Search results for "Interlacing"
showing 2 items of 2 documents
Pattern statistics in faro words and permutations
2021
We study the distribution and the popularity of some patterns in $k$-ary faro words, i.e. words over the alphabet $\{1, 2, \ldots, k\}$ obtained by interlacing the letters of two nondecreasing words of lengths differing by at most one. We present a bijection between these words and dispersed Dyck paths (i.e. Motzkin paths with all level steps on the $x$-axis) with a given number of peaks. We show how the bijection maps statistics of consecutive patterns of faro words into linear combinations of other pattern statistics on paths. Then, we deduce enumerative results by providing multivariate generating functions for the distribution and the popularity of patterns of length at most three. Fina…
Interlacing multiplexing techniques for optical morphological correlation
2006
We propose a novel approach to implement nonlinear morphological correlation. Previous implementation was based on a time sequential approach that consists on displaying different binary image decomposition in a joint transform correlator adding each joint power spectra sequentially. A second Fourier transformation of the sum of joint power spectra gives the correlation output. In this paper, we propose to interlace the different binary images into one single distribution. Then, we introduce the distribution in a conventional joint transform correlator. The correlation output gives the morphological correlation at a specific location. The advantage is important considering that no sequentia…