A ultrasonic flow measuring device, which is distinguished by a low energy consumption. A control/evaluation unit ascertains a plurality of sampled values (a.sub.i with i=1, 2, 3, . . . ) of a received measuring signal at defined points in time (t) of a predetermined time range and interpolates the sampled values by a continuous function (f(t)), wherein the continuous function (f(t)) is formed by a sum of a predetermined number (n .di-elect cons. N) of wavelets (W) and wherein each wavelet (W) corresponds to the product of a sampled value with a sine function.function. ##EQU00001## and with a Gaussian bell curve (e.sup.-.alpha.x.sup.2, .alpha. .di-elect cons. R).