Under various simplifying assumptions, the reflected signal y(t) in the interrogation of a substance by an ultrasonic wave is a convolution of the transmitted signal x(t) with a function h(t) that is related to the reflection coefficient of the medium in the direction of propagation. The function h(t) can, in principle, be determined by deconvolution. However, since the band B of the spectrum X(ω) of x(t) is finite, the frequency components of h(t) outside B cannot be found reliably. In this paper, a method is presented for extrapolating X(ω) beyond B. The resulting increase in resolution is limited only by the level of noise. The method is particularly effective if h(t) is a sum of impulses.