The velocity potential for finite surface water waves is expressed in terms of a double Fourier series expansion in the wave number and frequency. The Fourier coefficients are calculated from a numerical fit to the boundary conditions at the wave surface. This expansion differs from the Stokes expansion in that for each frequency corresponds a set of harmonic waves of varied wave numbers instead of a single harmonic wave. This velocity potential permits interactions between wave harmonics and can describe single periodic waves that deform with propagation (LAMB waves) and their wave particle kinematics. Stokes waves represent a special case of this larger class of deforming waves. For LAMB waves the energy in each harmonic component can transfer from the lower to the higher frequencies and vice versa, and the outward effect of this transfer is the modulation and demodulation of the waves. The changes in wave shape significantly affect the wave kinematics, and this is illustrated with a cosine wave. Also, the present solution for steep Stokes waves is shown to be of higher accuracy than the well-know Stokes' V solution and in close agreement with other higher-order Stokes wave procedures.