Definition of discretization of spectrum

[PF]

Hi,
  In the SWAN spectrum or the user-specified spectrum file (e.g., instat=6, bcfile=spectrum.dat'), the spectrum is
expressed as a matrix with Nf the number of frequencies (Hz) and Nd as the number of
directions (degr).  The spectrum is in the unit of m^2/Hz/degr.  Can you
elaborate more on how the discretization of the spectrum is conducted?  In
the following example, Nf=15, Nd=12.  How is the discrete spectrum density of
0.002403 m^2/Hz/degr at N(f)=3 (0.0545 Hz) and N(d)=4 (-90 degr) obtained?
If I have an analytical spectrum, which is a continuous function of
frequency and direction, F(f,d), how should I discretize the continuous
spectrum into a discrete spectrum matrix for Xbeach, F(f(i), d(j)), i=1,15, j=1,12), similar to the following example?
    Thanks.

PF

       15      
  0.0418 
  0.0477
  0.0545
  0.0622
  0.0710
  0.0810
  0.0924
  0.1054
  0.1204
  0.1375
  0.1569
  0.1791
  0.2045
  0.2334
  0.2664
      12
    -180
    -150
    -120
     -90
     -60
     -30
       0
      30
      60
      90
     120
     150
       0        0        0        0        0        0        0        0        0        0        0        0
0.000051 0.000242 0.000574 0.000956 0.001288 0.001482 0.001481 0.001296 0.000957 0.000579 0.000244 0.000051
0.000129 0.000610 0.001443 0.002403 0.003238 0.003725 0.003724 0.003234 0.002406 0.001454 0.000613 0.000128
0.000273 0.001287 0.003054 0.005084 0.006846 0.007872 0.007869 0.006837 0.005091 0.003076 0.001295 0.000271
0.000665 0.003152 0.007463 0.012402 0.016720 0.019229 0.019221 0.016690 0.012419 0.007518 0.003172 0.000662
0.001302 0.006159 0.014600 0.023222 0.032000 0.037618 0.037603 0.032644 0.024309 0.014716 0.006198 0.001296
0.002328 0.010909 0.026020 0.043301 0.058765 0.067109 0.067080 0.058281 0.043401 0.026213 0.011058 0.002317
0.003365 0.015922 0.037710 0.067200 0.086640 0.097150 0.097110 0.084380 0.062820 0.037991 0.016021 0.003349
0.003426 0.016230 0.038142 0.067562 0.089098 0.099010 0.098969 0.085995 0.064027 0.038724 0.016331 0.003410
0.002027 0.009612 0.022730 0.037790 0.050909 0.058529 0.058505 0.050841 0.037843 0.022898 0.009672 0.002018
0.000672 0.003178 0.007654 0.012656 0.016787 0.019440 0.019432 0.016870 0.012522 0.007594 0.003198 0.000669
0.000101 0.000479 0.001143 0.001890 0.002542 0.002924 0.002923 0.002539 0.001892 0.001144 0.000482 0.000101
0.000002 0.000011 0.000026 0.000043 0.000057 0.000066 0.000066 0.000057 0.000043 0.000026 0.000011 0.000002
       0        0        0 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001        0        0        0
       0        0        0        0        0        0        0        0        0        0        0        0
       0        0        0        0        0        0        0        0        0        0        0        0