Topological IIR Filters Over Simplicial Topologies via Sheaves

Sheaves over Topological Spaces

The category of sheaves over a topological space has a rich internal logic, but they also have a very rich geometric interpretation. In these notes I review the basic notions of sheaves over topological spaces, with an emphasis on the geometry of sheaves. I prove that sheaves are toposes, present the proof of the equivalence between the category of sheaves over X and the set of local homeomorph...

Homotopy theory of simplicial sheaves in completely decomposable topologies

Constructing Simplicial Complexes over Topological Spaces

The first step in topological data analysis is often the construction of a simplicial complex. This complex approximates the lost topology of a sampled point set. Current techniques often assume that the input is embedded in a metric – often Euclidean – space, and make significant use of the underlying geometry for efficient computation. Consequently, these techniques do not extend to non-Eucli...

Applying FIR and IIR Digital Filters over Video Image Processing

Digital Video is a stream of still images called frames, which are moved such that it gives an illusion of dynamics of the objects present in the image. Video image processing is basically processing of frames and updating frames with a minimum frame rate of 16 per second to give an illusion of motion picture. The objective of the research is all about the development of high throughput image p...

Adaptive periodic IIR filters

We consider adaptive periodic IIR ltering and present an extension of the Hyperstable Adaptive Recursive Filter (HARF). We give conditions for convergence of the parameter estimate error, involving passivity of certain operators in the identi cation loop, identi ability of the system parameters, and persistent excitation (pe). A necessary and su cient condition for identi ability is given and s...