Transient Nonstationary Behavior of a Delay Line Discriminator

The development of numerical methods for studying the transient nonstationary behavior of a delay line discriminator is presented. Expressions are developed for the mean and the variance of the output noise process. For the cases where the output is stationary, power density spectra are found.     

Signal-to-Noise Ratio in the Bandpass Output of a Discriminator

A formula is derived for the output signal-to-noise power ratio from a limiter-discriminator that is followed by an ideal (rectangular) bandpass filter. This signal-to-noise ratio is shown to be inversely proportional to the difference between the cube of the upper cutoff frequency and the cube of the lower cutoff frequency. The formula commonly utilized by designers for the discriminator output signal-to-noise ratio was derived for the case of a lowpass filter on the discriminator output. The bandpass and low-pass formulas are compared to indicate 1) the advantage of bandpass filtering for the discriminator output, and 2) the error incurred if the designer employs the low-pass formula to evaluate the performance of a bandpass filter design. Finally, the accuracy of a narrow-band approximation for the bandpass formula is evaluated.     

On the Mean Frequency Measurement System Using Correlation Detection

This paper is concerned with the problem of measuring the mean frequency of the power spectrum of a zero-mean, stationary, narrowband Gaussian random signal in the presence of additive Gaussian noise. Signal-to-noise ratios at the output of the mean frequency measurement system using correlation detection are analyzed in terms of input signal-to-noise ratio, input signal and noise bandwidths, and integration time. The results obtained are verified experimentally, and a comparison with a conventional zero-crossing detector is also made.     

Transmission Characteristics of an FM Signal Through a Hard Limiting Repeater

The response of an FM detector to an FM signal which is passed through a hard limiting repeater together with additive Gaussian noise is described. A general expression of the output SNR is derived that enables the determination of the threshold behavior. To clarify the feature of a transmission characteristic, a comparison with a linear repeater is also made. The output SNR is found to be larger than that of the linear system for all practical values of input CNR's.     

A Semi-Empirical Approach to the PLL Threshold

This correspondence considers the response of the PLL near threshold to an input consisting of a modulated carrier and white, Gaussian noise. For high input signal-to-noise power ratios ?, the output noise power is Gaussian with a parabolic spectrum. As ? is decreased, the PLL tends to lose lock which gives rise to impulses or ?spikes? in the output with a resulting white power spectrum. The additional output noise due to these ?spikes? causes a threshold in the output signal-to-noise ratio. Unfortunately the loss of lock rate in the PLL depends on the modulation as well as the noise power. A semiempirical approximate expression for the loss of lock rate as a function of the noise and sinusoidal frequency modulation is presented and is used to determine the optimum design procedure for PLL's to demodulate FM signals of varying modulation indexes, ?.     

An Analysis of the Performance of the Oscillating Limiter Driven by FM Signals Corrupted by Noise

The behavior of the oscillating limiter (OL) driven by FM signals is surveyed, and its performance with signal corrupted by noise is investigated. For high values of the carrier-to-noise ratio (CNR), if the frequency deviation of the signal is small in comparison with the locking range of the OL, it is calculated, and experimentally verified, that a system OL discriminator is equivalent to a system bandpass limiter discriminator followed by a linear network whose frequency response has been specified. When the frequency deviation is not so small, the baseband noise power increases with it; a formula is given that allows the calculation of this power when the signal is such that the circuit operates in quasistationary fashion. For low values of the CNR, a mathematical analysis presents unsurmountable difficulties. However, heuristic argumentation leads to an interpretation of the operation of the OL in the threshold region, which is substantiated by an experimental investigation. The results of this paper enable a comparative evaluation of a system OL discriminator and a system bandpass limiter discriminator, to which the former reduces when the feedback path in the OL is open.     

The Output Pdf of a Polarity Coincidence Correlation Detector

A general expression is derived for the probability density function of the output of a cross correlator, the inputs of which are assumed to consist of clipped sine waves of similar frequency plus uncorrelated, stationary Gaussian noise. The correlator output is shown to be a piecewise linear function of the random phase difference between the two input processes; hence, the density function for the correlator output is obtained by a relatively simple transformationfrom the probability density function of the random phase difference.     

Signal-to-Noise Ratios in Self-Biased-Pwer-Law Amplifiers with Saturation

The relation between the output signal-to-noise ratio (SNR) and the input SNR is presented for the bandpass self-biased third-law amplifier with saturation, when the input is composed of sinusoidal carrier and zero-mean stationary narrowband Gaussian noise. It is found that significant improvement in the output SNR at low input SNR's can be achieved by the self-biased third-law amplifier with saturation operated in class A. The results obtained are also verified experimentally.     

