Impulse Response Determination by Cross Correlation

This paper describes the design of a digital cross correlator and its application in determining the impulse response in linear systems. The output of the cross correlator, which correlates the input and the output of a linear system excited by noise, is the same as the response of the linear system to a pulse which is identical to the noise autocorrelation. The impulse response error is defined as the normalized mean-square deviation of the actual from the true impulse response. A digital computer simulation confirms that the conventional technique yields the same impulse error as the correlation technique, when the width of the input rectangular pulse is equivalent to the width of the noise autocorrelation function. The operation and design of the digital correlator are discussed. An advantage of the specially designed digital correlator over a general-purpose digital computer is to operate in real time without problems of software and storage. The presented experimental and digitally computed results show that the digital correlator can accurately determine the impulse response, even in presence of perturbations. Only the correlation technique allows measurement of system impulse response without disturbing normal operation. Suggestions are made to simplify the design and improve the speed (bandwidth capability).     

An Experimental Determination of Distortion and Delay in the FM-FM Telemetry System of the Saturn Space Vehicle

The distortion of the FM-FM Saturn telemetry system for dc input (static error) has been the subject of many studies. The purpose of this correspondence is to measure the additional distortion (dynamic error) that results when the input signal is time-varying. A digital method is developed for measuring both the system delay and the system mean square error for various input signals.     

Performance of the g-h Filter for Tracking Maneuvering Targets

The g-h filter is often used as a tracking filter. Assuming that the target under track is modelled as a constant-velocity system with a correlated random acceleration, equations are derived for the covariances of the filtered and predicted estimates. These equations are useful to predict the performance of the filter and to select suitable parameters so as to improve performance.     

Fourier Transform and Ambiguity Function of Piecewise Polynomial Functions

A general systematic procedure is described for computing the Fourier transform and the ambiguity function of waveforms that are piecewise polynomial. The procedure can be implemented by hand or programmed for execution by a digital computer. The main advantage of the technique is that integration is replaced by a finite summation. Examples include the computation of characteristic function, moments, and the ambiguity function of an amplitude modulated linear FM signal.