2ND-ORDER FOURIER SYNTHESIS OF BROAD-BAND ACOUSTIC-SIGNALS USING NORMAL-MODES

A scheme for approximate normal-mode calculation of broadband acoustic signals in the time domain is proposed based on a second-order Taylor expansion of eigenvalues and eigenfunctions with respect to frequency . For the case of a Gaussian impulse source a closed-form expression i s derived for the pressure in the time domain. Using perturbation theo ry, analytical expressions are obtained for the involved first and sec ond frequency-derivatives of eigenvalues,and eigenfunctions. The propo sed approximation significantly accelerates arrival-pattern calculatio ns, since the eigenvalues, the eigenfunctions and their frequency-deri vatives need to be calculated at a single frequency, the central frequ ency of the source. Furthermore, it offers a satisfactory degree of ac curacy for the lower and intermediate order modes. This is due to the fact that essential wave-theoretic mechanisms such as dispersion and f requency dependence of mode amplitudes are contained in the representa tion up to a sufficient order. Numerical results demonstrate the effic iency of the method.