TL;DR: In this article, the authors investigated the differential stability of the 2 phase modes and found that the asymmetric phase mode was less stable as the frequency of oscillation increased, while the symmetric mode was more comfortable than the alternate phase mode.
Abstract: By watching each other's lower oscillating leg, 2 seated Ss kept a common tempo and a particular phase relation of either 0 degrees (symmetric mode) or 180 degrees (alternate mode). This study investigated the differential stability of the 2 phase modes. In Experiment 1, in which Ss were instructed to remain in the initial phase mode, the alternate phase mode was found to be less stable as the frequency of oscillation increased. In addition, analysis of the nonsteady state cycles revealed evidence of a switching to the symmetric phase mode for the initial alternate phase mode trials. In Experiments 2 and 3, Ss were instructed to remain at a noninitial phase angle if it was found to be more comfortable. The transition observed between the 2 phase modes satisfies the criteria of a physical bifurcation--hysteresis, critical fluctuations, and divergence--and is consonant with previous findings on transitions in limb coordination within a person.
TL;DR: In this paper, an eigenstructure-based method for direction finding in the presence of sensor gain and phase uncertainties is presented, which provides estimates of the Directions of Arrival (DOA) of all the radiating sources as well as calibration of the gain and phases of each sensor in the observing array.
Abstract: An eigenstructure-based method for direction finding in the presence of sensor gain and phase uncertainties is presented. The method provides estimates of the Directions of Arrival (DOA) of all the radiating sources as well as calibration of the gain and phase of each sensor in the observing array. The technique is not limited to a specific array configuration and can be implemented in a'ny eigenstructure-based DOA system to improve its performance.
TL;DR: A general description of phase measurement by digital heterodyne techniques is presented in which the heterodyning is explained as a filtering process in the frequency domain.
Abstract: A general description of phase measurement by digital heterodyne techniques is presented in which the heterodyning is explained as a filtering process in the frequency domain Examples of commonly used algorithms are given Special emphasis is given to the analysis of systematic errors Gaussian error propagation is used to derive equations for the random phase errors of common algorithms
TL;DR: In this paper, a Coriolis mass flow rate meter that is substantially immune to noise has been proposed, where the phase difference that occurs between real and imaginary components of the discrete Fourier transform (DFT) of both the left and right velocity sensor waveforms evaluated at the fundamental frequency at which the flow tubes vibrate is measured.
Abstract: Apparatus and accompanying methods for use therein for a Coriolis mass flow rate meter which is substantially immune to noise, and more particularly, to such a meter that is substantially unaffected by noise that occurs at substantially any frequency different from a fundamental frequency at which the flow tube(s) in the meter vibrate Specifically, the meter relies on measuring mass flow rate by determining the phase difference that occurs between real and imaginary components of the discrete fourier transform (DFT) of both the left and right velocity sensor waveforms evaluated at the fundamental frequency at which the flow tubes vibrate The fundamental frequency is located, during an initialization operation, by providing a power spectrum, determined through use of the DFT, of one of the sensor signals and then selecting that frequency at which the magnitude of the power spectrum reaches a maximum value In addition, the frequency at which both velocity sensor signals is sampled is readjusted in response to any change in the phase of one of the velocity sensor signals, as transformed using the DFT, in order to assure that the sampling frequency always remains substantially equal to a pre-defined integer multiple of the fundamental frequency Furthermore, the meter, through use of the numerical value of any such phase change, also provides a density indication which is also substantially immune to such noise
TL;DR: The first measurements of the phase of the infrared-visible sum-frequency generation signal are presented, and two techniques are introduced and applied to the determination of the polar orientation of a selected group of atoms within an adsorbed molecule.
Abstract: We present what are to our knowledge the first measurements of the phase of the infrared-visible sum-frequency generation signal. We introduce two techniques and apply the measurements to the determination of the polar orientation of a selected group of atoms within an adsorbed molecule.
TL;DR: In this paper, a quasi-phase matched second-harmonic generation has been observed in a periodically poled nonlinear optical polymer waveguide with spin-coated polymers.
Abstract: Quasi‐phase‐matched second‐harmonic generation has been observed in a periodically poled nonlinear optical polymer waveguide. Key elements in this demonstration include novel nonlinear optical polymers that can be spin coated, the design and fabrication of periodic electrodes for periodic poling and the optimization of waveguide parameters to obtain single‐mode waveguides with a large overlap between fundamental and harmonic modes. Phase matching of the d33 nonlinear optical coefficient occurs over a distance L=230 μm.
