We present a method, based on the properties of wavelet transforms, fo
r inferring an irrotational velocity field from its observed radial co
mponent. The method is comparable in its objective to POTENT but it of
fers in addition a natural smoothing that does not lose information, a
nd 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 d
ata, which reproduce, with and without noise, the cosmic velocity fiel
ds. The results validate the principles of the method, and illustrate
its properties. An application to the observed cosmic velocity fields
is in progress.