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This paper examines the capabilities of the class of linear FM spread-spectrum signals within the context of potential communications systems usage in order to establish some performance criteria and bounds that permit comparison with other spread-spectrum formats. A systematic basis is provided for parameter selection for this class of signals by examining the interaction a mong the frequency-modulation indices, time-bandwidth product, and cross-talk criteria that determine the number of effective linear FM signals (or channels) that can be used within the constraints of a bounded time-frequency region. A general expression is derived relating N, the number of useful signals, R2, a cross-talk parameter, ToWo, the mean time-bandwidth product, and ?max and ?min, the maximum and minimum FM rates of the signal set. Canonic signal processor structures are described for ensembles of linear FM signals that have either constant duration or constant bandwidth. It is then shown that the signal modulation format can be modified in accordance with classical paired-echo theory to expand the utility of this class of signals in both synchronous and nonsynchronous operations to yield the equivalent of time-division and code multiplexing. Possible applications for this signal format are discussed.

Radio-navigation systems in which position is determined as the intercept of two range-difference hyperbolae require a minimum of three transmitters to provide a pair of base lines, which are inclined to each other at an angle as close to 90° as practicable. Calculation of position in such systems, e.g. Decca, Loran &c., is generally a relatively complex process as the hyperbolae intersect at a random and widely varying angle.

The problem of minimum time frequency transitions in phase-locked loops with both phase and frequency controls applied is investigated using Pontryagin's maximum principle. Typically, a type II secondorder loop with a damping ratio of 0.707 subjected to a step change in the frequency of its input signal is considered and switchless control strategies that force the transients in the loop to settle down in minimum time are obtained.

This paper discusses the approach used in the design of an automatic discriminator calibrator system. This design led to analysis of the use of bi-stable multibrators to obtain a fractional countdown of the output frequency of a crystal oscillator. The final counter waveform is filtered to extract only a sinusoidal component of the square wave from the counters. Some properties of fractional counters are discussed, including the use of a 382.5:1 counter in the calibrator system.

In certain applications it is necessary to measure the center frequency of a symmetrical power spectrum in the shortest possible time. Two instrumentations for short‐time frequency measurement, the autocorrelator and the frequency discriminator, are examined for their ability to accomplish this task. The analysis compares the performance of the two systems and indicates the effect of such factors as signal‐to‐noise ratio and filter adjustment.

This paper is concerned with various aspects of the characterization of randomly time-variant linear channels. At the outset it is demonstrated that time-varying linear channels (or filters) may be characterized in an interesting symmetrical manner in time and frequency variables by arranging system functions in (timefrequency) dual pairs. Following this a statistical characterization of randomly time-variant linear channels is carried out in terms of correlation functions for the various system functions. These results are specialized by considering three classes of practically interesting channels. These are the wide-sense stationary (WSS) channel, the uncorrelated scattering (US) channel, and the wide-sense stationary uncorrelated scattering (WSSUS) channel. The WSS and US channels are shown to be (time-frequency) duals. Previous discussions of channel correlation functions and their relationships have dealt exclusively with the WSSUS channel. The point of view presented here of dealing with the dually related system functions and starting with the unrestricted linear channels is considerably more general and places in proper perspective previous results on the WSSUS channel. Some attention is given to the problem of characterizing radio channels. A model called the Quasi-WSSUS channel is presented to model the behavior of such channels. All real-life channels and signals have an essentially finite number of degrees of freedom due to restrictions on time duration and bandwidth. This fact may be used to derive useful canonical channel models with the aid of sampling theorems and power series expansions. Several new canonical channel models are derived in this paper, some of which are dual to those of Kailath.

This paper derives relationships which express the contribution of ground-receiver noise and round-trip transit time to the errors in two-way radio Doppler measurements. Only one method of Doppler measurement is considered. This is the method of counting the number of cycles in a given time interval. From this measurement the signal frequency may then be determined. In usual tracking systems this frequency measurement is further utilized to determine the range-rate of the vehicle with respect to the tracking station. The power-spectral densities of additive-receiver noise and oscillator-frequency noise are assumed white. This situation prevails when the random disturbances are thermal in origin. This is a tractable assumption when one seeks fundamental accuracy limitations for Doppler measurement. The results of this paper should be useful to those concerned with radio tracking and, in particular, tracking of space probes.

