Showing papers on "Sine wave published in 1968"

Non-linear capillary instability of a liquid jet

Abstract: A third-order theory has been developed to study capillary instability of a liquid jet. The result shows that the asymmetrical development of an initially sinusoidal wave is a non-linear effect with generation of higher harmonics as well as feedback into the fundamental. The growth of the surface wave is found to depend explicitly on the dimensionless initial amplitude of the disturbance and the dimensionless wave-number k of the wave. For the same initial disturbance, the wave is found to have a maximum growth rate at k = 0·7 in agreement with the linearized theory. For the same wave-number, the growth is proportional to the initial amplitude of the disturbance. The cut-off wave-number and the fundamental frequency (or growth rate for the unstable case) of the wave for a given k are found to be different from the linearized theory. Furthermore, at the cut-off wave-number, the present theory shows the disturbance experiences a growth which is proportional to t2. The excellent agreement between Donnelly & Glaberson's experiment and Rayleigh's linearized theory is found to be due to their method of measurement.

Auditory Responsivity in the Human Neonate

Abstract: ELECTROMYOGRAPHIC, autonomic and electroencephalographic responses were recorded from human neonates during stimulation with sine and square wave tones and with human voices. This communication will concentrate on the analysis of the electromyograms, both because of their importance in reflecting behavioural changes, and because changes in autonomic activity, such as heart rate acceleration, are associated with movements. The “artificial” sounds were chosen so as to have certain structural similarities to the “biological” sound: they were either sine wave components of it or selected fundamentals with superimposed high frequencies. Sine wave and square wave tones of the following frequencies, rising by octaves, were selected: 125, 250, 500, 1,000 and 2,000 Hz. Further sine and square wave tones at 70 Hz were added because preliminary studies had suggested that responses to sound frequencies lower than 100 Hz may have especially interesting properties. Recordings of a male and of a female voice saying “baby” were also included.

The transient for Stokes's oscillating plate: a solution in terms of tabulated functions

Abstract: The motion of a semi-infinite incompressible fluid caused by the sinusoidal oscillation of a plane flat plate is termed Stokes's problem. When the plate starts from rest in a still fluid a transient solution must be added to Stokes's well-known steady-state result. This paper presents a closed-form expression for the transient solution. Previous answers have contained a non-standard integral which could not be evaluated. The answer presented herein contains exponentials and error functions of a complex argument. These functions are readily available in newer mathematical tables. Graphs of the transient solution are presented for both sin (T) and – cos (T) boundary conditions. Velocity distributions in the fluid are also plotted and it is found that the transient period is essentially complete in one-half cycle for the cosine oscillation and in a full cycle for the sine wave case.

Dynamic Analysis of Muscle Spindle Endings in the Cat Using Length Changes of Different Length‐Time Relations

Abstract: Primary and secondary muscle spindle endings in the ankle extensors of the cat were studied in response to length changes of ramp, triangular wave, sine wave and parabolic wave form with the intention of finding the most suitable input signal for an extensive dynamic analysis of the spindle during constant fusimotor input. In dynamic tests the spindle endings were not found to obey linear length-response transfer functions; no support for a power function relation could be obtained.Sine wave analysis was therefore not considered suitable for the purpose of determining the transfer functions.Attention was directed towards the use of step changes of velocity and of acceleration of length changes.No evidence for a specific sensitivity to acceleration was found in responses to ‘parabolic’ length changes.Responses interpreted as due to mechanical properties in the spindle elements resembling ‘stiction’ were obtained when ‘ramp’ length changes were applied.These effects were largely avoided when recurring ‘triangular’ length changes of constant velocity were used.It is concluded that the dynamic analysis might be adequately performed by subjecting the musscle spindles to periodically recurring length changes of triangular wave form giving step changes in velocity.

