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SHCrossPowerDensityLC (Fortran) |
spherical harmonics software package, spherical harmonic transform, legendre functions, multitaper spectral analysis, fortran, Python, gravity, magnetic field |
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Compute the cross-power spectral density of two complex functions for a single spherical harmonic degree.
cpsd
= SHCrossPowerDensityLC (cilm1
, cilm2
, l
)
cpsd
: output, complex(dp)
: The cross-power spectral density of the two complex functions for spherical harmonic degree l
.
cilm1
: input, complex*16, dimension (2, lmaxin1
+1, lmaxin1
+1)
: The first complex function expressed in complex spherical harmonics.
cilm2
: input, complex*16, dimension (2, lmaxin2
+1, lmaxin2
+1)
: The second complex function expressed in complex spherical harmonics.
l
: input, integer
: The spherical harmonic degree. This must be less than or equal to the minimum of lmaxin1
and lmaxin2
.
SHCrossPowerDensityLC
will calculate the cross-power spectral density of two complex functions expressed in complex 4-pi normalized spherical harmonics for a single spherical harmonic degree l
. This is calculated as:
cpsd = Sum_{i=1}^2 Sum_{m=0}^l cilm1(i, l+1, m+1) * conjg[cilm2(i, l+1, m+1)] / (2l + 1)
.
shpowerlc, shpowerdensitylc, shcrosspowerlc, shpowerspectrumc, shpowerspectrumdensityc, shcrosspowerspectrumc, shcrosspowerspectrumdensityc