In comparing the similarity between time, frequency, and phase measurements as used in the induced polarization method of geophysical prospecting, parameters must first be defined and the basis for comparison established. The conditions for mathematical equivalence then follow in a natural sequence. Laboratory measurements are made on a variety of rock samples to indicate the type of comparison and correlation expected from field measurements. Results indicate that frequency domain and phase measurements are equivalent, but two frequency domain measurements are needed to produce the same amount of polarization information as a single phase measurement. Frequency and time domain measurements will be similar but never equivalent due to the basic differences in their respective parameter definitions.

MANY are familiar with raster patterns, particularly the example seen on the face of television receivers. In order to present the most picture information with least bandwidth, such regular raster patterns are stabilized by synchronizing signals, derived by subdividing the frequency produced by a piezoelectric crystal stabilized oscillator. However, the simplicity of using an independent, stable oscillator for each of the vertical and horizontal deflection waves has been appealing. This was especially so for the extensive circuitry and subdivision needed to furnish the high-speed scans and quadruple interlace required when Avion-Alexandri carried out a U.S. Air Force RADC contract to pursue the experiments in electronic image processing done at the National Bureau of Standards.1

Sweepers, wide-band noise pulses found in the HF range, have been observed at many locations on the globe. They display a changing frequency vs time characteristic. Two types, described as alpha and beta, have been noted. The duration of the beta type is so short that as it sweeps through 500-kc bandwidth its time rate of change of frequency exceeds the time resolution of the equipment. It appears singly or as multiples but most commonly as a double or triple event. The gross features of beta sweepers appear similar to those of atmospherics. Alpha sweepers display a measurable rate of change of frequency with time. They appear in trains; no multiple has yet been found. Alpha sweepers may result from man made or industrial processes, or may arise from solar or cosmic plasma interactions. In appearance on the f-t plane they resemble some solar radio noise bursts. Both sweeper types constitute interference to radio wave communications, especially to wideband systems. Measured sweeper intensities have varied from microvolts to millivolts at a bandwidth of 500 kc. HF sweeper intensities are modified by propagation conditions, distance from the source, solar activity, etc. For example, during the peak of solar activity both alpha and beta sweepers at 26 Mc would propagate more efficiently because of the higher existing MUF.

An important aid in the analysis and display of speech is the sound spectrogram, which represents a time-frequency?intensity display of the short-time spectrum.1-3 With many modern speech facilities centering around small or medium-size computers, it is often useful to generate spectrograms digitally, online. The fast Fourier transform algorithm provides a mechanism for implementing this efficiently.

The problem of generating a periodic voltage signal whose Fourier-series representation is given by a band of essentially uniform-amplitude frequency components is examined in this paper. A mathematical background is first established for the purpose of comparing various techniques. Three separate methods of generating the periodic voltage signal are then presented and discussed.

The synthesis of radar ambiguity functions is approached using burst-pulse time-frequency waveform coding. Noting that the parameters that define the central response of the ambiguity function for these code classes also define the waveform code, a statistical decision procedure based upon the central response is employed to obtain Bayes-type codes. The selection of the code parameters is subject to restrictions imposed by the noncentral response of the ambiguity function. Three classes of random time-frequency codes are treated: 1) uniform amplitude, uniform pulsewidth matched codes; 2) uniform amplitude, nonuniform pulsewidth matched codes; and 3) uniform amplitude, uniform pulsewidth with receiver amplitude mismatch.

The dynamic response of an averaging type FM discriminator to a general FM input is analysed on the assumption that the zero crossing of the input signal initiates impulses which are applied to a low pass filter. The boundaries between which the output voltage of that filter is varying are evaluated. The faithful decoding may start after an initial settling-down period which is often found to be short compared with the actual period of the measurement. In order to show the practical use of the result obtained, two examples are given which deal with a linear and a parabolic change of the frequency with time.

Using crystal-controlled frequency-shift techniques, this system provides fast operation with a high degree of reliablity. This discussion describes the design requirements and tells how they were met.

Sound in a frequency band from 4·1 kHz to 4·5 kHz was transmitted between a fixed source and fixed receivers, for ranges of 7 and 18 km in shallow coastal water. Simultaneous records of sound level were made at 12 frequencies spaced 36 Hz apart, and the whole arranged to form a time-frequency display. One sample display clearly shows symmetrical patterns due to the changing interference of several normal modes. The patterns arise since the mode parameters depend on water depth, which in turn changes through the tidal cycle. The measured pattern slope agrees with predictions from a simple theory, and it is also possible to calculate the number of modes participating. Another pattern shows modifications which are explained in terms of the tidal flow.