Minimum rms bandwidth of M time-limited signals with specified code or correlation matrix

Abstract: The minimum rms (root-mean-square) bandwidth of M real equi-energy time-limited signals is derived for the case of either a specified code or a specified correlation matrix. The minimum bandwidth depends only on the nonzero characteristic roots of the correlation matrix, or equivalently, of a matrix derived from column properties of the code. The optimum waveforms depend additionally on the characteristic vectors of the respective matrix and are given by linear combinations of a time-limited fundamental sine wave and its harmonics. An upper bound on the minimum rms bandwidth is approximately proportional to the rank of either matrix. Applications to several codes and correlation matrices are given, including some best binary group codes, which indicate a worthwhile saving of bandwidth for the optimum waveforms as compared with conventional waveforms. The energy concentration of these optimum rms waveforms compares very favorably with that of the time-truncated prolate spheroidal wave functions, which concentrate most energy in an assigned frequency band. Furthermore, the optimum rms waveforms are easier to generate and process.

Low frequency sine wave generator circuit

Abstract: A sinusoidal signal generator circuit comprising at least two bridge circuits each comprising two pairs of series-connected bidirectional current control means connected across a source of direct current DC voltage, each bridge circuit having a pair of output terminals at the juncture of the current control means said pairs of current control means at very low frequencies like 60 cycles per second being connected directly in series. The noncorresponding current control means of the pairs of current control means of each bridge circuit are rendered nonconductive sequentially and in different combinations to produce different rectangular pulse output waveforms at the output terminals of said bridge circuit, each waveform respectively comprising positive and negative going pulses of the same amplitude relative to zero, the pulses of the different waveforms each cycle preferably being different in number and phase and of different magnitude, so the waveforms combine in both additive and subtractive relation to produce a resultant stepped sinusoidallike resultant waveform.

Effect of two-dimensional multiple sine-wave protrusions of the pressure and heat-transfer distributions for a flat plate at Mach 6

Abstract: Effect of two dimensional multiple sine wave protrusions on pressure and heat transfer distributions for flat plate in hypersonic flow

Dual speed gated counter

Abstract: Counting apparatus for determining the elapsed time between a reference pulse and the next following positive peak of a delayed sine wave irrespective of the DC level of the sine wave. The apparatus comprises a clock pulse source producing full rate and half rate pulses which are applied through respective gates to a single pulse counter. The first (full rate) gate is turned on by the reference pulse and is turned off upon the first following positive-going crossover of the delayed sine wave. The second (half rate) gate is turned on simultaneously with the termination of the first gate and is turned off upon the next following negative-going crossover of saId delayed sine wave.

Photoelastic Study of High-Frequency Stress Waves Propagating in Bars and Plates

Abstract: This paper deals with the photoelastic analysis of stress waves in bars and plates subjected to damped sinusoidal loading. The device used to apply the loading is a piezoelectric transducer which produces about 10 cycles of a decaying sine wave. The wavelength of the stress wave which propagates along the square bar is comparable to the thickness of the bar. A strobotac, or a microflash, is used as light source flashing with a continuously variable delay. The isochromatics and isoclinics can be seen directly by eye as static patterns. More than 100 repetitions of illumination can be used, permitting the use of fine grain film. The specimens are relatively thick, but by using embedded polarizers and analyzers, two-dimensional solutions can be obtained. Good correlations with theoretical computations are shown for phase and group velocities. Stress distributions are determined along the center line and the edge of the bar.

First and second passage times of sine wave plus noise

Abstract: This paper is concerned with the first and second passage times of a stationary random process, I(t, a), consisting of a sinusoidal signal of amplitude (2a)1/2 plus stationary Gaussian noise with a finite expected number of zeros per unit time. This type of random process is present at the output of the IF amplifier of a radio or radar receiver during the reception of a sinusoidal signal immersed in Gaussian noise. Approximate integral equations are developed whose solutions yield approximate proba-ability densities concerning the first and second passage times of I(t, a). The resulting probability functions are presented in graphs for the case when the frequency of the sine wave is located in the center of a band of noise. Related results concerning the approximate distribution function of the absolute minimum or absolute maximum of I(t, a) in the closed interval [0, τ] are also presented.

