# 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.

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