Generalized prolate spheroidal wave functions associated to a particular space-limited 2D band-pass operator

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In this report, we analyze the eigenspace of a space-limited 2D band-pass operator whose transfer function is concentrated in an annular sector of the Fourier plane. This can be viewed as a linear imaging operator for a compact-support object function. The eigenspace analysis is useful to evaluate the performance of some image processing methods based on the compact-support constraint, such as the Gerchberg and the Landweber methods. The case analyzed here is more general than the ones considered in previous works, where a complete annular transfer function was assumed. For a fixed relative bandwidth, the eigenpairs of the operator are presented as functions of the angular aperture of the annular sector.