Distance measuring systems

Abstract: A distance measuring system comprising means for transmitting a sinusoidal wave or a sinusoidally modulated wave and receiving the same after reflection on a target and means for converting the phase shift, due to the propagation of this wave out and back, into a measuring signal the frequency of which is proportional to the travelling distance of said wave.

Electronic halftone image generator

Abstract: 1295646 Facsimile systems RCA CORPORATION 21 Nov 1969 [26 Nov 1968] 57127/69 Heading H4F In a half tone facsimile system, wherein an electron beam 17 produces regularly occurring dots of variable size on the face of a cathoderay tube 16 in response to continuous signals, e.g. from a flying spot scanner 24, photomultiplier 36 and a viewed transparency 12 (or opaque photograph reflecting light), the amplitude of the continuous signals is used to vary the intensity of the electron beam, to vary the time it is biased on, and to vary the amplitude of a transverse spot wobble superimposed on the substantially linear, vertical, raster scan. In the embodiment shown, which produces a negative image on the tube 16 and therefore a positive on a film 18 viewing the tube, a clock 56 produces pulses which are halved in frequency and used to actuate a sample and hold device 52 receiving the continuous signals. The stepped output signal 53 modulates a sine wave signal from a generator 72 and is fed to a "wobble" coil 74, i.e. in this case a relatively large signal produces a relatively small spot wobble. The frequency of the spot wobble is such that the light spot 15 overlaps itself in every alteration. The signal 53 is also fed to a bias grid 78 so that the beam is more intense for large amplitude spot wobble, thus ensuring correct recording on the film 18. The pulses of half clock frequency are also used to produce at 82 isosceles triangular waves coextensive with the steps of signal 53, which are compared at 80 with the steps of signal 53, Fig. 3 (not shown). In the period wherein the triangular wave exceeds the signal step, the beam 17 is biased on, and since isosceles waves are used, the centres of the spots are regularly spaced. The circuitry within the dotted line ensures that even and odd pulses from the clock 56 are used on alternate linear scans, thereby producing a 45 degree screen effect on the tube 16, Fig. 2 (not shown). For off-line working, the signal 53 may be stored, 67, 69, and the same tube may be used for scanning and reproduction.

Electrical frequency detecting device and method

Abstract: An electrical device and method for determining whether a plurality of input pulses occur at a repetition rate which is above or below a given reference rate involves the use of a timing means in the form of a capacitor timing circuit which is discharged by each input pulse and which is charged to a predetermined triggering level and produces output pulses if such input pulses do not occur at or above the reference rate. A waveto-pulse converter is connected with the input of the basic device to adapt it for use in determining the frequency of input signals in the form of sine waves, square waves or other cyclical waves other than pulses. A flip-flop and an AND or NAND gate may be connected to the output of the basic device to produce output pulses when the input signal has a frequency or pulse repetition gate greater than the reference frequency or rate, and two units may be combined to produce a band detector for determining whether the input signal has a frequency or pulse repetition rate falling within a given band.

A Predictable Subnanosecond Step Generator

Abstract: Determination of the response of a time domain instrument to a voltage step is preferable to determination in terms of its response to sine waves. Unfortunately the output waveshape of a voltage or current step generator cannot be evaluated as easily as that of a sine wave source. Consequently, investigators rely (or should rely) upon waveform predictability rather than waveform measurement when employing step generators in system characterization. One form of a predictable step generator is discussed that is useful in the subnanosecond to tens of nanoseconds time region after the step edge. A practical realization of this form is given that has predictability to within 1 percent in that time region from 350 picoseconds to 6 nanoseconds after an 80-picosecond rise-time step edge.

