Zero Phase Shift Research Articles

Low-pass distributed RC filter using an MOS transistor with near zero phase shift at high frequencies

The signal transfer properties of an MOS transistor biased with zero drain-to-source voltage, under a four-terminal excitation, are examined. Analytical expressions for the admittance matrix are developed. These results are applied to the study of a distributed RC low-pass filter with phase shift recovery at high frequencies. Calculations for the filter gain and phase characteristics, including the transistor parasitics, are presented. This filter has been used successfully in the design of self-biasing high-gain gigahertz-band amplifiers. The analytical expressions can be easily incorporated in a circuit simulation program to accurately model distributed RC effects. >

Interaction of impulsively generated vortex pairs with bodies

A vortex pair, impulsively generated from a planar nozzle, is shown to have a degree of vorticity concentration in good agreement with inviscid theory, providing well-posed initial conditions for interaction with basic types of bodies (cylinders and plates). The scale of these bodies ranges from the same order as, to over an order of magnitude smaller than, the scale (distance between centres) of the incident vortex pair.The fundamental case of a (primary) vortex pair symmetrically incident upon a very small cylinder shows rapid growth of a secondary vortex pair. These secondary vortices quickly attain a circulation of the same order as that of the corresponding primary vortices within a distance smaller than the lengthscale of the primary vortex pair. At this location, the temporal variation of integrated vorticity of primary and secondary vortices attains a maximum simultaneously. This zero phase shift between arrival of vorticity maxima provides the basis for formation of counter-rotating, primary–secondary vortex pairs, where both the primary and secondary vortices move at the same phase speed.Visualization shows that the mode of secondary vortex formation is highly sensitive to the degree of symmetry of the initial encounter of the incident vortex pair with the body. The symmetrical mode of (in-phase) secondary vortex formation shows very rapid growth of large-scale secondary vortices; their development is relatively independent of the particulars of body shape and scale. On the other hand, the antisymmetrical mode takes two basic forms: large-scale secondary vortex formation, with the phase shift between their formation determined by the lengthscale of the body; and small-scale, antisymmetrical shedding of secondary vortices from the body occurring for a body lengthscale an order of magnitude smaller than that of the incident vortex pair. Correspondingly, there are several types of distortion of the cores and trajectories of the primary (incident) vortices.

Digital Filtering and Spectral Analysis of the Low Intensity ABR

Spectral analysis along with zero and standard-phase shift digital filtering were performed on evoked potentials recorded from 12 normal hearing subjects. The results indicated a progressive shifting of the mean spectral content of the ABR toward the low frequencies as the stimulus intensity was lowered. Despite this, the effects of zero-phase shift high-pass digital filtering at 100 Hz (36 dB/oct) did not significantly differ between waveforms elicited by a 75 dB nHL, 55 dB nHL, and 35 dB nHL stimulus. The major response frequency of the ABR is related to the distance between the peak (IV/V) and the following major trough (approximates one-half the response period). In waveforms where the major trough occurred before 10 msec, the use of 100 Hz, 36 dB/oct, zero-phase shift high-pass filters produced only a small reduction in response amplitude, even at low stimulus intensity levels. Waveforms which had a major trough (Na1) between 10 to 15 msec were reduced in amplitude by 100 Hz, 36 dB/oct, zero-phase shift high-pass filters (the longer period of the response energy in these waveforms corresponds to a lower energy frequency). However, this trough has a latency that prevents it from being recorded on a 10 msec time base or defined as an ABR. Based on these results, the use of zero-phase shift high-pass filters with a high-pass cutoff frequency that is equal to or less than the resolution of the time base (1/time base) appears to be a desirable method of reducing muscle artifact and other electrical contamination of the ABR.(ABSTRACT TRUNCATED AT 250 WORDS)

A method of digital filtering to enhance the peaks of evoked potentials: application to auditory brainstem responses.

The aim of this paper is to propose a method of data processing for the analysis of evoked potentials, in particular for auditory brainstem responses. The present method has been developed to simplify and speed up the interpretation of the recordings by means of an enhancement of the response peaks. Even for experienced observers, identification of the response waves and subsequent latency measurements may sometimes constitute a difficult task, due to the presence of residual noise or to interference between the temporal waveforms of adjacent peaks and troughs. The method is implemented with a digital non-causal (zero-phase shift) filter, based on the convolution with a finite impulse response, to make the computation time compatible with the use of low-cost microcomputers. The performance is shown to be very good in several examples.

High pass digital and analog filtering of the middle latency response.

