Periodicity transforms

Periodicity transforms

This paper presents a method of detecting periodicities in data that exploits a series of projections onto “periodic subspaces.” The algorithm finds its own set of nonorthogonal basis elements (based on the data), rather than assuming a fixed predetermined basis as in the Fourier, Gabor, and wavelet transforms. A major strength of the approach is that it is linearin-period rather than linear-in...

Periodic Wavelet Transforms and Periodicity Detection

The theory of periodic wavelet transforms presented here was originally developed to deal with the problem of epileptic seizure prediction. A central theorem in the theory is the characterization of wavelets having time and scale periodic wavelet transforms. In fact, we prove that such wavelets are precisely generalized Haar wavelets plus a logarithmic term. It became apparent that the aforemen...

Periodicity and Almost-periodicity

Poincaré Duality and Periodicity, Ii. James Periodicity

Let K be a connected finite complex. This paper studies the problem of whether one can attach a cell to some iterated suspension ΣK so that the resulting space satisfies Poincaré duality. When this is possible, we say that ΣK is a spine. We introduce the notion of quadratic self duality and show that if K is quadratically self dual, then ΣK is a spine whenever j is a suitable power of two. The ...

Filarial Periodicity

Thu periodicity of the fever in infections with \ \ Filaria bancrofti in this country is not strictly periodic or regular. The parturition cycles of different adult female worms may fail to be simultaneous, whilst some parturition cycles may fail to produce fever or other symptoms. Every attack does not always mean fever, nor is every filarial attack of fever followed by lymphatic manifestation...