degrees of freedom for signal

  1. degrees of freedom for signal profile from avk:

    symbol description unit variable name
    \(d^{x}_{s}(i)\) degrees of freedom for signal per level   <x>_dfs {:,vertical}
    \(A^{x}(i,j)\) AVK of a profile x   <x>_avk {:,vertical,vertical}

    The pattern : for the first dimensions can represent {latitude,longitude}, {time}, {time,latitude,longitude}, or no dimensions at all.

    \[d^{x}_{s}(i) = A^{x}(i,i)\]
  2. degrees of freedom for signal from degrees of freedom for signal profile:

    symbol description unit variable name
    \(d^{x}_{s}\) degrees of freedom for signal   <x>_dfs {:}
    \(d^{x}_{s}(i)\) degrees of freedom for signal per level   <x>_dfs {:,vertical}

    The pattern : for the first dimensions can represent {latitude,longitude}, {time}, {time,latitude,longitude}, or no dimensions at all.

    \[d^{x}_{s} = \sum_{i}{d^{x}_{s}(i)}\]