The general problem is stated and typical solutions indicated. Characteristics of governors and of frequency- and load-control devices are briefly explained, and effects on generator and tie-line loads are summarized. Illustrating the principles enunciated, interconnected systems in southern Ontario and adjacent portions of Quebec totaling 1,650,000-kw generating capacity are described, also operating experience with automatic frequency control, and automatic load control of two ties, one of which is a 45,000-kw frequency-changer set inter-connecting systems of relatively large capacity.

In order to determine the ac properties of laminated magnetic-core materials, a digital assembly has been developed to measure the mean half-period value nearly independent of frequency. Conventional integrating digital voltmeters are unsuitable for such measurements if the frequency fs of the unknown voltage does not fit the equation f s ?? T o = ``integer,'' where T o is the integrating time of the DVM. This error can be reduced considerably by the designed double-integration method. A FET switch supplies the analog signal to a low drift integrator generating a dc output corresponding to the voltage-time integral over n periods (n = integer). The signal switch is triggered internally by the unknown voltage or externally by one or two reference signals of the same frequency. Thus it is possible to sample any interval of the unknown voltage by appropriate phase shifting. The integrator dc-output voltage is converted to a proportional frequency, which is fed to a counter with variable gate time T m . If the signal frequency f 8 = 1 / T 8 = (n + k)/To, (-1/ 2 ??? k ??? + 1/2), T m will be reduced or increased by kT s . The systematic error is a function of (k/f)2. The overall accuracy in the frequency range 25 Hz-1 kHz and the voltage range 15 mV-7.5 V is better than 5-10???4. Additionally, the equipment measures the arithmetic mean and, with an internal dc reference, the angle between the zero crossings of two voltages.

Induction resolvers are commonly used as coordinate converters in many systems in which vector resolution is required. In systems that require several coordinate conversions, the error due to the conversion mechanism may limit the accuracy of the system. Because of the inherent nonlinear nature of coordinate conversion, this error is, in general, difficult to determine. In this paper, a resolver model and a statistical basis for computing the error due to the conversion mechanism are developed. Two example resolver coordinate converters and the confidence limits for their resolution accuracy are presented.

The constant-amplitude random function generator described in this report resulted from the need for an electronic generator which would combine some of the properties of random noise waveshapes with the known characteristics of periodic, constant-amplitude waves. In this instance, a wave shape was desired which had as a main feature a constant peak-to-peak amplitude, but whose path between peaks was in some way randomly chosen.

This paper describes the principles used in controlling the load in a large interconnected system. Automatic frequency controllers with time-error correction and tie-line controllers with frequency bias and time-error correction have been developed for co-ordinating the operations of interconnected systems of any size and geographical extent. Automatic control of two or more stations simultaneously within a group is described, and the relation of the auxiliary frequency controllers to the speed governors is also discussed.

A sampled-data model of the human operator in compensatory tracking is proposed. The model assumes that the operator's behavior is characterized by sampling, data reconstruction and extrapolation operations. The spectral characteristics of the new model are presented.

A satellite and space vehicle tracking system of the Doppler type, known as DOPLOC, is described. The characteristics of the heart of the system, a phase-locked tracking filter, are discussed from the viewpoints of bandwidth, signal-to-noise ratio, and accuracy of Doppler frequency measurement. System sensitivity to low energy signals is shown to be 2 × 10-29 watts at a bandwidth of 1 cps. Tracking ranges vs frequency are given for constant gain and constant aperture antennas. The advantages of DOPLOC in satellite tracking programs are briefly discussed.

One of the limitations of FM/CW radars, often quoted in the literature, is in their inability to handle multiple targets. Several variations of a comparatively simple Range/Range Rate Display, capable of handling and resolving a large number of targets when used in conjunction with an FM/CW radar, are presented. The FM/CW plane and means for resolving target ambiguities are discussed, as well as system features, which, when used in conjunction with the displays, enable multiple target range and velocity information to be obtained and utilized simultaneously.

The development and construction of a visual voice-frequency transmission-measuring set is described, and a short summary of its applications is included. The instrument provides for the display of measurements of level, impedance, return loss, impedance comparison and level comparison on the face of a CRT (cathode-ray tube) as a function of frequency. The values in db (decibels) or ohms are read directly from a calibrated graticle. The instrument described is the latest of a series whose initial development was begun in 1941.

