Taylor Series as Wide-sense Biorthogonal Wavelet Decomposition

—Pointwise-supported generalised wavelets are introduced, based on Dirac, doublet and further derivatives of (t). A generalised 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.