A method is described for improving the accuracy of the natural frequencies obtained from the Fourier transform of the structural response to an impulse. Results are presented from tests in which the input was at a single frequency and from impulse tests on an aluminium plate. It is shown to be possible to obtain frequency resolution of one-tenth of the spacing between the frequency points produced by the Fourier transform, at a low cost in terms of computer time and store. The natural frequencies of the aluminium plate obtained by this method are also compared with those measured when using steady state excitation. Excellent agreement is shown between the results obtained by using the two techniques.