Individual Frequency Components Research Articles

Orthogonal decomposition technique for ionospheric tomography

AbstractThe possibility of reconstructing two‐dimensional electron‐density profiles in the ionosphere with ionospheric tomography is significant. However, due to the nature of the imaging system, there are several resolution degradation parameters. In order to compensate for these degradation parameters, a priori information must be used. This article introduces the orthogonal decomposition algorithm for image reconstruction, which uses the a priori information to generate a set of orthogonal basis functions for the source domain. This algorithm consists of two simple steps: orthogonal decomposition and recombination. In the development of the algorithm, it is shown that the degradation parameters of the imaging system result in correlations among projections of orthogonal functions. Gram–Schmidt orthogonalization is used to compensate for these correlations, producing a matrix that measures the degradation of the system. Any set of basis functions can be used, and depending upon this choice, the nature of the algorithm varies greatly. Choosing the basis functions of the source domain to be the Fourier kernels produces an algorithm capable of isolating individual frequency components of individual projections. This particular choice of basis functions also results in an algorithm that strongly resembles the direct Fourier method, but without requiring the use of inverse Fourier transforms.

Ground roll: Rejection using polarization filters

Ground roll noise on land data sets overwhelms the desired reflection seismic signal unless special steps are taken in data acquisition and processing to control it. This is usually done in the field by the design of group arrays for data acquisition. On the other hand, if multicomponent data are acquired, it is possible to remove ground roll during processing using polarization analysis. Even though this processing is computation‐intensive, the potential exists for obtaining results similar to conventional data acquisition, but with deployment of fewer sensors in the field with minimal group array effects. It also has potential for deriving new information. We describe a two‐dimensional polarization‐filter analysis for use with vertical and in‐line sensors. A time‐domain spectral matrix technique is developed since the recorded seismic signal is the superposition of multiple signals in the time domain, each with different frequency content and time‐varying polarization. This technique is implemented by decomposing the signal into individual frequency components using narrow band‐pass filters and defining the polarization characteristic using sliding time windows. We show that both incoherent noise and specific linearly polarized constituents can be successfully filtered.

Conductance oscillations periodic in the density of one-dimensional electron gases.

Results are reported of a detailed study of the conductance oscillations in one-dimensional (1D) Si inversion layers. A comparison is made with results for GaAs accumulation layers. The conductance oscillates by as much as a factor of 100 and is accurately periodic in the number of electrons per unit length. The period varies randomly from sample to sample, and changes when a single sample is warmed to room temperature and remeasured at low temperature. Multiple periods are often observed, and the amplitude of the individual frequency components can be altered by moving the electron gas from side to side with a transverse electric field. These observations suggest that the period is determined by the distance between charged defects near the 1D channel. Measurements of the temperature dependence indicate that the oscillatory conductance reflects a periodic energy for a thermally activated conductance mechanism as well as a parallel oscillatory tunneling mechanism. The period of the conductance oscillations is found to be surprisingly independent of magnetic field B. However, the random modulation of the amplitude of the oscillations is reduced by a B field normal to the semiconductor surface, as it is by increasing temperature.

Segmented fourier transform and its application to fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry: ion abundances and mass measurements

A method has been developed to analyze quantitatively the frequency components of digitized time-domain signals. This method, named segmented Fourier transform (SEFT), has been applied to Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry where it enables accurate ion abundance and mass measurements to be made, thereby minimizing errors stemming from the sampled nature of the signal, the non-uniformity of the frequency distribution of the excitation power, the spectral peak overlap, and the non-uniformity of the spectral line shapes due to non-uniform relaxation of the individual frequency components. The results satisfy the theoretical expectations and show that from very modest data sets ion abundances with accuracies of about 0.1% and mass measurements with errors in the low parts per million range can be gained. Even for broad-band mass spectra recorded under conditions appropriate to ion/molecule reaction studies at relatively high cell pressures of up to 2×10 −6 torr, the above accuracies can be maintained. In this respect the SEFT method is superior to known alternative data handling methods, which under the same conditions allow errors of up to 300% and hundreds of parts per million for ion abundance and mass determinations, respectively.

