxia, mild hypoxia, rebreathing and mild hypercapnia. Coherent averaging of several ventilatory responses from each sleep state reduced the variability while maintaining a high time-resolution.

An optical dilatometer for picometre displacements

A HeNe laser driven optical dilatometer with differential properties, which can measure displacements with a resolution of m over the flat frequency range from 0 to 1 kHz, is described. Its principal feature is a parallel arrangement of two, mirror symmetrical, optical paths of which one has an actively operated measurement sample to be studied and the other a similar, passive sample. The arrangement ensures good short- and long-term stability, thus allowing coherent averaging of sample responses over extended periods of time. Resolution thereby increases to m when averaging over 10 000 responses. Since both channels are about equally affected by environmental mechanical disturbances, an algorithm compares the outputs from the parallel channels and rejects correlated vibration and noise components. This increases resolution by an additional factor of five under a reduction in the frequency response. It brings the total obtainable resolution of the dilatometer to m. The instrument is low cost and operates at normal room temperature, pressure and humidity. Since the spring constant of the lever sensing dilatation is , thus exerting negligible force on the sample, the instrument is particularly suitable for the study of small (piezoelectric) strains of soft biological tissues, but is not limited to such applications.