Digital filtration with zero and standard-phase shift characteristics was performed on unfiltered auditory evoked potentials recorded from 10 adult subjects. Standard-phase shift filters were seen to distort the response. Mild phase shift distortion often augmented the IV/V-Na1 amplitude (auditory brain stem response). When recording the IV/V-Na1 amplitude on a narrow timebase (20 msec), we recommend using a phase shift filter that has a high-pass cutoff frequency approximating 15 Hz and a slope of 12 to 24 dB/octave, in order to take advantage of the observed phase shift augmentation. The augmentation of the IV/V-Na1 amplitude is at the expense of the IV/V-Na2 amplitude. Thus, this phase shift distortion is not desirable if a long timebase (50 msec) is used. If a high-pass standard-phase shift filter of 100 Hz is used to eliminate muscle artifact, a reduction in the IV/V-Na1 amplitude from phase shift distortion is seen compared to the zero-phase shift control. In site-of-lesion testing, a nondistorted waveform produced by digital zero-phase shift filtration is also desirable over a distorted analog response. It is recommended that the slow wave activity of the response be recorded with a timebase of at least 40 to 50 msec and with a filter that produces minimal or no phase shifting. The major recorded response will be the Na trough and Pa peak. Evoked response units with steep filters will phase shift the response and produce a reduction in the IV/V-Na amplitude and a concomitant augmentation of the latter middle latency response waveforms.(ABSTRACT TRUNCATED AT 250 WORDS)

Zero Phase Error Tracking Algorithm for Digital Control

A digital feedforward control algorithm for tracking desired time varying signals is presented. The feedforward controller cancels all the closed-loop poles and cancellable closed-loop zeros. For uncancellable zeros, which include zeros outside the unit circle, the feedforward controller cancels the phase shift induced by them. The phase cancellation assures that the frequency response between the desired output and actual output exhibits zero phase shift for all the frequencies. The algorithm is particularly suited to the general motion control problems including robotic arms and positioning tables. A typical motion control problem is used to show the effectiveness of the proposed feedforward controller.

Short latency somatosensory and spinal evoked potentials: Power spectra and comparison between high pass analog and digital filter

Medium nerve somatosensory evoked potentials (SSEPs) and intraoperative spinal evoked potentials were analyzed using different analog and zero phase shift digital high pass filter and by power spectrum. Additionally, high pass analog and digital filtering was performed on various sine, triangular and rectangular waves manufactured by a wave form generator. Recordings were also transformed to the 1st and 2nd time derivatives. The great abundance of spectral energy for scalp recorded median nerve SSEPs was below 125 c/sec but lower energy fast frequency components consistently extended to 500 c/sec. Power spectrum of the Erb's point compound nerve action potential revealed a wide band of spectral energy commencing at about 50–100 c/sec, peaking at about 250–270 c/sec and extending to nearly 1000 c/sec. This suggests that synchronous axonal activity generates predominantly faster frequencies above 100 c/sec. High pass analog filter confers phase non-linearity which results in various distortions including latency shift and a morphological change which may be visually similar to the 1st or 2nd time derivatives. High pass zero phase shift digital filter removes selected low frequencies without accompanying phase distortion. This accentuates fast peaks seen at open bandpass as well as transition points between baseline and component ascent or descent. Zero phase shift digital filter may also generate peaks that are not visualized at open pass but which reflect the sum of frequencies which were not removed by filtering. These peaks do not necessarily correspond to discrete singular neuroanatomical structures. Although peaks observed in high pass analog and digital filter appear similar and comparable, their underlying activity may be of different origin. This is because high pass analog filter projects a considerable amount of overlap from earlier onto later waves. For clinical correlation it is important that restricted bandpass analog or digitally filtered recordings be compared with open pass data. Only those peaks visualized in both open and restricted bandpass can be considered authentic. Examples of spinal and scalp SSEPs indicate that selective filtering may, under certain circumstances, distinguish axonal or lemniscal from synaptic generators.

An improved microwave interferometer technique for plasma density measurements

An improved technique has been developed for microwave interferometer measurements of plasma density, where the most useful features of previously described techniques are combined. Phase angles from a few degrees to several times 360 degrees can be measured without ambiguity, and there are no phase angles with zero phase shift sensitivity. Reductions of the microwave power (e.g. due to absorption in the plasma) with up to a factor 100 can be taken into account in the evaluation of the measurements. With low power in the test beam, a polar display of the test beam phasor is possible. The minimisation of errors due to imperfect components, and due to uncertainties in the measured quantities, is investigated theoretically and experimentally. The method of evaluation eliminates the influence also of rather large imperfections of the components. The construction and testing of an interferometer based on this technique is described.

Effects of high-pass filter frequency and slope on BAEP amplitude, latency and wave form

The effects of increases in analogue high-pass filter frequency and slope on the BAEP were investigated in a group of 20 subjects. Frequency effects were additionally compared to the wide-band recorded signal and slope effects to a zero-phase shift filter, all filters being digitally simulated. Absolute amplitude, latency and interpeak latency were significantly reduced by both progressive filter frequency and steepness. Additionally, different effects on the ascending and descending limbs of waves I, III and V were observed which explain wave form distortions. The results suggest that filtering should be limited to, at most, 6 dB/oct and 100 Hz frequency.

