NOISE-REDUCTION IN TIGHT WEYL-HEISENBERG FRAMES

被引:26
作者
MUNCH, NJ
机构
[1] Institutt for Matematiske Realfag, Universitetet Tromsø, 9000, Tromsø
关键词
WEYL-HEISENBERG FRAME; STATIONARY PROCESS; FREQUENCY DOMAIN; RECONSTRUCTION ERROR;
D O I
10.1109/18.119726
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
The functions g that give rise to tight Weyl-Heisenberg frames based on time and frequency discretization steps q0 and p0 with p0q0 = (2-pi)/k (k is-an-element-of N) are characterized and the noise reducing properties of such frames are examined. It is shown that when the frame coefficients c(m,n)(f) of a function f are subject to stationary noise n the average squared L2-norm of the corresponding noise-contribution to the reconstruction of f is down by a factor proportional to k2 for a fixed number of sample points. Also a measure of "local error" of the reconstruction is introduced as opposed to the global L2-error. For a given noise n, formulae are derived for the optimal choice (or choices) of the basis function g, in the sense of minimizing this local error.
引用
收藏
页码:608 / 616
页数:9
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