Coding of phase structure in complex sounds by bullfrog auditory‐nerve fibers

This experiment explored how the peripheral coding of the spectral and temporal structure of a complex communication signal is affected by the phase relations between individual frequency components in the sound. Complex sounds with 21 components, all of which were harmonics of a common, low‐frequency fundamental (100 Hz), were digitally synthesized. The frequencies and amplitudes of the individual components matched those of the bullfrog's species‐specific advertisement call. For one stimulus, the 21 components were generated in cosine phase, and for the other stimulus, the 21 components were in random phase. Most amphibian papilla (AP) and basilar papilla (BP) fibers synchronized to the envelope only of the phase‐coherent stimulus, and the complex spectral structure of the stimulus was not accurately encoded by population firing patterns. Envelope synchronization to the random‐phase stimulus was not seen in the responses of some mid‐frequency‐sensitive AP and BP fibers, although low‐frequency‐sensitive AP fibers responded similarly to both stimuli. Behavioral experiments suggest that bullfrogs can discriminate between in‐phase and random‐phase versions of their advertisement calls.

Dependence of interaural time relationships in the cat upon sound source direction and frequency

Using a probe microphone surgically implanted near each eardrum of an anesthetized cat, the time waveform was recorded in both ears in response to a click as the azimuth and elevation of a loudspeaker were varied. Two forms of interaural time delay (ITD) were calculated. Arrival time (AT) for each ear was based upon the leading edge of the click waveform and the first measure of ITD was taken as the difference in AT for the two ears. The FFT analysis of the time waveforms also yielded the interaural phase difference (IPD) for the individual frequency components. The phase-derived ITD was calculated as IPD/ω and enabled study of the dependence of ITD upon frequency. Both measures of ITD varied systematically with azimuth and elevation and reached values greater than would be expected from the interaural distance. Kuhn [Directional Hearing, edited by W. Yost and G. Gourevitch, (Springer, Berlin, 1987), Chap. 1] has shown for the human that ITDs for low and high frequencies are in the ratio of 3:2, respectively. The present study yields similar findings in the cat and confirms and extends earlier work.

Uncertainties in the cross-spectral method for acoustic intensity under semireverberant conditions

Measurements were performed, under semireverberant conditions, to examine uncertainties in the two-microphone cross-spectral method for determining acoustic intensity. Calculations of the pressure gradient error, the error associated with the correction for phase mismatch, and the cross-spectrum random error are discussed. The results of preliminary tests performed under free-field and plane-wave conditions are also presented. The influence of semireverberant conditions on the accuracy of the intensity measurement was studied through the use of a standing-wave tube as a reference sound source. With the tube source placed in a 112-m3 room having reverberation times of about 0.5 s, the radiated power was determined both from the intensity measured inside the tube and from the intensity integrated over a spherical surface enclosing the source. For a measurement system configured to limit the errors listed above to 0.5 dB under free-field conditions, phase correction and random errors of several decibels occurred for measurements in the semireverberant room, when determined for the individual frequency components of the Fourier analysis spectrum. However, the calculated 1/3-octave-band sound power levels agreed within ±0.5 dB for the bands from 160 to 630 Hz. Reductions of the errors by selecting a probe configuration to increase the cross-spectrum phase, increasing the number of time records sampled, and, for measurements within a tube, increasing the tube radius are discussed.

Efficient generation of surface acoustic waves by thermoelasticity

Short laser pulses were used for generating surface acoustic waves (SAW’s) on optically opaque solids via the thermoelastic effect. The spatial and temporal shapes of the laser pulses were either a spot or a line of variable total width δ=2a with a Gaussian power distribution. Maximal efficiency is obtained when a=vRτ(vR: Rayleigh velocity, 2τ: total laser-pulse length). This condition is caused by interference effects between the individual frequency components radiating from the area of the thermoelastic source. If the intensity of the laser beam were 100% modulated at a given frequency, maximal efficiency would occur if kR=(2)1/2/a (kR: wave vector of the SAW’s).

The tracking performance of a narrowband phase-locked loop in the mobile multipath environment

The paper describes the behaviour of narrowband phase-locked loops in the mobile multipath environment. It is shown that the loop will often track individual frequency components of the pilot's spectrum and that the loop can give rise to frequency-tracking errors of upto ±ωd rad/s in estimating the nominal frequency of the received pilot.

