Title :
On a criterion of selecting the best mother wavelet based on fluency wavelet analysis
Author :
Katagish, Kazuki ; Urushiyam, Takeshi ; Toraichi, Kazuo ; Wada, Koichi ; Yoshikawa, Fumito ; Morokami, Shigemitsu
Author_Institution :
KDD R&D Labs., Saitama, Japan
Abstract :
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 λsup (2/), and then generalize the fluency wavelet analysis. By varying both parameters λ(1/) and λsup (2/), piecewise polynomials with an asymmetric property can be generated. Generalized “fluency wavelet analysis” can analyze waveforms nearby the above singular points more precisely
Keywords :
piecewise polynomial techniques; signal processing; waveform analysis; wavelet transforms; asymmetric property; characteristic points detection; discontinuous points; fluency wavelet analysis; mother wavelet selection; non-differentiable points; piecewise polynomials; signal analysis; signal periodicity estimation; signal space; waveform analysis; Continuous wavelet transforms; Fourier transforms; Hilbert space; Laboratories; Polynomials; Research and development; Signal analysis; Systems engineering and theory; Wavelet analysis; Wavelet transforms;
Conference_Titel :
Communications, Computers and Signal Processing, 1997. 10 Years PACRIM 1987-1997 - Networking the Pacific Rim. 1997 IEEE Pacific Rim Conference on
Conference_Location :
Victoria, BC
Print_ISBN :
0-7803-3905-3
DOI :
10.1109/PACRIM.1997.620003
