Abstract: A ultrasonic flow measuring device, which is distinguished by a low energy consumption. A control/evaluation unit ascertains a plurality of sampled values ?, 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 ? N) of wavelets (W) and wherein each wavelet (W) corresponds to the product of a sampled value with a sinc function ( sin ? ( x ) x ) and with a Gaussian bell curve (e???2, ? ? R).