function vdx_fn = vdx_fn_perd_1st(f_n)
global V; global delx;
[Nx,Nv,Nz]= size(f_n);
vdx_fn = zeros(Nx,Nv,Nz);
v = repmat(V',[Nx,1,Nz]);

    vdx_fn =(v + abs(v))/2.*f_n + (v - abs(v))/2.*circshift(f_n,-1);
    vdx_fn = (vdx_fn - circshift(vdx_fn,1))/delx;
    1;
    