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Spherical Harmonic Analysis and Model-Limited Extrapolation on the Sphere

Summary: Spherical Harmonic Analysis and Model-Limited
Extrapolation on the Sphere:
Integral Equation Formulation
Rodney A. Kennedy, Wen Zhang and Thushara D. Abhayapala
Abstract--The classical problem of extrapolation of a bandlim-
ited signal from limited time domain data is revisited for signals
defined on the sphere. That is, given limited or incomplete mea-
surements of an isotropic low pass signal on the unit sphere, S2
find the unique extrapolation to the complete unit sphere. Signals
defined on the unit sphere arise in a number of applications,
such as beampatterns in azimuth and elevation and head related
transfer functions. Our investigations explore the role of integral
equation operators in characterizing the extrapolation problem
which leads to an iterative algorithm analogous to that obtained
in the time-frequency case.
A fundamental problem in signal processing is that of
extrapolation of bandlimited signals from incomplete time
domain data. That is, knowing a signal on a finite time interval


Source: Abhayapala, Thushara D. - Department of Information Engineering, Australian National University


Collections: Computer Technologies and Information Sciences