Multiplying huge integers of n digits can be done in time O(n log(n)) using Fast Fourier Transforms (FFT), instead of the O(n) time complexity normally required. In this paper we present this technique from the viewpoint of polynomial multiplication, explaining a recursive divide-and-conquer approach to FFT multiplication. We have compared both methods of multiplication quantitatively and prese...

This paper reviews P´olya urn models and their connection to random trees. Basic results are presented, together with proofs that underly the historical evolution of the accompanying thought process. Extensions and generalizations are given according to chronology: • P´olya-Eggenberger’s urn • Bernard Friedman’s urn • Generalized P´olya urns • Extended urn schemes • Invertible urn schemes ...

We adapt Guth's polynomial partitioning argument for the Fourier restriction problem to context of Kakeya problem. By writing out induction as a recursive algorithm, additional multiscale geometric information is made available. To take advantage this, we prove that direction-separated tubes satisfy version Wolff axioms. Altogether, this yields improved bounds maximal conjecture in~$\Bbb{R}^n$ ...

The Spectrum Sliding Analysis (SSA) is a dynamic spectrum analysis in which the next analysis interval differs from the previous one by including the next signal sample and excluding the first one from the previous analysis interval. Such a spectrum analysis is necessary for time-frequency localization of analyzed signals with given peculiarities. Using the well-known Fast Fourier Transform (FF...

The discrete Fourier transform(DFT) has been widely applied in the field of signal processing. There are lots of architectures available in literature which are of computing N point DFT type. Such algorithms are called as FFT computation algorithms. However in some applications we need to computer the DFT for some of selected output bin indices only. One of such example is signal monitoring and...

Harmonic sliding analysis (HSA) is a dynamic spectrum analysis [1] in which the next analysis interval differs from the previous one by including the next signal sample and excluding the first one from the previous analysis interval. Such a harmonic analysis is necessary for time-frequency localization [2] of analysed signal given peculiarities. Using the well-known Fast Fourier transform (FFT)...

Cohen's class of Time-Frequency Distributions (CTFDs), which includes the spectrogram and the Wigner-Ville distribution, has significant potential for the analysis of non-stationnary signals. In order to efficiently compute long signals time-frequency representations, we propose fast algorithms using a recursive approach. First, we introduce a recursive algorithm dedicated to the spectrogram co...

In a practical training for the Faculty of Electrical Engineering at Eindhoven University of Technology, a literature search to the past developments concerning the Phase Correlation algorithm was carried out and the algorithm was implemented. The Phase Correlation algorithm is a method for measuring the motion in a video sequence, based on the Fourier shift theorem. It was found that an enhanc...

This paper investigates the recursive Morton ordering of two-dimensional arrays as an efficient way to access hierarchical memory across a range of heterogeneous computer platforms, ranging from many-core devices, multicore processor, clusters, and distributed environments. A brief overview of previous research in this area is given, and algorithms that make use of Morton ordering are described...

Much effort has gone into the understanding of regularization in ill-posed problems in computer vision. Yuille and Grzywacz were among the first to propose use of the Gaussian Tikhonov regularizer for image registration, illustrating the ideal properties of this regularizer for preserving motion coherence. Nielsen et al. later described the intricate connection between the Gaussian Tikhonov reg...