Complex wavelet transforms with allpass filters

Authors:
Felix C. A. Fernandes;Ivan W. Selesnick;Rutger L. C. van Spaendonck;C. Sidney Burrus
Affiliations:
Texas Instruments, DSPS R&D Cr., Texas Instruments, Dallas, TX;Electrical Engineering, Polytechnic University, 6 Metrotech Center, Brooklyn, NY;Electrical and Computer Engineering, Rice University, Houston, TX;Electrical and Computer Engineering, Rice University, Houston, TX
Venue:
Signal Processing - Special section: Hans Wilhelm Schüßler celebrates his 75th birthday
Year:
2003

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Abstract

Complex discrete wavelet transforms (DWT) have significant advantages over real wavelet transforms for certain signal processing problems. Two approaches to the implementation of complex wavelet transforms have been proposed earlier. Both approaches require discrete-time allpass systems having approximately linear-phase and (fractional) delay. This paper compares the results when different allpass systems are used. In the earlier work, maximally flat delay allpass systems were used. In this paper, it is shown that an allpass system designed according to the minimax criterion yields improvements for the complex DWT.