A synthesis procedure for 90° fan filters

The synthesis of fan filters [1] is approached using a procedure developed by Hirano and Aggarwal [4] and an index transformation given by Chang and Aggarwal [5] which rotates the prototype frequency response <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">45°</tex> . A polynomial factorization reduces the realization algorithm to a series-parallel combination of four one-dimensional all-pass filters. A simplified structure for digital all-pass filters is indicated. An efficient method of approximating zero phase shift is indicated. The associated numerical synthesis procedure consists of evaluating a single equation for a number of arguments. The realization of a fan filter based on an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> th-order one-dimensional prototype requires <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M - 1</tex> multiplications per point.

Secular variation as recorded in lake sediments: a discussion of North American and European results

Type-curves depicting secular variations in declination and inclination through Holocene time have been constructed by stacking data from individual cores of lake sediment from east-central North America and the U.K. There is a strong positive correlation in declination with zero phase shift froiti 0 to 4500 14 C years b.p. but from 4500 to 8500 14 C years b.p. the correlation is strongly negative , which we interpret in terms of fluctuations in intensity of standing geomagnetic sources. A source located under the Atlantic Ocean appears to have been dominant before ca . 4500 14C years b.p., and then another similar source located either to the east or to the west of both observation areas gained dominance. However, the inclination type-curves show optimum positive correlation for a phase shift of ca. 400 years, suggesting that the geomagnetic sources that caused them were drifting westward at ca. 0.2 degrees a year. There is no way of adjusting the timescales so as to obviate this apparent paradox. Secular variations of the total geomagnetic vector have been investigated by noting the sense (clockwise, anticlockwise) of looping of the v.g.p. paths, though this cannot be interpreted uniquely in terms of westward or eastward drifting sources in the core, as demonstrated by specific radial dipole models.

Distortion of the middle latency auditory response produced by analog filtering.

The effect of analog filtering on the middle latency auditory response (MLAR) was investigated. Substantial waveform distortions and latency shifts were found when using similar filter settings as reported in the literature. The waveform changes amounted to complete polarity reversal of the Na-Pa-Nb pattern due to the high-pass cut-off with a steep slope characteristic. The analog filters were simulated by recursive digital filters and compared with symmetrical digital filters having the same cut-off frequency and slope. MLAR waveform and latencies were scarcely affected by the digital zero-phase shift filters. In contrast, the oscillations in the step function response of the analog filter elucidated how early activity of the MLAR is folded onto later components, leading to a much larger late activity than present physiologically. Since physiological interpretations of the MLAR ought to rely on unbiased recordings, minimal usage of analog filtering is recommended.

Effects of analog and digital filtering on brain stem auditory evoked potentials

Most investigators of the brain stem auditory evoked potentials utilize analog filters to reduce the noise content of the averaged signals, but different investigators use different filter bandwidths. Data presented in this note compare the effects of different upper and lower cutoff frequencies for both analog and zero-phase shift digital filters. Effects on response wave form and on measured values of amplitude and latency of wave V are considered. It is concluded that, for given cutoff frequencies, analog filtering causes more distortion of the response than digital filtering, due primarily to phase distortion introduced by the analog filter. It is likely that differences in filter cutoff frequencies, especially lower cut-off frequencies, are a significant source of variability in results reported by different investigators.

Short-range correlations with pseudopotentials. VI

Short-range pseudopotentials are required to be added to the realistic nucleon-nucleon interactions to achieve healing in the correlated wave functions in such a way as to produce zero-phase shift. The introduction of pseudopotentials leads to an effective interaction and an effective Hamiltonian. The differential cross sections for the two direct stripping nuclear reactions $^{28}\mathrm{Si}(d,p)^{29}\mathrm{Si}$ and $^{40}\mathrm{Ca}(d,p)^{41}\mathrm{Ca}$ have been calculated. In the present calculations, the effective interaction has been derived from the different realistic nucleon-nucleon potentials, Hamada-Johnston, Yale, Tabakin, and Reid potentials and also from the potential $A$ calculated by us. Our present theoretical calculations for the angular distributions have been fitted to the experimental data where good agreement is obtained. The spectroscopic factors extracted from our present work are found to be more reliable.NUCLEAR REACTIONS $^{28}\mathrm{Si}(d,p)$ $E=18.0$ MeV; $^{40}\mathrm{Ca}(d,p)$ $E=7.0$ MeV; measured $\ensuremath{\sigma}(\ensuremath{\theta})$; pseudopotentials; optical model parameters; DWBA analysis; extracted spectroscopic factors.