TL;DR: In this article, the rotor position of a brushless DC motor with an accuracy of π/m electrical radians within one electrical period, and provided enough information to enable starting the motor in the correct direction with certainty.
Abstract: The present method and apparatus detects the rotor position of a brushless DC motor with an accuracy of π/m electrical radians (where m=the number of motor phases) within one electrical period, and provides enough information to enable starting the motor in the correct direction with certainty. After starting the motor in an open loop mode of one or two steps, a closed loop mode may be switched on, using a dynamic indirect position detection as is already well known in the technology. More specifically, the position at start is determined by the injection of short current pulses in different motor phases, each phase or pair of phases being energized first by a pulse of one polarity and of the opposite polarity. The sign of the time difference between the rise times of the induced voltages is detected. By performing a succession of these tests on different phases or pairs of phases of the standing motor, a table of results is established which clearly defines the position of the rotor relative to the motor phases. The same table then defines what polarity currents should be applied to each phase to reliably and certainly start the motor in the proper direction.
TL;DR: In this article, the rotor position of a brushless DC motor with an accuracy of π/m electrical radians within one electrical period, and provided enough information to enable starting the motor in the correct direction with certainty.
Abstract: The present method and apparatus detects the rotor position of a brushless DC motor with an accuracy of π/m electrical radians (where m = the number of motor phases) within one electrical period, and provides enough information to enable starting the motor in the correct direction with certainty. After starting the motor in an open loop mode of one or two steps, a closed loop mode may be switched on, using a dynamic indirect position detection as is already well known in the technology. More specifically, the position at start is determined by the injection of short current pulses in different motor phases, each phase or pair of phases being energized first by a pulse of one polarity and of the opposite polarity. The sign of the time difference between the decay times of the induced voltages in the un-energized phase is detected. By performing a succession of these tests on different phases or pairs of phases of the standing motor, a table of results is established which clearly defines the position of the rotor relative to the motor phases. The same table then defines what polarity currents should be applied to each phase to reliably and certainly start the motor in the proper direction.
TL;DR: In this paper, it was shown by simulation and experiment that selective pulses designed to invert or excite magnetization over a limited frequency window induce significant phase shifts over a bandwidth much larger than the chosen window.
TL;DR: In this article, a phase shift occurs between a phase of the light transmitted through the phase shift layer and a phase transmitted through a portion of the mask having no phase shift layers.
Abstract: A mask includes a transparent layer (2) which is transparent with respect to a light which is used for an exposure, and a mask pattern layer (5) which is formed on the transparent layer. At least a portion of the mask pattern layer (5) is made up solely of a phase shift layer (3a) for transmitting the light, so that a phase shift occurs between a phase of the light transmitted through the phase shift layer and a phase of the light transmitted through a portion of the mask having no phase shift layer.
TL;DR: In this paper, a sinusoidal phase modulating laser diode interferometer is proposed that is insensitive to vibrations of the optical components and fluctuations in the optical wavelength of the diode.
Abstract: We propose a sinusoidal phase modulating laser diode interferometer
that is insensitive to vibrations of the optical components and
fluctuations in the optical wavelength of the laser diode. These external
disturbances cause fluctuations in the phase of the interference signal.
After we analyze the sinusoidal phase modulation in a laser diode interferometer,
we describe the method of the feedback control of the injection
current of the laser diode to eliminate the phase fluctuations of the interference
signal. We construct two sinusoidal phase modulating interferometers
for movement measurements and surface profile measurements,
respectively. The experimental results make it clear that the interferometers
work well in mechanically noisy circumstances.
TL;DR: In this article, a first or ranging light beam which functions as a carrier is modulated with a first radio frequency f 1 ; a second amplitude modulated light beam source function as a local signal at a frequency f 2 for a heterodyne conversion of the first frequency F 1 ; and an electro-optical detector receives both modulated and local source light beams and functions as mixer.
