The speech enhancement problem is approached by the Fourier–Bessel (FB) expansion of the speech and noise. The application of this expansion to the enhancement of the speech signals degraded with additive noise is described. The method is based on the subtraction of the FB coefficients of the estimated noise from the coefficients of the noisy speech. The difference in two sets of coefficients is then used to synthesise the enhanced speech. The inherent lowpass filtering property of the FB reconstruction with a finite number of coefficients is revealed.