  We investigate here a generalized construction of spherical wavelets/needlets
which admits extra-flexibility in the harmonic domain, i.e., it allows the
corresponding support in multipole (frequency) space to vary in more general
forms than in the standard constructions. We study the analytic properties of
this system and we investigate its behaviour when applied to isotropic random
fields: more precisely, we establish asymptotic localization and uncorrelation
properties (in the high-frequency sense) under broader assumptions than
typically considered in the literature.