Harmonic sine wave data transmission system

Abstract: A data loop exchanges digital information in the form of sequential combinations of fundamental and third harmonic sine wave signals. The transmitted signal is formed by selectively gating the output signals from phase and frequency synchronized fundamental and third harmonic oscillators in signal periods between zero crossings of the fundamental signal. The received signals are amplitude detected at the midpoint of each signal period. The oscillators associated with one transmission circuit of the loop are synchronized to the oscillators of the other transmission circuit so that digital information may be simultaneously exchanged between the terminal devices of the loop.

Heat transfer and pressure distributions due to sinusoidal distortions on a flat plate at Mach 20 in helium

Abstract: Heat transfer and pressure distribution due to two-dimensional repetitive sine wave distortions on flat plate at Mach 20 in helium

Measurement of Shutdown Margin

Abstract: A method was developed and investigated for directly measuring the shutdown margin in a reactor operating at a subcritical steady state. Measurements were made on the Iowa State University UTR-10 reactor with conditions ranging from almost critical to fully shutdown. The method is based on the fact that the frequency dependent transfer function of the reactor is a measure of the response of the reactor to an input disturbance. The magnitude of the transfer function of a subcritical reactor depends on the frequency of the disturbance and the steady-state multiplication factor. Since the multiplication factor is a measure of the reactivity, the amplitude of the transfer function is a direct indication of the shutdown margin. A sinusoidal disturbance was introduced by means of an oscillator operating in the center of the core. The oscillator was operated at a fixed frequency of 10 cps in order to eliminate the frequency dependence. The fluctuation was measured by a BF3 detector located against the outside of the core opposite the oscillator. The signal emitted by the detector contained bombardment noise and instrument noise in addition to the desired information. The signal was passed through a band-pass filter and was then cross-correlated with a pure sine wave to obtain the transfer function. A plot of the transfer function vs. the multiplication factor was a smooth function from which the multiplication factor could be found with a confidence of ± 0.04% near critical and with a confidence of ± 0.17% in the fully shutdown condition.

Square and Sine Wave Modulation of the Beam from a 3 MV Van de Graaff Accelerator

Abstract: Methods of producing square and sine wave beam modulation of a 3 MV Van de Graaff accelerator are described. Square pulses are produced at frequencies from 100 kc to zero with up to a 100% duty cycle and a minimum pulse length of 8 μsec. The ratio of the off‐current level to the on‐current level is less than 5×10−4 and can be further reduced by a post‐acceleration deflection system to less than 10−5. The unit, which is triggered from a command pulse external to the machine, is in the top terminal of the Van de Graaff and has shown itself to be highly reliable over some 1000 h of machine operation. The sine wave modulation unit described here operates in the range 80–1000 cps with a modulation depth of up to 90% and higher harmonic contamination of less than 1%.

Phase-sensitive detector having means for synthesizing a sine wave plus harmonics

Abstract: THERE IS PROVIDED A PHASE-SENSITIVE DETECTOR FOR A SIMPLE HARMONIC WAVEFORM INCLUDING MEANS FOR SYNTHESIZING A SINE-WAVE PLUS HARMONICS BY GENERATING A PULSE TRAIN IN WHICH THE PULSES ARE EFFECTIVELY WEIGHTED -E, O+E AND IN WHICH THE PULSE CLOCK RATE, NUMBER OF PULSES AND PULSE DISTRIBUTION ARE SO ARRANGED THAT THE AMPLITUDES OF SELECTED HARMONICS IN THE SYNTHESIZED SINEWAVE ARE MINIMIZED, MEANS FOR MULTIPLYING THE INCOMING SINE-WAVE WITH THE SYNTHESIZED SINE-WAVE, MEANS FOR INTEGRATING THE RESULTANT AND MEANS RESPONSIVE TO THE VALUE OF THE INTEGRATED RESULTANT FOR ADJUSTING THE PHASE OF THE SYNTHESIZED SINE-WAVED RELATIVE TO THE PHASE OF THE INCOMING SINE-WAVE.

