Abstract
AbstractDuring past more than 30 years, the time-frequency analysis on L 2(ℝ) such as wavelet and Gabor analysis has been extensively studied, but the time-frequency analysis on L 2(ℝ+) has not, where L 2(ℝ+) is the space of square integrable functions on the half real line ℝ+. It is because ℝ is a group under addition, while ℝ+ is not. This leads to L 2(ℝ+) admitting no nontrivial shift-invariant system. The present article gives a survey on the time-frequency analysis on L 2(ℝ+). It only focuses main ideas instead of concrete results. Readers may refer to listed references for details.KeywordsFrameTime-frequencyWavelet analysisGabor analysisDilation-and-modulation systemMathematics Subject Classification (2010)Primary 42C40; Secondary 42C15
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