Abstract: A first or ranging light beam which functions as a carrier is amplitude modulated with a first radio frequency f 1 ; a second amplitude modulated light beam source functions as a local signal at a frequency f 2 for a heterodyne conversion of the first frequency f 1 ; and an electro-optical detector receives both modulated light beams and functions as a mixer. Electro-optical heterodyning of the modulations on the ranging and local source light beams is accomplished by mixing RF modulations on the first light beam with RF modulation on the second light beam in the electro-optical detector to thereby produce a resultant, relatively lower difference frequency (f 1 -f 2 ) that is more readily processed by available electronic components. Distance measurement is represented by a phase shift of the relative low frequency difference of the heterodyned modulation signals when compared to a reference, unshifted phase of the same frequency.
TL;DR: In this paper, a second phase locking loop is added to a conventional phase lock loop to form a phase tracking system which provides a precisely constant phase shift over a full range of frequencies of the signal captured by the conventional phase locked loop.
Abstract: The output signal of a phase tracking system maintains phase coherence with the dominant input signal while tracking the frequency of that same dominant input signal without additional phase shifting circuitry Circuitry having a second phase locked loop is added to a conventional phase locked loop to form a phase tracking system which provides a precisely constant phase shift over a full range of frequencies of the signal captured by the conventional phase locked loop
TL;DR: In this article, the phase and frequency discriminator characteristics of a digital phase-frequency detector (DPFD) were analyzed in detail, and analytical expressions that correctly predict the high-frequency behavior of the circuit were derived.
Abstract: The phase and frequency discriminator characteristics of a digital phase-frequency detector (DPFD) are analyzed in detail. Analytical expressions that correctly predict the high-frequency behavior of the circuit are derived. The results show excellent agreement with measurements and computer simulations. >
TL;DR: In this paper, the phase lock operation between the VCO output as the reference signal and the input signal in the buffer memory is carried out after the PLL is kicked off with the optimum initial phase and the optimum center frequency determined in the initial training mode.
Abstract: A phase lock loop for a digital input signal has a phase detector, a loop filter, a digital voltage controlled oscillator (VCO), an initial phase difference calculator, a center frequency difference calculator and an input buffer memory. In an initial training mode prepared in the PLL operation, an optimum initial phase and an optimum center frequency of the VCO to complete a lock-in state is searched for the input signal stored in the buffer memory. By estimating the initial phase difference and the center frequency different between the input signal and the VCO output with repetitive kick-offs in calculators, optimum values mentioned above are obtained. In a normal operation mode as a second mode in which the PLL operates normally as a conventional PLL, a phase lock operation between the VCO output as the reference signal and the input signal in the buffer memory is carried out after the PLL is kicked off with the optimum initial phase and the optimum center frequency determined in the initial training mode.
TL;DR: In this paper, an optimized Coriolis mass flow meter is presented, which has improved stability to excitations caused by external influences by determining by modal analysis of the flow conduit a location for the sensor means that minimizes the influence of external excitation of one or more of the first in phase bending mode, the first out of phase twisting mode, and the second out of Phase bending mode.
Abstract: An optimized Coriolis mass flow meter is disclosed which has improved stability to excitations caused by external influences. A primary source of improvement involves determining by modal analysis of the flow conduit a location for the sensor means that minimizes the influence of external excitation of one or more of the first in phase bending mode, the first out of phase bending mode, the first out of phase twist mode, the second out of phase twist mode, the second out of phase bending mode and the third out of phase bending mode.
TL;DR: In this paper, a laser is used to generate coherent laser beams, which are then coupled with photodetectors to measure the relative phase between the signals from each photodeter and signal amplitude determining means for determining the relative amplitude of the signals.
Abstract: Means for measuring parameters associated with particles is disclosed. A laser (25) is provided for generating a pair of coherent laser beams (32, 34). These beams are directed along an axis and cross to define an interference pattern constituting a sample volume (16). A collection apparatus (46, 48, 50) for sensing light scattered by particles or the like within the sample volume (16) is provided. The collected light is directed onto photodetectors (50) which are coupled to signal phase determining means (54) for measuring the relative phase between the signals from each photodetector (50) and signal amplitude determining means to measure the relative amplitude of the signals. Sizing means (56) are coupled to the signal phase (54) and amplitude measuring means for determining the size of the particles. Means are disclosed for determining the change in the effective cross-section of the sample volume due to size variations of the particles passing through the sample volume (16).
TL;DR: In this paper, the phase angle of the magnetic flux is detected and the phase current is computed on the basis of phase current, and a q-axis-current control phase and a reference potential phase are determined based on the result of pulse-width-modulation computation and phase angle.