Frequency Measurement Techniques

Abstract: This paper considers the problem of digital frequency measurement of band-limited sampled data signals. The signal is assumed to be a fixed sine wave in noise over the measurement interval. The advent of low-cost A/D converters and the drastic price reductions predicted for IC's in the near future make techniques of this type appear practical for special-purpose digital hardware as well as a general-purpose computer. The probability density function is determined for frequency measurements based on the nth root of the ratio of the derivative of the signal to the signal itself, or its quadrature component. The results are compared with the instantaneous rate of change of phase technique. In addition, attention is paid to techniques for computing the derivatives of a signal. It is shown that a Lagrange formulation yields an excellent approximation to the first and second derivatives as long as the signal is sampled at no less than twice the Nyquist rate. Finally, it is shown that for a given error, sampling at approximately twice the Nyquist rate minimizes the number of arithmetic operations required per unit time and bandwidth.

Application Of The Fast Fourier Transform To The Calculation Of The Optical Transfer Function

Abstract: The calculation of the optical transfer function from lens design data by digital computer has become common today. The optical transfer function describes the imaging of a spatial sine wave by the optical system. The amplitude of a sine wave is described by the modulation, M, given by the equation© (1968) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Signal-to-Crosstalk Power Radio in Smoothly Limited Multichannel FDM Signals

Abstract: The passage of multichannel frequency division multiplexed (FDM) signals through an amplitude limiting nonlinear device produces crosstalk in each channel output due to intermodulations among signals in all channels. The signal power S 0 to crosstalk power N c ratio in any particular channel determines signal degradation. This paper considers multichannel FDM signals passing through a saturated bandpass amplifier with transfer characteristic of smoothly limiting error function curve, and determines a lower bound of S_{0}/N_{c} as a function of q , which is related to the limiting level. By invoking the central limit theorem, the FDM signals are represented by a Gaussian noise, excepting the signal in the channel where S_{0}/N_{c} is to be determined. The signal in the channel under consideration is represented by a constant amplitude sine wave. When an assumption that the input noise power spectral density is symmetric about the center band is made, such as a Gaussian power spectrum considered in the analysis, the computation of a lower bound for S_{0}/N_{c} was equivalent to the consideration of the center channel, where the crosstalk power is maximum. The problem is an extension of an earlier work by Cahn, who considered an idealized saturation amplifier. The result is presented in a graph where it is seen that an infinite clipping case of the present analysis agrees with that of Cahn.

Apparatus for generating an approximation to a sine wave including a reading head with two spaced areas for scanning an optical grating

Abstract: The invention is concerned with a reading head for moving in relation to an optical grating for giving a position signal. The position signal may be made very nearly the true sine wave by appropriate choice of the spacing between apertures in the head in relation to the pitch of the grating and/or by appropriate shape of the apertures.

A Comparison between Two Methods of Determining the Thermal Diffusivity of a Moist Soil1

Abstract: Two types of solutions of the heat flow equation were discussed and proposed recently as methods for evaluating the thermal diffusivity of soils. The first one is the harmonic solution for a sine heat wave while the second uses the Laplace transform for solving the heat flow equation. This work was carried out in order to compare the thermal diffusivity values obtained by using these two solutions. Experimental data were analyzed for dry soil as well as for wet soil having 4.5, 7.8, and 14.5% water on dry weight basis. The thermal treatments were: three types of heat waves, a sine wave, half square and a full square wave, all having an amplitude of 6C and periods of 8 and 16 min. For dry soil the sine wave solution yielded lower values than the Laplace solution did. For the wet soil the same trend was observed for the short period while for the longer period a cross-over, namely, higher values were obtained using the sine wave solution than those obtained by the Laplace solution. These differences are discussed in the light of the experimental conditions and moisture transfer during the heating period.

An improved phase shifter for phase sensitive detectors

Abstract: A method is described in which a phase shift is produced, between an input sine wave and an output square wave, which is calibrated over the range -25° to +385° for a wide frequency range. The circuit is intended for use with phase sensitive detectors which are required to work with variable reference frequencies.