text: Power spectra are needed for each of the  points on the surface; this encapsulates information about the turbulence intensity for each point. Under IEC standards, only one power spectrum is used; that is, all  points have the same turbulence intensity.
  With the power spectra, the spectral matrix can be formed. This a -by- matrix. The main diagonal of the spectral matrix contains the previously defined spectra for all  points on the surface. The off-main diagonal elements contain all the cross spectra between the points. The cross spectra are determined by the following function:
  Due to the symmetry of the coherence matrix, only  elements are independent. This property can be exploited to lighten memory requirements when writing a programme to simulate the Sandia method.
  The spectral matrix, , can be written as the matrix product of a matrix, , and its transpose. That is,
   is ultimately needed to obtain the complex Fourier co-efficients of the Fourier transforms of the time series of the wind speeds at all the points on the surface. Note - if the Fourier transform of a time domain function, , is , then the resultant spectrum is ; for multiple time domain functions, the Fourier co-efficients can be stored in a matrix, which then means that the above equation is applicable.
  Obviously, there are an infinite number of solutions to the above expression; consequently, the assumption that  is a lower triangular matrix is made such that only one solution exists. The solution can be found via a Cholesky decomposition. The resultant  matrix can be thought of as the weighting factors for the
  linear combination of N independent, unit-magnitude, white-noise inputs that will
  yield N correlated outputs with the correct spectral matrix.
  To get the complex Fourier co-efficients associated with the Fourier transform of the time series of the wind speeds, a column vector,  is obtained by multiply the  matrix by a column vector containing  values of Gaussian white noise, , as shown below:
  The column vector gives the Fourier co-efficients for all points on the grid at a given frequency. This is then built up into a two dimensional matrix which covers the complex Fourier co-efficients for all points across all frequencies. Then, an inverse fast Fourier transform is performed to get the time series. That is,