We present a method, based on the properties of wavelet transforms, for inferring an irrotational velocity field from its observed radial component. The method is comparable in its objective to POTENT but it offers in addition a natural smoothing that does not lose information, and a separation of the scales. This has required us to conduct for the first time a wavelet analysis based essentially on the redundancy of the transform components in frequency-displacement space, and in three spatial dimensions. We test the method, in this paper, on simulated data, which reproduce, with and without noise, the cosmic velocity fields. The results validate the principles of the method, and illustrate its properties. An application to the observed cosmic velocity fields is in progress.