On a criterion of selecting the best mother wavelet based on fluency wavelet analysis

This paper proposes a new criterion to select the mother wavelet suited for precisely detecting characteristic points on signals, such as non-differentiable points and discontinuous ones, and estimating the periodicity of each signal. The criterion is based on fluency wavelet analysis. We introduce the signal space ^mS, by which signals are characterized, spanned by piecewise polynomials of degree (m-1) with a parameter of only (m-2) times continuous differentiability and then formulate the fluency wavelet analysis. In addition, we introduce new parameters λ^{(1/) and λ}sup (2/), and then generalize the fluency wavelet analysis. By varying both parameters λ^{(1/) and λ}sup (2/), piecewise polynomials with an asymmetric property can be generated. Generalized “fluency wavelet analysis” can analyze waveforms nearby the above singular points more precisely