Abstract: A current component, in which a phase angle is different by a predetermined reference angle from a magnetic flux occurring in an inductive load, is brought to a q-axis current. The q-axis current is computed on the basis of phase current. A phase angle of the magnetic flux is detected. A q-axis-current control phase and a reference potential phase are determined on the basis of the result of pulse-width-modulation computation and the phase angle. The q-axis-current control phase is controlled in a pulse-width-modulation manner. A potential of the remaining reference potential phase if fixed to a reference potential. Thus, interference among the phases is prevented to reduce current ripple.
TL;DR: In this article, the phase position of pulses formed in a phase-locked loop is compared with the phase positions of pulses derived from a reference signal, and the phase error signal is amplified with a factor N (28) before adding or subtracting the correction value.
Abstract: The present invention relates to frequency synthesis with a controlled oscillator (20) included in a phase locked loop, where the frequency of the oscillator output signal is divided (22) periodically by different integers, such that the frequency is, on average, divided by a value which is equal to an integer N plus or minus a numeric fraction whose absolute value is smaller than one. The phase position of pulses formed in this way is compared with the phase position of pulses which derive from a reference signal (10, 12), therewith forming a phase error signal. For the purpose of suppressing periodic variations of an oscillator control signal as a result of phase jitter, there is added or subtracted to the phase error signal, in a known manner, a correction value (24, 26) which is dependent on the aforementioned numeric fraction. In order to eliminate the need to multiply the correction value by a factor which is proportional to the inverted value of the integer N, the phase error signal is instead amplified with a factor N (28) prior to adding or subtracting the correction value. The loop bandwidth is also held constant in this way.
TL;DR: A technique for nondestructive testing based on phase shifting TV holography and digital image processing is presented, which calculates the phase modulation of the object light caused by object deformation and smoothed the resulting deformation phase image to obtain a better signal-to-noise ratio.
Abstract: We present a technique for nondestructive testing based on phase shifting TV holography and digital image processing With this technique we calculate the phase modulation of the object light caused by object deformation The resulting deformation phase image is smoothed to obtain a better signal-to-noise ratio Smoothing is done by a new low pass filtering procedure we call phase shifting convolution This procedure is based on smoothing of two phase images: the original phase image and a second image obtained by spatial phase shift of the original phase image By combining the two smoothed images we obtain an image without smoothing errors close to the 2π phase ambiguities in the deformation phase image To detect surface areas with local inhomogeneous deformations indicating material defects, we calculate and display the deformation phase gradients Examples with testing of composite materials are shown
TL;DR: In this article, the position at start of a standing motor is determined by the injection of short current pulses in different motor phases, each phase or pair of phases being energized first by a pulse of one polarity and of the opposite polarity.
Abstract: The present method and apparatus detects the position with an accuracy of π/m electrical radians (where m=the number of motor phases) within one electrical period, and provides enough information to be able to start in the correct direction with certainty. More specifically, the position at start is determined by the injection of short current pulses in different motor phases, each phase or pair of phases being energized first by a pulse of one polarity and of the opposite polarity. The sign of the difference between the induced voltage is detected. By performing a succession of these tests on different phases or pairs of phases of the standing motor, a table of results is established which clearly defines the position of the rotor relative to the motor phases. The same table then defines what polarity currents should be applied to each phase to reliably and certainly start the motor in the proper direction. Additionally, a method and apparatus is presented which uses the static position detection method to accelerate the motor to a medium speed. The method shortens the duration of the drive pulse as the motor accelerates ensuring a smooth acceleration without the possibility of back oscillation.
TL;DR: In this paper, an alternating signal is applied to the object to be traced and the field produced by this signal is detected remotely from the object, and the phase relationship of the detected signals is investigated to determine unambiguously the position of the object concerned.
Abstract: A system for tracing routes of conductors is disclosed. An alternating signal is applied to the object to be traced (12), and the field produced by this signal is detected remotely from the object. In order to distinguish between signals produced by the object being traced and those produced by nearby conductors (14) due to capacitive coupling, the alternating signal has first and second components, related in frequency and phase, and the field is detected at a plurality of positions. The phase relationship of the detected signals is investigated to determine unambiguously the position of the object concerned. In one embodiment, the second frequency component is a harmonic of the other. In another embodiment the frequency of the second component is the frequency of the first, plus or minus a sub-harmonic of the first.
TL;DR: Possibilities of optical noncontact diagnostics of random phase objects are studied, based on measurements of transverse coherence function, scintillation index, and amplitude and phase dispersion of the field resulting from interaction with the object.
