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The analysis of ultrasonic signals in the frequency domain offers advantages over processing in the time domain. The principal methods are discussed to derive phase velocity and attenuation data from the Fourier spectra of the measured signals. An extension of these methods is pointed out. It yields a higher resolution and accuracy and is particularly useful for thin specimens where separate echoes are difficult to obtain. The method also allows corrections for coupling layers. The underlying theory is easily implemented in a software code for automated signal processing systems. Good agreement of theory and experimental data is obtained. © 2000 American Institute of Physics.