The discrete Gabor analysis behaves excellently in digital signal processing. Now that defined on the real line ℝ has seen great achievements, but that defined on half real line ℝ + has not. Due to ℝ + being not a group under usual “+”, the discrete Gabor analysis on ℝ + differs from that defined on ℝ. Due to R+ being a addition group under a new addition “⊕”, this paper addresses discrete periodic Gabor analysis on ℝ + associated with such addition. Using “⊕”-based discrete Zak transform, we characterize a class of discrete periodic Gabor frames (Riesz bases, orthonormal bases) on ℝ + and their weak Gabor duals. Several examples are also provided to illustrate our results.
Zhang et al. (Fri,) studied this question.