A.A. Monakov

The article analyses the Mellin matched filter. The filter permits to obtain a maximum signal-to-noise ratio at its output independently on the input signal duration (scale). The filter properties are similar to the North Fourier matched filter, which also maximizes the output signal-to-noise ratio and is invariant to the time delay of the input signal. Introduction of the Mellin matched filter into the theory of signal processing permits to produce such a definition of the wide-band ambiguity function that is a direct generalization of the narrow-band ambiguity function formulated by P. Woodward. In particular the main sections of the proposed ambiguity function correspond to the outputs of the North - Fourier and Mellin matched filters, and the volume of the ambiguity body is equal to the product of two universal constants of the signal - its energy and the admissibility constant known in the wavelet transformation theory. Problem of the signal scale estimation illustrates the practical implementation of the Mellin matched filter. It is shown that the estimation can be performed via determination of the position of the output signal maximum and its subsequent recalculation into the scale estimate. It is demonstrated that this estimate is rather vulnerable to abnormal errors in case of low signal-to-noise ratios. It is possible to mitigate the influence of abnormal errors through the reduction of the estimate searching range. Computer simulation proves that the search range reduction facilitates the production of efficient estimates. The proposed method can be used in radio and acoustic location, as well as in telecommunication systems to estimate the duration of signals.