Probability Density Function at the Output of the Delay-Lock Discriminator

The first-order probability density at the output of the correlation network of the delay-lock discriminator is determined using the methods developed by Arthur, Kac, and Siegert. The analysis assumes that the input signal is stationary and Gaussian and that the discriminator is locked on. No restrictions are made on the bandpass filter characteristics in the channels.     

High power factor AC/DC/AC converter with random PWM

A three-phase AC/DC/AC converter is presented with a power factor preregulator to improve the power quality in the input side and a pseudorandom noise generator to reduce the emitted acoustic noise and the mechanical vibration for an induction motor drive. The space vector modulation with hysteresis current control for a voltage source rectifier is adopted to simplify the hardware circuit. A control scheme is presented to drive the supply current following the reference current. The amplitude of reference current for the pulsewidth modulation (PWM) rectifier is derived from the DC bus voltage regulator and the estimated output power. Random switching frequency technique for a three-phase PWM inverter system to reduce the annoying tonal noise and resonant vibration from an induction motor is described. By randomly varying the instantaneous PWM switching frequency from one cycle to the next, the frequency distribution of harmonics is spread in a wide frequency range. The major advantage for using such a strategy is the nonrepetitive output spectral characteristic that results in reduction of torque pulsations in motor drive systems. The nearly unity power factor at the three-phase rectifier and the absence of acoustic noise concentrated at the specific tones which is usually present with conventional sinusoidal modulation are verified by the experimental tests     

Output Signal-to-Noise Ratio for Amplitude and Intensity Modulated Laser

General expressions are obtained for output SNR for both amplitude- and intensity-modulated lasers, where bandlimited Gaussian noise has been chosen as a modulating signal, and in the presence of background light. Two types of modulating signals are considered: the baseband and bandpass modulating signals. Detailed calculations are made for output SNR when an ideal narrowband optical filter is used. The dependence of output SNR on several parameters, such as the center frequency of the modulating signal, the effective average quantum rate, and input SNR, are discussed. In addition, the difference in performance between amplitude and intensity modulation is discussed. The detection characteristics of the homodyne system are also considered.     

Detection of Known Signals in Nonstationary Noise

The basic design of a nonlinear, time-invariant filter is postulated for detecting signal pulses of known shape imbedded in nonstationary noise. The noise is a sample function of a Gaussian random process whose statistics are approximately constant during the length of a signal pulse. The parameters of the filter are optimized to maximize the output signal-to-noise ratio (SNR). The resulting nonlinear filter has the interesting property of approximating the performance of an adaptive filter in that it weights each frequency band of each input pulse by a factor that depends on the instantaneous noise power spectrum present at that time. The SNR at the output of the nonlinear filter is compared to that at the output of a matched filter. The relative performance of the nonlinear system is good when the signal pulses have large time-bandwidth products and the instantaneous noise power spectrum is colored in the signal pass band.     

Calculation of Output Noise Variances for Discrete Time-Invariant Filters

Certain calculations to minimize output noise variance are introduced. Many applied problems in sampled data systems require that data be smoothed in the presence of noise for the prediction of future positions, velocities, or accelerations. Smoothing coefficients in discrete time-invariant filters are computed to minimize the output noise variance, but under the constraints that the function and derivatives be predicted ahead. The output noise variance is seen to be a function of the input noise, the number of input signals (N+1) that the filter has to smooth, and the prediction time ?T. Four examples are given in the derivation of smoothing coefficients for step and ramp inputs subjected to either almost white noise or Gaussian-Markoff noise. The examples illustrate the number of constraint relations that the filter smoothing coefficients must satisfy for function and/or derivative convergence under noise-free conditions. The smoothing coefficients are also a function of the type of noise input into the system or the discrete filter. From the examples, it can be observed that as N becomes larger, the output noise variance becomes smaller, but the computation time is increased.     

