function zeta = vxtozeta(vx,F,h,z)
% VXTOZETA - Converts velocities to surface elevations
%  This function converts current meter velocities to surface elevations
%  using linear theory, shallow water wave velocity, with all units in meters,
%  seconds and m/s.
%
%  DECLARATIONS
%		 vx = vector of velocity data to be converted.
%		 F  = sampling frequency in samples/sec.
%       h  = is water depth
%       z  = distance current meter is from the bottom.
%

% Doug Wilson, OHSU

recl = length(vx);
spctres = 2048;
if(recl/spctres < 1)
  spctres = recl;
end
vxsp   =  spectrum(vx,spctres);
[Y,III] = max(vxsp(:,1));
Peak_per = spctres./(III*F); %CRS thinks this is off by 1 freq bin
		  
% convert velocities into surface heights
g = 9.81;
sigma = 2*pi/Peak_per;	  %  Wave angular velocity (mean sort of)
kappa = sigma/sqrt(h*g);  %  Wave number = 2pi/L (linear shallow)
zeta = sinh(kappa*h)*vx./(sigma*cosh(kappa*(h-z)));