Four-frequency channels avoid the prior slot interference that handicaps single-frequency collision avoidance systems of equal message-slot capacity. Crosstalk between adjacent frequency channels is adequately limited If the receiver response to adjacent-channel signals is attenuated at least 52 dB. With 5-MHz channel separation, 48-dB crosstalk rejection was achieved in a test receiver by restricting the RF pulse rise time and decay time to 0.2 ?s minimum. Crosstalk resulting from biphase modulation can be effectively attenuated by limiting the minimum envelope transition time to 0.2 ?s. The effect of pulse rise time and decay time on the energy density spectrum is discussed.

To satisfy already existing needs for higher precision in various time measurements, a world-wide system of synchronized clocks is required. One possible method for accomplishing such a system, the transportation of operating precision clocks, is discussed. Particular consideration is given to the use of atomic clocks in this connection, and methods of maintenance of synchronization by means of phase tracking of a central master clock via VLF transmissions are reviewed. Project WOSAC, a Signal Corps project of world-wide synchronization of atomic clocks based upon the principles discussed, is outlined and results already achieved are described.

This paper describes an electronically variable time-elay network that has been developed specffically for time-delay steering of a phased-array antenna. The network consists of microwave dispersive delay lines and two broad-band mixers; its delay is a function of the mixers' local oscillator frequency. The particularly advantageous feature of this network is that its phase is invariant with delay. It can, therefore, be used on a subarray basis, and at IF, without affecting the phase progression across the array. Alternative techniques, such as electron-beam delay lines and digitally switched line lengths, require external phase correction. A breadboard model of the network has been built and tested. Low-loss folded-tape meader lines provide the dispersive delay. The center frequency of the model is 3 GHz; it handles an instantaneous bandwidth of 300 MHz. Delay variation of 25 ns is provided. The spurious responses of the network are 30 dB down.

Utilization of high frequencies for over-the-horizon surveillance necessitated a refined approach to the determination of actual ray paths. Various ray-tracing programs have been developed. The basic problem lies in accurately determining values of the appropriate ionospheric parameters. A possible means is by utilization of oblique sounding devices located at the path terminals to provide 1) relative propagation time difference (?t) between the modes, 2) maximum frequency propagated by any given mode (MUF), and 3) difference in MUF between the various modes (?MUF). The technique has not been fully verified; preliminary results are encouraging.

A simple instrument for measurement of eye movements has permitted demonstration of the fact that changing the characteristics of the target-position signal has important effects on the nature of the biological servomechanism controlling the movements. In particular, there is an adaptive predictor that allows the system to overcome its innate delays upon exposure to a regular input pattern.

Filtering a set of (2N + 1) sampled data consists in taking a weighted average of these data. The operation can be compared to that of a linear transducer, characterized by its frequency response. The only filters discussed in this paper are those for which the weights are either symmetric or skew symmetric about the center weight. With these types of filters, it is possible to design low low-pass filters to determine means and trends, low-pass filters to smooth data, sampling filters for frequency analysis, differentiators, integrators, etc. It is shown that least square polynomial fitting and Fourier analysis of sampled data are particular cases of filtering. Power of filtering techniques and precautions to take in their use for data processing are discussed

THE mathematical synthesis problem in linear servomechanism design is to find the description of the system when the desired output response to a given input is specified. The desired output, however, is often defined as the best that can be obtained, where the word ?best? has several connotations which include fastest transient response, minimum overshoot, and minimum tendency toward persistent oscillations. Under the assumption that there are no restrictions on the values that a sufficient number of system parameters may take, it is possible to apply suitable criteria and select the optimum response in a normalized time scale. The optimum response may then, theoretically at least, be reproduced, by adjustment of the system parameters, to an arbitrary time scale.

With respect to the present inquiry, cochlear analysis of an applied signal is considered to be given by the distribution of amplitudes along the partition. Since Ohm and Helmholtz, this form of resolution has been thought to correspond to the result of a straightforward Fourier analysis. The present paper intends to show that cochlear models of the Bekesy‐type perform a time/frequency analysis in the sense of Gabor. Along the existing time/frequency continuum, the response to sinusoidal signals represents one extreme, approaching a pure Fourier (frequency) analysis, and the response to transients the other extreme, approaching a pure time (waveform) analysis. Responses to all other signals arrange themselves between those two extremes; i.e., the resolution depends upon spectral as well as temporal features of the applied signal.With modulated signals, a process of demodulation occurs. Its origin was finally traced to hydrodynamic events which take place in the region of rapid phase changes of the traveli...

