  The idea of renormalization and scale invariance is pervasive across
disciplines. It has not only drawn numerous surprising connections between
physical systems under the guise of holographic duality, but has also inspired
the development of wavelet theory now widely used in signal processing.
Synergizing on these two developments, we describe in this paper a generalized
exact holographic mapping that maps a generic N-dimensional lattice system to a
N+1-dimensional holographic dual, with the emergent dimension representing
scale. In previous works, this was achieved via the iterations of the simplest
of all unitary mappings, the Haar mapping, which fails to preserve the form of
most Hamiltonians. By taking advantage of the full generality of biorthogonal
wavelets, our new generalized holographic mapping framework is able to preserve
the form of a large class of lattice Hamiltonians. By explicitly separating
features that are fundamentally associated with the physical system from those
that are basis-specific, we also obtain a clearer understanding of how the
resultant bulk geometry arises. For instance, the number of nonvanishing
moments of the high pass wavelet filter is revealed to be proportional to the
radius of the dual Anti deSitter (AdS) space geometry. We conclude by proposing
modifications to the mapping for systems with generic Fermi pockets.