Abstract: Possibilities of optical noncontact diagnostics of random phase objects are studied, based on measurements of transverse coherence function, scintillation index, and amplitude and phase dispersion of the field resulting from interaction with the object. The advantages of these methods are increased speed and accuracy compared with commonly used methods. Interference measurements of second-and higher-order correlation parameters of the field phase is demonstrated which can be used to find the corresponding probability density distribution function for objects with phase statistics differing from Gaussian. The sensitivity threshold of the methods is estimated to be ~0.005 microm when measuring surfaces with slight roughness.
TL;DR: In this article, the authors proposed a light wave range finder capable of efficiently creating a signal necessary for measurement and capable of performing the measurement in a short time, which includes: a light emission element 11 for emitting a range finding light 28; signal generators 33, 34 for generating a plurality of proximity frequencies; intermittent pulse generators 35, 36 for producing a pulsed modulation signal in a prescribed width; an emission optical system for sequentially switching and emitting an intermittent modulation range-finding light for each proximity frequency; a light reception part 21 for receiving a reflected distance measuring light 28';
Abstract: PROBLEM TO BE SOLVED: To provide a light wave range finder capable of efficiently creating a signal necessary for measurement and capable of performing the measurement in a short timeSOLUTION: A light wave range finder includes: a light emission element 11 for emitting a range finding light 28; signal generators 33, 34 for generating a plurality of proximity frequencies; intermittent pulse generators 35, 36 for generating a pulsed modulation signal in a prescribed width; an emission optical system for sequentially switching and emitting an intermittent modulation range finding light for each proximity frequency; a light reception part 21 for receiving a reflected distance measuring light 28'; the other signal generators 55, 56 for generating a frequency signal having a difference of the predetermined frequency; frequency conversion parts 39, 43, 44, 57, and 58 for converting the frequencies into difference frequencies by mixing; and a calculation control part 52 The calculation control part intermittently generates respective proximity frequencies so that the pulse width of the intermittent modulation distance measuring light is made shorter than the cycle of the difference frequency A difference frequency waveform is calculated A phase is obtained from the waveform for one cycle of the difference frequency, a precise measuring distance is calculated, a mutual phase difference of the difference frequency waves is calculated, a rough measuring distance value is calculated, and the distance is measured from the rough measuring distance value and the precise measuring distance valueSELECTED DRAWING: Figure 2
TL;DR: In this article, a ring oscillator is used to generate a calibration signal (316) oscillating at a first frequency and a power source that supplies a compensated power signal to the ring oscillators (304).
Abstract: A device and method are presented which allow the precise generation of signals within an integrated circuit (200) that are calibrated to an external reference signal (306). The device consists of a ring oscillator (304) which generates a calibration signal (316) oscillating at a first frequency and a power source that supplies a compensated power signal to the ring oscillator (304). The first frequency is variable based on the voltage of the compensated power signal. A phase detector (401) is used to detect the relative phase of the calibration signal and the external reference signal (306). The compensated power signal is also used for critical data paths within the integrated circuit (200) where precise timing is required. In a tester, a plurality of signals (218) may be extracted from the ring oscillator (304) using a series of taps. These signals will oscillate at the same frequency as the calibration signal (316), but will be phase shifted. The signals may be combined with multiplexors (403,404) to form a test signal (226) which is applied to a device unter test (DUT). Further, in order to make transparent propagation delay, delayed calibration signals (317) may be generated.
TL;DR: In this paper, a triode plasma reactor with first, second and third electrodes for forming a plasma in a reaction chamber from a reactant gas includes a phase modulated potential generator for generating time varying potentials.
Abstract: A triode plasma reactor having first, second and third electrodes for forming a plasma in a reaction chamber from a reactant gas includes a phase modulated potential generator for generating time varying potentials on the second and third electrodes which are phase modulated versions of one another. The phase modulated versions may also include a fixed phase shift between them. By time varying the phase angle relative to a set phase shift, a new dimension of time varying control for the reactor may be obtained. Phase modulation at frequencies from audio frequencies to radio frequencies may be provided. Phase modulation may be accomplished digitally or in the analogue domain.
TL;DR: In this paper, the rotational position of a standing motor is determined by the injection of short current pulses in different motor phases, each phase or pair of phases being energized first by a pulse of one polarity and of the opposite polarity.
