Bin-centred difference scheme

For a bin-centred difference scheme:

1. start at bin n = (n_max / 2) + 1
   1. start with $\delta$ = 1
   2. if $\delta$ is even compute the second order structure function D(n,$\delta$) as the segment mean of the square of the velocity difference between the bins separated by distance $\delta$r₀ centered around bin n:
      
      D(n, $\delta$) = $⟨$ [v’(n+($\delta$/2), t) - v’(n-($\delta$/2), t)]² $⟩$
      
      where the angled brackets indicate the mean across all t for the data segment yielding a velocity difference after the application of the Level 1 QC criteria
   3. if $\delta$ is odd compute the second order structure function D(n,$\delta$) as the segment mean of the mean of the square of the velocity difference between the bins separated by distance $\delta$r₀ centered on the upper and lower extent of bin n:
      
      dv'_lo(n, $\delta$, t) = v’(n+floor($\delta$/2), t) - v’(n-ceil($\delta$/2), t)
      dv'_hi(n, $\delta$, t) = v’(n+ceil($\delta$/2), t) - v’(n-floor($\delta$/2), t)
      
      where ceil and floor indicate the upper and lower integer value respectively, then
      
      D(n, $\delta$) = $⟨$ [dv'_lo(n, $\delta$, t)² + dv'_hi(n, $\delta$, t)²] / 2 $⟩$
      
      the angled brackets again indicating the mean across all t in the data segment yielding a velocity difference after the application of the Level 1 QC criteria
   4. increment $\delta$ and repeat steps until $\delta$ = n_max
2. increment n and repeat steps until n + (n_max / 2) exceeds the bin number for which valid v’ are available