Application of cepstral techniques for the determination of reflection coefficients for dispersive systems--I. Theory and numerical results

Abstract A new technique for the determination of reflection coefficients arising in dispersive systems is presented. The method makes use of cepstral analysis, which relies on a single measured signal. In earlier studies cepstral methods have been applied to reflection coefficient determination for non-dispersive media. However, in a system where the propagating waves are dispersive the reflection properties cannot be estimated using this method. In this paper we will describe how cepstral methods may be extended to accommodate this, by incorporating the dispersion relation into the procedure. This results in a cepstrum in which the independent variable is space such that at a point determined by the distances between the measurement and reflectors, functions related to the reflection coefficients appear. Theory is derived and computational results are obtained for the flexural wave propagation in a beam. The theory is compared with experiment which is discussed in Part II.