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).