Both Sylvester matrix and convolution are defined by two polynomials. If one of them has small degree, then the associated Sylvester linear system can be solved fast by using its PFD interpretation of the convolution equation. This can immediately simplify the refinement of approximate convolution by means of Newton’s iteration, where we also incorporate the PFD refinement techniques or alterna...

We propose a new method for computing the 2-d Minkowski sum of non-convex polygons. Our method is convolution based. The main idea is to use the reduced convolution and filter the boundary by using the topological properties of the Minkowski sum. The main benefit of this proposed approach is from the fact that, in most cases, the complexity of the complete convolution is much higher than the co...

The quaternion Fourier transform (qFT) is an important tool in multi-dimensional data analysis, in particular for the study of color images. An important problem when applying the qFT is the mismatch between the spatial and frequency domains: the convolution of two quaternion signals does not map to the pointwise product of their qFT images. The recently defined ‘Mustard’ convolution behaves ni...

This paper proposes a convolution forest kernel to effectively explore rich structured features embedded in a packed parse forest. As opposed to the convolution tree kernel, the proposed forest kernel does not have to commit to a single best parse tree, is thus able to explore very large object spaces and much more structured features embedded in a forest. This makes the proposed kernel more ro...

Convolution and Deconvolution is having wide area of application in Digital Signal Processing. Convolution helps to estimate the output of a system with arbitrary input, with knowledge of impulse response of the system. Linear systems characteristics are completely specified by the systems impulse response, as governed by the mathematics of convolution. And with the knowledge of impulse respons...

This paper continues the investigation in digital signal processing of spectral analysis on certain non-commutative nite groups|wreath product groups. We describe here the generalization of discrete cyclic convolution to convolution over these groups and show how it reduces to multiplication in the spectral domain. Finite group based convolution is deened in both the spatial and spectral domain...

We present a very simple and fast algorithm to compute the convolution of an arbitrary sequence x with a sequence of a specific type, a. The sequence a is any linear combination of polynomials, exponentials and trigonometric terms. The number of steps for computing the convolution depends on a certain complexity of a and not on its length, thus making it feasible to convolve a sequence with ver...

Since the introduction of the behavioral approach to systems theory by Willems [13, 14, 15, 16, 17] the main emphasis has been on discrete time systems. Papers dealing with continuous time systems generally have assumed from the start that a set of differential equations was given. In his thesis Soethoudt has given necessary and sufficient conditions on the behavior of a continuous time system ...

The pronounced convolution of the human cortex may be a morphological substrate that supports some of our species' most distinctive cognitive abilities. Therefore, individual intelligence within humans might be modulated by the degree of folding in certain cortical regions. We applied advanced methods to analyze cortical convolution at high spatial resolution and correlated those measurements w...