Taylor级数作为广义双正交小波分解
Taylor Series as Wide-sense Biorthogonal Wavelet Decomposition
摘要：
基于Dirac、doublet和delta的进一步导数，引入了点支撑广义小波。广义双正交分析导致标准泰勒级数和新的双泰勒级数，可以解释为劳伦特施瓦茨分布。一个Parseval式的身份也来自泰勒级数，表明泰勒级数支持的能量定理。引入了称为导数图的信号的新表示法，其类似于谱图。这种方法证实了小波在现代信号分析中的影响。
英文摘要：
Pointwise-supported generalized wavelets are introduced, based on Dirac, doublet and further derivatives of delta. A generalized biorthogonal analysis leads to standard Taylor series and new Dual-Taylor series that may be interpreted as Laurent Schwartz distributions. A Parseval-like identity is also derived for Taylor series, showing that Taylor series support an energy theorem. New representations for signals called derivagrams are introduced, which are similar to spectrograms. This approach corroborates the impact of wavelets in modern signal analysis.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
