SHTOOLS --- Tools for working with spherical harmonics

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SHPowerSpectrumDensity

Compute the power spectral density of a real function.

Usage

pspectrum = pyshtools.SHPowerSpectrumDensity (cilm, [lmax])

Returns

pspectrum : float, dimension (lmax+1)
The power spectral density of the function.

Parameters

cilm : float, dimension (2, lmaxin+1, lmaxin+1)
The real function expressed in real spherical harmonics.
lmax : optional, integer, default = lmaxin
The maximum spherical harmonic degree used in calculating the power spectrum. This must be less than or equal to lmaxin.

Description

SHPowerSpectrumDensity will calculate the power spectral density of a function expressed in real spherical harmonics. For a given spherical harmonic degree l, this is explicitly calculated as:

pspectrum(l) = Sum_{i=0}^1 Sum_{m=0}^l cilm[i, l, m]**2 / (2l + 1).

See also

shpowerl, shpowerdensityl, shcrosspowerl, shcrosspowerdensityl, shpowerspectrum, shcrosspowerspectrum, shcrosspowerspectrumdensity, shadmitcorr

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