Generalized sign Fourier uncertainty

Generalized Fourier -

We study a generalization of the Fourier-Mukai transform for smooth projective varieties. We nd conditions under which the transform satisses an inversion theorem. This is done by considering a series of four conditions on such transforms which increasingly constrain them. We show that a necessary condition for the existence of such transforms is that the rst Chern classes must vanish and the d...

Sparse Generalized Fourier Transforms ∗

Block-diagonalization of sparse equivariant discretization matrices is studied. Such matrices typically arise when partial differential equations that evolve in symmetric geometries are discretized via the finite element method or via finite differences. By considering sparse equivariant matrices as equivariant graphs, we identify a condition for when block-diagonalization via a sparse variant ...

Generalized Haar – Fourier Transform

We give a new generalization for Haar functions. The generalization starts from the Walsh-like functions and based on the connection between the original Walsh and Haar systems. We generalize the Haar– Fourier Transform too.

Signal reconstruction from Fourier transform sign information

Uncertainty Principle of the 2-D Affine Generalized Fractional Fourier Transform

The uncertainty principles of the 1-D fractional Fourier transform and the 1-D linear canonical transform have been derived. We extend the previous works and discuss the uncertainty principle for the two-dimensional affine generalized Fourier transform (2-D AGFFT). We find that derived uncertainty principle of the 2-D AGFFT can also be used for determining the uncertainty principles of many 2-D...