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We have analyzed the error propagation in the classical delay estimation based on the identification of the maximum of the cross correlation between the input signals. The resulting error propagation model has the form of a linear combination of the errors additional to the signal samples. These errors are weighted by the derivative of the input signals at the sampling instants. Based on the error propagation model we have further found an upper bound to the square of the estimation error. The use of the model is demonstrated by two simple examples.