Fourier transfrom of 2D, disordered, soft-sphere, NVT displacement field

For my most disordered 2D system (gamma=1.0) I computed the average projection of displacement fields onto transverse plane wave traveling along the x direction. Essentially i computed the quantity:
U' = sum(n: 0-->N-1) {exp(2*pi*i*(n/N)*x)*Uy}

Here is an example of the real part of the plane wave with n=5 & N=60:The above is the 'cos' part, the 'sin' is merely shifted by half a fringe-width.

Now the following is a plot of , averaged over 4 million timesteps at T=0.0025.

The different curves are for different window sizes, the number in the legend denotes the number of particles along the horizontal axis (radius=1.0). On the vertical axis, the square amplitude is measured in units of particle size, while on the hor axis the wavevector is in unit on 1/particleSize. For comparison, above is the corresponding plot for the ordered system, gamma=0.0.