To avoid the undesired angular expansion of sampling grid in discrete non-isotropic Stockwell transform, this communication we propose a scale-dependent discretization scheme that controls both radial and expansions unison. Based on new scheme, derive sufficient condition for construction frames L2(R2).

The Fourier transform can be thought of as a map that decomposes a function into oscillatory functions. In this paper, we will apply this decomposition to help us gain valuable insights into the behavior of our original function. Some particular properties of a function that the Fourier transform will help us examine include smoothness, localization, and its L2 norm. We will conclude with a sec...

We establish the inverse Lebedev expansion with respect to parameters and arguments of the modified Bessel functions for an arbitrary function from Hardy’s space H2,A, A> 0. This gives another version of the Fourier-integral-type theorem for the Lebedev transform. The result is generalized for a weighted Hardy space Ĥ2,A ≡ Ĥ2((−A,A);|Γ(1+Rez+iτ)|2dτ), 0 < A < 1, of analytic functions f(z),z = R...

We introduce the operator Z that is often called the Zak transform. Our definition is a bit different from the one that usually appears in the literature. We will discuss this difference and will also give a historical account that the reader may find particularly interesting. In order to do this, however, we need to present our treatment of the operator Z (and Z̃) which shows that the Fourier t...

The aim is to reconstruct a signal function x ∈ L2 if the phase of the Fourier transform x̂ and some additional a-priori information of convex type are known. The problem can be described as a convex feasibility problem. We solve this problem by different Fejér monotone iterative methods comparing the results and discussing the choice of relaxation parameters. Since the a-priori information is p...

The neonatal period is critical for seizure susceptibility, and neocortical networks are central in infantile epilepsies. We report that application of 4-aminopyridine (4-AP) to immature (P6-P9) neocortical slices generates layer-specific interictal seizures (IISs) that transform after recurrent seizures to ictal seizures (ISs). During IISs, cell-attached recordings show action potentials in in...