Abstract: The invention relates to a method of converting sampling conversion with a predetermined ratio between an input frequency (Fsin) and an output frequency (Fsout). It comprises an initialization phase (40-44) of selective configuration, according to the conversion ratio, of an under-sampling filter and a band-pass filter, and a real time phase comprising the stages of selective over-sampling (45), over-sampling by a factor of two and selective band-pass filtering (46), over-sampling by a factor of sixty four (47) and polynomial interpolation of the quadratic “B-Spline” type (48). The invention also relates to a device (4) for implementation of the method.