Geologic time series from deep-sea sediments: Time scales and distortion by bioturbation

In order to evaluate the time- and frequency-domain characteristics of geologic time series obtained from deep-sea sediments, two important problems must be considered. First, an accurate time scale must be established for the sediment records to be studied. An accurate time scale is a basic requirement for such techniques as spectral and cross-spectral analysis. Secondly, the distortion of a geologic time series by sedimentation processes such as bioturbation must be considered if inferences are to be made about the mechanisms controlling climatic and oceanographic processes reflected in the geologic record. Recently, it has been suggested that the periodic components in paleoclimatic records which can be related to variations in the Earth's orbital parameters, can be used as a means for providing very detailed control for late Pleistocene sediment sections. A time scale is estimated by tuning an individual frequency component in a climate record to an orbital parameter. The tuning procedure commonly uses the technique of bandpass filtering which removes all frequency components except the one equivalent to an orbital parameter and then adjusting the geologic time scale so that the filtered record and orbital record align. Since bandpass filtering will produce a periodic record from any data set, a question is raised as to the circularity of this tuning approach. A series of numerical experiments using synthetic time series are used to determine if the tuning of a geologic record artificially induces improved correlation and increased periodic character in a climatic record. These experiments indicate that the tuning does not artificially induce these effects. Thus, it is suggested that the careful use of orbital tuning provides a powerful means of defining a geologic time scale. The degree to which bioturbation distorts a paleoclimatic record is studied by comparing the spectra of oxygen-isotopic records obtained from cores with sedimentation rates ranging from 1 to 12 cm 1000 yr −1. It is shown that the systematic change in the variance spectra of these records that is predicted by models of bioturbation cannot be observed for sedimentation rates greater than 2 cm 1000 yr −1. This can be explained in part if bioturbation is a function of sedimentation rates. If this is the case, then bioturbation must proceed to depth of tens to hundreds of centimeters. However, it seems likely that the degree to which bioturbation alters the climate signal preserved in deep-sea sediment cores has been overestimated.

On the efficient two-dimensional energy coding characteristics of spatial vision

Recent evidence indicates that the vertebrate visual system possesses units whose receptive fields may be represented as narrow-band orientation and frequency specific filters. It has been indirectly demonstrated that equivalent psychophysical units act in such a way as to not discriminate the individual frequency components within each frequency band. Here we directly demonstrate this to be the case with digital images and so show an efficient energy code for spatial vision.

Keyer system for an electronic organ

A keying system provides selectable decay times for individual frequency components of a tone to be generated by an electronic organ having a top octave generator producing a multiplicity of rectangular wave signals, and a plurality of associated divider circuits. The keying system comprises a keying block having a plurality of keyer sections. Each keyer section has a first keyer channel comprising at least two MOSFET transistors which are connected in series. At least one keying section further comprises a second keyer channel similar to the first keyer channel, a voltage threshold circuit which has a selectable threshold and switching circuitry to select output signals from either the first or second keyer channel of the one keying section. Each channel of the keying block is connected between a supply voltage and a load resistor which is in turn connected to a reference potential. Rectangular wave signals from the top octave generator and divider circuits are applied to the gates of a first transistor in all keyer channels of the keying block. Upon the depression of a key on a playing keyboard, a keyer envelope signal is directly applied to the gate of a second transistor of all first channels of all keyer sections; and the keyer envelope signal is applied to the gate of a second transistor of the second keyer channel of the one keyer section through the threshold circuit. The output signals from the first keyer channels are rectangular waves modulated by the keyer envelope signal. The output signals from the second channel of the one keyer section are rectangular waves modulated by the keyer envelope signal shifted by the threshold of the voltage threshold circuit. The modulated rectangular wave signals from the first channels of the keyer sections and the selected channel of the one keyer section are passed through filters and combined by output circuitry to sound the desired tones.

Spectral basis of human frequency‐following response to the “missing fundamental”

Psychophysical studies of the “dominance” and “existence” regions of the “residue” underscore the importance of peripheral frequency analysis in the perception of pitch. However, the means by which the peripheral analysis of individual frequency components is transformed into a unitary percept dominated by the pitch of the residue, remains obscure. Farfield, vertex‐derived. frequency‐following responses (FFR), representing the integrated synchronized activity of phase‐sensitive neurons most likely situated in the inferior colliculus, were recorded during presentation of multicomponent (n = 2, 3, 4), harmonically related tone bursts. The frequency spectrum and waveform periodicity of FFR to low‐order harmonics (harmonic ranks 3–5) are clearly dominated by a frequency corresponding to the “missing fundamental”. The amount of energy in this frequency band diminishes considerably with increasing harmonic rank, becoming negligible for harmonics above the thirteenth. The existence of a parallel between psychophysical and FFR measures of pitch strength raises the possibility that in the brainstem auditory pathway, the “transmission code” for residue pitch is based on neural periodicity.