Postfiltering in Digital Beamformers

Assuming a sinusoidal signal superimposed on a narrow-band Gaussian noise as the input to a receiving array, the output power and signal-to-noise ratio of a digital beamformer with postfiltering were formulated so that subsequent calculations could be made without an analysis in the frequency domain. The formulation utilized the quantizer functions previously given by the author and certain spectral power distribution factors originally attributed to Davenport but more rigorously derived and discussed in the present work. A numerical study based on this formulation for a DIMUS array in a correlated noise field reveals that except for certain rare circumstances, postfiltering generally improves the output SNR or array gain. It is demonstrated that the amount of postfiltering gain not only varies with array input SNR but also depends strongly upon the spacing-to-wavelength ratio, and its meaningful interpretation can only be made in conjunction with both the clipping and noise correlation losses. In particular, balancing postfiltering gain against the two losses suggests that receiving arrays with element spacings smaller than one-half of the operating wavelength may be used to the advantage of system design under certain conditions.     

Planck-LFI 44 GHz back end module

This work describes the principle of operation, assembly and performance of one branch of the 44 GHz back end module (BEM) for the Planck low frequency instrument (LFI). This subsystem constitutes a fully representative branch of the qualification-model version (QM). It includes waveguide to microstrip transition, GaAs pseudomorphic high electron mobility transistor (PHEMT) low noise amplifiers (LNA), bandpass filter, square-law detector and dc amplifier. The fundamentals of the design of the RF part are described and all of the components have been tested individually before integration. Using single tone and wideband noise stimuli, the output voltage has been measured for several input powers, in order to obtain the sensitivity factor of the complete BEM. The effective bandwidth and the equivalent noise temperature have been calculated from the measurements, taking into account the frequency dependence on the noise source and the BEM. Finally, the low frequency output power spectrum has been obtained and a maximum 1/f knee frequency around 200 Hz has been measured with a 3 dB output signal video bandwidth above 50 KHz.     

Efficient power supply for the microwave electrothermal thruster(MET)

A resonant switch-mode power supply for the microwave electrothermal thruster (MET) is presented in this paper. The converter is operated with soft-switching at high frequency and exhibits a high efficiency. The soft switching technique used in this converter and the current-source inductor at the input minimize the EMI noise. Electric isolation between input and output is achieved with a center-tap transformer, whose magnetizing inductance is used as the resonant inductance of its resonant tank. The resulting high power density and increased reliability of the converter make it very suitable for aerospace applications. Simulation and experimental results of a 28 V/4.5 kV example are also presented     

Effect of Sampling Time Jitter on Array Performance

The effect on array SNR of errors in sampling times (jitter) isan analyzed for the "Bryn processor." Jitter is modeled as a discrete-paramter er random process, and expressions for array SNR are determined as a function of signal and noise spectra and jitter characteristics. For a plane wave signal, it is found that jitter in the data used to design the processor has no effect on output SNR if the noise is independent between channels. However, jitter in the input (evaluation) n) data can cause a substantial loss in peak array SNR and in the array's frequency selectivity. These losses can be expected to increase as the high-frequency content of the data increases. The Bryn processor also loses its interpretation as a likelihood ratio processor in the presence of jitter. The effect of jitter can be reduced in many cases by increasing the sampling rate.     

Theory of LDV Tracking Systems

The application of frequency-tracking systems to the analysis of laser doppler velocimeter (LDV) signals degraded by background noise has been studied both theoretically and experimentally. Expressions are derived for both the correlation function and the expected value of the phase derivative in the general case of noise off center from the Doppler frequency, and these results are specialized to specific cases of practical interest. Laboratory measurements of output signal-to-noise ratio (SNR) and dc error, for varying input SNR and noise center frequency offset, show good agreement with the theoretical predictions.     

基于鉴相器的矢量跟踪环设计

基于鉴相器的矢量跟踪环是锁定导航卫星码和载波的一种跟踪算法,这种算法适合于在弱信号环境下进行跟踪。矢量环不仅充分利用信号跟踪和导航状态解算之间的内在耦合关系,而且每一通道中采用鉴相器和锁频环结合的方式,系统一步内完成信号跟踪和导航解算任务。反馈控制量NCO是由导航滤波器和环路内部滤波器共同产生。实验表明,矢量跟踪环具有快速重捕获特性,能够在弱信号的环境下运行,比起传统环路有更小的跟踪误差。     

Signal Interference and Improvement of Signal-to-Noise Ratios in a Half-Wave Linear Detector

Signal interference in the half-wave linear detector has been studied only for amplitude modulation. In this paper, we treat signal interference for both an amplitude-and an angle-modulation communication system. The input to the half-wave linear detector is assumed to be composed of an amplitude-modulated wave, an angle-modulated wave, and narrow-band Gaussian noise. In particular, when strongweak relations exist in the input processes, a detailed analysis for the output component is presented to clarify some useful output properties.