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Signals with finite time support are frequently used in active sonar and radar processing. In these applications, for efficient computations, it is necessary to have a compact description of the signals' shape and time evolution. For this purpose, the Hermite series expansions are used in this paper to approximate an arbitrary enveloped linear frequency modulated signal. The Hermite basis functions are based on the product of Hermite polynomials and a Gaussian function. The analytical expressions for the Fourier transform of linear frequency modulated (LFM) Hermite functions are presented. It is proposed to use the Fourier transform of LFM Hermite functions for efficient computation of the wideband cross-ambiguity function (WCAF) for target parameter estimation in active sonar processing. Efficient 2-D search methods are also proposed to obtain parameters from the WCAF.