Space-Time Kinetic Energy Spectra in Mid-Latitudes

Abstract Several features of the one-sided space-time spectrum of the zonal and meridional wind components are discussed. The spectra show bands of energy corresponding to eastward moving disturbances, a transition from a red to a nearly white frequency spectrum with increasing wavenumber, and abrupt transitions to a power law dependence on zonal wavenumber for individual frequency components.

Use of geomagnetic storms in magnetotelluric interpretation

Consideration of electromagnetic diffusion into a conducting medium leads to the observation that individual frequency components of transient electromagnetic fields can be considered to penetrate the medium with a velocity that depends on frequency. In addition to being attenuated as they propagate, these components are reflected at the interfaces between layers of different conductivity. An interpretive procedure based on these observations was developed [Towle, 1971] after Wait [1954] first noticed that resolution of the conducting layers in the transient response of a two-layered conducting medium was possible.

Use of a Two-Dimensional Array to Receive an Unknown Signal in a Dispersive Waveguide

A relatively simple method is discussed for estimating the phase velocity and direction of an unknown plane-wave signal, propagating across two-dimensional array in a dispersive waveguide. The finite Fourier transform is applied to the output signal of each sensor, and the phases of the smoothed frequency components calculated. The phases of the components are linearly regressed on sensor positions to produce estimates of the wave slowness components. Neither the phase nor group velocity dispersion curves need to be known, except for upper and lower estimates of the range. By smoothing over frequency and transforming, estimates are obtained of the direction and phase velocity of the signal. The precision of estimates depends on the signal-to-noise ratio, the square root of the number of sensors, and the number of wavelengths that fall in the array. Each frequency is treated separately, so that the direction and phase velocity are obtained as a function of frequency. Since the individual frequency components of the signal are separated, the signals observed on a large array can be combined, even though the dispersion is appreciable over the array. For good signal-to-noise power ratios, the dispersion curves are a direct result from the analysis.

Weighting Function for Evaluation of Random Television Interferences with Different Standards

Although much information is available about the random noise visibility in various television systems, none refers to the interpretation of the results in terms of the particular television standard. The author assumed a linear summation on noise visibility of the individual frequency component of the noise spectra, and concluded that the video weighting function in different television standards must be identical except that its reference frequency is varied in proportion to the line frequency. The validity of the analysis was supported by experiments on the relative visibility of the octave-band random noises with twelve television standards including the four different ones now in use.

Lunar Geomagnetic Variations

THERE have been several attempts to detect lunar tidal variations in the ionosphere from the geomagnetic records1. These earlier attempts used the method of classical harmonic analysis, and sought to determine the amplitude of the important semidiurnal component. The availability during the International Geophysical Year of continuous geomagnetic data from many stations has made it possible to use power spectrum analysis, and resolve the individual frequency components of the lunar effect on the magnetic record2. The results of such a spectrum analysis for Godhavn are displayed in Fig. 1. The components with periodicities centred around the separately. The various components are identified by the symbolism adopted by Schureman3 and Bartels4 for tidal components.

Transients in cylindrical antennae

The transient response of the radiation field of a driven cylindrical antenna is investigated for the particular case of a step-function excitation. The theoretical analysis makes use of Fourier's theorem to express the response as an integral over the response to all individual frequency components. The response as a function of time shows damped oscillations with a frequency determined by the first resonance frequency of the antenna. The response of the same antenna used as a receiver in a transient plane wave field is shown to be related to the radiation response by a simple integration process. By proper loading of the dipole, transient times of the order of the time needed for wave to travel along the dipole axis can be obtained. An experimental investigation is described in which the reception of a transient field due to a shock-excited distant transmitter is observed.

A note on the frequency distribution of an FM/FM signal

An approximate expression is derived giving the amplitude and phase of the individual frequency components of an fm/fm signal when the input is a sinusoid. The approximation is subject to the restrictions that the subcarrier frequency be large in comparison to the highest modulation frequency, and that the ratio of subcarrier deviation to subcarrier frequency be much less than unity. Some qualitative properties of the frequency spectrum are pointed out and discussed, and illustrations of representative single sub-carrier-frequency distribution are presented. Although subject to the above restrictions, the results are shown to be applicable to present day fm/fm telemetry techniques.