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SHCrossPowerSpectrumDensity
Compute the cross-power spectral density of two real functions.
Usage
cspectrum
= pyshtools.SHCrossPowerSpectrumDensity (cilm1
, cilm2
, [lmax
])
Returns
cspectrum
: float, dimension (lmax
+1)- The cross-power spectral density of the two functions.
Parameters
cilm1
: float, dimension (2,lmaxin1
+1,lmaxin1
+1)- The first function expressed in real spherical harmonics.
cilm2
: float, dimension (2,lmaxin2
+1,lmaxin2
+1)- The second function expressed in real spherical harmonics.
lmax
: optional, integer, default = min(lmaxin1
,lmaxin2
)- The maximum spherical harmonic degree to calculate the cross-power spectral density. This must be less than or equal to the minimum of
lmaxin1
andlmaxin2
.
Description
SHCrossPowerSpectrumDensity
will calculate the cross-power spectral density of two functions expressed in real spherical harmonics. For a given spherical harmonic degree l
, this is explicitly calculated as:
cspectrum(l) = Sum_{i=0}^1 Sum_{m=0}^l cilm1[i, l, m] * cilm2[i, l, m] / (2l + 1)
.
See also
shpowerl, shpowerdensityl, shcrosspowerl, shcrosspowerdensityl, shpowerspectrum, shpowerspectrumdensity, shcrosspowerspectrum, shadmitcorr
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