Abstract: The present method and apparatus detects the position with an accuracy of π/m electrical radians (where m=the number of motor phases) within one electrical period, and provides enough information to be able to start in the correct direction with certainty. After starting the motor in an open loop mode of one or two steps, starting the rotor in the correct direction, the closed loop mode may be switched on, using a dynamic indirect position detection as is already well known in the technology. More specifically, the position at start is determined by the injection of short current pulses in different motor phases, each phase or pair of phases being energized first by a pulse of one polarity and of the opposite polarity. The sign of the difference between the induced voltages is detected. By performing a succession of these tests on different phases or pairs of phases of the standing motor, a table of results is established which clearly defines the position of the rotor relative to the motor phases. The same table then defines what polarity currents should be applied to each phase to reliably and certainly start the motor in the proper direction. The present invention includes a method and apparatus for optimizing the duration of the short current pulses used in determining the rotational position of the rotor.
TL;DR: In this article, an experimental balanced optical phase-locked loop was constructed using two 1320 nm diode-laser pumped miniature Nd:YAG lasers with a natural frequency of 13.5 kHz and a damping factor of 0.6, the loop phase error is less than 13.3 degrees when the received signal power P/sub s/ is -65 dBm.
Abstract: An experimental balanced optical phase-locked loop was constructed using two 1320 nm diode-laser pumped miniature Nd:YAG lasers. With a natural frequency of 13.5 kHz and a damping factor of 0.6, the loop phase error is less than 13. degrees when the received signal power P/sub s/ is -65 dBm. For signal powers P/sub s/>or=-62 dBm, the phase error is 0.3 degrees , and is virtually independent of the signal power. When the natural frequency is 74 kHz, the damping factor is 0.03, and the DC gain is 68 MHz, the loop exhibits a chaotic behavior: it maintains the frequency lock, but not the phase lock. Using a phase-locked loop, phase-shift keying homodyne transmission is demonstrated at 140 Mb/S and 2 single-moded fiber is -62.8 dBm, corresponding to 25 photons/b. >
TL;DR: In this article, a generalized phase shifting interferometiy is proposed, where the reference phase, instead of being setto predetermined values, is directly evaluated at each time the interference fringe data are read.
Abstract: This paper describes a generalized phase shifting interferometiy where the reference phase, instead of being setto predetermined values, is directly evaluated at each time the interference fringe data are read. The evaluation of the phase shifted is achieved by introducing the FF1' method for analyzing additional straight fringes on theinterfering plane. The repeatability in the measurements of an optical surface is V500 when the generalized algorithm with 8 data acquisitions is used. 1. INTRODUCTION The phase shifting interferometry has unique characteristic of 2-D phase distribution measurement without scanning. In phase shifting inteiferometry the relative phase is varied in a predetermined manner and the phase distribution is evaluated from the modulated interferograms according to these shifted phases.1 It has been shown that phase extraction algorithms in phase measurement interferoinetry can be developed from the principleofleast-squares estimation.2 The generalized data reduction algorithm for heterodyne interferometry is proposed,
TL;DR: In this article, the phase difference between real and imaginary components of the discrete Fourier transform (DFT) of both the left and right velocity sensor waveforms evaluated at the fundamental frequency at which the flow tubes vibrate is measured.
Abstract: Apparatus and accompanying methods for use therein for a Coriolis mass flow rate meter which is substantially immune to noise, and more particularly, to such a meter that is substantially unaffected by noise that occurs at substantially any frequency different from a fundamental frequency at which the flow tube(s) in the meter vibrate. Specifically, the meter relies on measuring mass flow rate by determining the phase difference that occurs between real and imaginary components of the discrete fourier transform (DFT) of both the left and right velocity sensor waveforms evaluated at the fundamental frequency at which the flow tubes vibrate. The fundamental frequency is located, during an initialization operation, by providing a power spectrum, determined through use of the DFT of one of the sensor signals and then selecting that frequency at which the magnitude of the power spectrum reaches a maximum value. In addition, the frequency at which both velocity sensor signals is sampled is readjusted in response to any change in the phase of one of the velocity sensor signals, as transformed using the DFT, in order to assure that the sampling frequency always remains substantially equal to a pre-defined integer multiple of the fundamental frequency. Furthermore, the meter, through use of the numerical value of any such phase change, also provides a density indication which is also substantially immune to such noise.