A DME concept is described based on the measurement of conditions associated with the standing waves permitted by an instantaneous range. It is shown that for a given power the instrument will operate at greater ranges with higher space resolution than is possible by direct transit time measurements. The role of oscillator stability in limiting the range of interferometers is investigated, and it is concluded that a standing wave DME can tolerate an oscillator instability bandwidth as great as c/2R.

A two-way microwave link between the Naval Research Laboratory and the Navy Observatory has been established to transfer both time and frequency information with high accuracy. Time and frequency information is transmitted simultaneously by algebraically adding together a precision 1 MHz signal and 1 pps, thus providing continuous phase information for frequency comparison and epoch time by the pulse. Phase resolution is better than 10 nanoseconds and determination of epoch time better than 0.1 microseconds. Seven precision standards have been intercompared via the microwave link. Continuous phase recording since September 1969 has shown no diurnal dependence and very little effect due to seasonal and temperature changes. A second microwave link has been established between The Naval Observatory and the Naval Research Laboratory's satellite research communications terminal in Waldorf, Maryland. (Author)

An analysis is conducted of the behavior of a single and double canceller moving target indicator (MTI) receiver in the presence of concentrated clutter. For the antenna beam, an analytical expression that also takes sidelobes into account has been used. In particular, the effect of limitation in the IF characteristic on cancellation has been studied. As a result, the improvement factor, defined as the ratio between the signal-to-clutter ratios at the input and at the output of the canceller, is considerably reduced by the nonlinearity.

Recent work on gas cell frequency standards has led to a clearer understanding of the capabilities of such systems. The physics of the quantum mechanical system allows the designer to start with a linewidth of approximately 1 part in 108 and with a signal-to-noise ratio, in a one-second noise bandwidth, in excess of 104. Carefully engineered systems have been demonstrated to have high stability with high reliability and small weight and volume. Frequency stability, which is the important quality of a standard, has been studied over a wide range of averaging and measurement times. A plot of standard deviation of frequency stability ? shows a broad minimum of ?= 2.5×10-12 for a run of 40 hours; a ?= 2×10-11 for a run of 15 minutes (? second averaging time); and ? = 4×10-11 for a run of 330 days.

The preprocessing of optical information in the visual system takes place in the two-dimensional homogeneous nervous nets of the retina and the geniculate body. These networks can be considered as band-pass filters for space-dependent oscillations if the input stimuli are independent of time. If the synapses of the neurons have timefrequency dependent properties the performance of the system in the space domain, which is important for pattern recognition, is determined by the time dependence of input signal. For a description of these networks in this investigation the space spectrum for various values of the time frequency ω is used. The answers of real nervous nets can be interpreted by the model when the two-dimensional input signals are switched, flickered or moved. For this reason these dynamic stimuli are necessary for an analysis of the cortex. The theoretical combination of space- and time-dependent filtering is essential for an understanding of cortical transformations.

Fourier analysis is used to show that the frequency spectrum of the output voltage of the linear detector of a spinning-goniometer direction-finding receiver varies as a function of time for a CW received signal. A filter for the second detector is considered having a bandwidth which varies with time in a similar way, thus effecting a ?match? between the signal and the filter. A simple signal-to-noise ratio analysis shows that an improvement in signal-to-noise ratio is possible, compared to performance of a time-invariant system. The improvement is described by the equation I = 10 log10 T/T1, where T is the observation time and T1 is the basic period of the envelope of the input signal to the second detector produced by goniometer modulation.

A new principle that makes possible nonquantized altitude information so that the accurate range of altimeters can be extended to include low-level operation is described. A frequency shifter is inserted between the local oscillator and the mixer in order to remove the inherent error in conventional altimeters that makes them objectionable for low-altitude operation. The authors show how the characteristic of the amplifier can be shaped diferently and point out that the strength of the return signal and the inherent amplitude modulation determine the most suitable characteristic for any particular operating condition.

THE MECHANICAL transients analyzer1,2 provides a fast and simple method of obtaining the complete solutions to the performance equations of servomechanisms under any type of operating condition. It has been found to be applicable to the detailed analysis of specific systems. Also, because of the great rapidity with which parameters of a basic system can be changed once that system is set up, the analyzer is admirably suited to generalized studies of various types of systems. This paper presents a general study that has been made of variable-voltage angular-position servomechanisms. The data give dominant system frequencies and damping rates for a two time delay system with simple error control and for a wide range of parameters. Similar data are presented for error control plus optimum anticipation time constants, together with other performance characteristics. Because of the many curves required for the same type of analysis of the several variations of resistance-capacitance-feedback and other forms of antihunt or damping devices, they will not be treated here.