Short-range correlations and pseudopotentials. V

Deformed Hartree-Fock-Bogoliubov calculations have been carried out with an effective interaction derived from the different Hamada-Johnson, Yale, Tabakin, and Reid potentials and from the potential $A$ calculated by us. Short-range pseudopotentials are introduced to these potentials to achieve healing in the correlated wave functions and to produce zero-phase shift in the pair state. The deformed Hartree-Fock-Bogoliubov method has been applied to the $2p\ensuremath{-}1f$ shell even-even nuclei. Intrinsic quadrupole moments $〈Q_{0}^{}{}_{}{}^{2}〉$, quadrupole moments of the first excited states ${Q}_{2+}$, and the reduced transition probabilities $B(E2) ({0}^{+}\ensuremath{\rightarrow}{2}^{+})$ have been calculated. The angular momentum projected spectra for these nuclei have also been obtained. The present calculations of quadrupole moments, transition probabilities, and angular momentum spectra for the different Ti, Cr, Fe, and Ni isotopes are in good agreement with the experimental results.NUCLEAR STRUCTURE $^{44,46,48,50}\mathrm{Ti}$, $^{48,50,52,54}\mathrm{Cr}$, $^{52,54,56,58}\mathrm{Fe}$, $^{58,60,62,64}\mathrm{Ni}$; calculated intrinsic quadrupole moments, quadrupole moments of the first excited states, reduced transition probabilities, projected angular momentum spectra and energy levels; pseudopotentials. Hartree-Fock-Bogoliubov method.

Nonlinear Integrator With Zero Phase Shift

In the present paper a nonlinear integrator is introduced which produces zero phase shift in comparison with -90° phase shift of linear integrator and the phase of -38° of nonlinear integrator introduced by Clegg [1]. The proposed nonlinear integrator is a combination of a 90° phase lead nonlinear network and a linear integrator. Synthesis and operation of the non-linear integrator as well as possible applications are also presented.

Comments on the paper: “Phase Distortion and Hilbert Transformation In Multiply Reflected and Refracted Body Waves”, By G. L. Choy and P. G. Richards

In a recent paper Choy and Richards (1975) have demonstrated that phase-shifted arrivals can introduce systematic travel-time errors due to relative changes in the peak and trough positions of the arrival wavelets. The method they suggest to correct the problem is to cross-correlate an estimated zero-phase-shifted wavelet with the seismogram after all the arrivals have been restored to a zero phase shift. The peaks of the cross-correlation are then taken as the reference times for the arrivals. This method is awkward to use in practice because the arrivals will in general be phase-shifted by various angles that are not usually known a priori. This necessitates that each arrival be treated separately by searching for the correct restoring phase shift. The purpose of this note is to point out the existence of a much easier method which is simply to compute the envelope of the cross-correlation of the seismogram with an estimated zero-phase-shifted wavelet (Helmberger and Wiggins, 1971).

Two-pass recursive digital filter with zero phase shift

A two-pass recursive scheme is proposed for realizing zero phase shift filters with arbitrary magnitude characteristics. The first pass is performed in forward time and the second in reverse time. The effect of initial and reverse time transients is discussed, and a scheme for quasi on-line adaptation is presented.

Short-range transparent potentials

In classical mechanics the asymptotes of the trajectory, rather than the exact path of the particle in the interaction region, determine the differential cross-section. If a potential causes a localized distortion of the orbit of a particle without changing the asymptotes of the trajectory, then such a potential is transparent and has no observable effect in a scattering experiment. However, if one determines the path of the particle, or measures the time delay caused by the passage of the particle through the potential, then in general, it is possible to find the force law, or to verify the correctness of a given form of interaction. In the quantum-mechanical description of the scattering process, the concept of the path of a particle becomes meaningless. Then a transparent potential may be defined as the potential which produces zero phase shift for all energies in a given angular-momentum state. Using the quantal formulation of the collision lifetime, we show that only for a class of transparent potentials the time delay is nonzero and therefore this class of interactions has an observable two-body effect.

Phase distortion of biological signals: Extraction of signal from noise without phase error

Analog filtering can produce distortion of signals by shifting phase. The signal-to-noise ratio achieved by averaging a small number of signals buried in noise will be improved greatly if that signal ensemble is averaged upon itself so that the time of signal onset varies over a predetermined series of intervals (interference filtering). The result of interference filtering is similar to the one obtained by sharp bandpass filtering, but provides zero phase shift. Transfer functions were constructed for first, second and third order interference filters. Effectiveness of interference filtering is demonstrated with synthesized signals and biological data. Distortion of signal shape and time characteristics were demonstrated in biological data where signal-to-noise ratio had been improved by analog frequency filtering.