Novel computational structure for real-time wavelet analysis
V.P. Devassia, M. G. Mini, Tessamma Thomas · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2003
The advent of high-speed signal processors combined with real-time complex algorithms has resulted in truly elegant industrial systems and controllers. Wavelet Transform (WT) is one among the smart signal processing tools, which has already excelled over the conventional ones. In this paper we present an efficient implementation structure for real-time computation of the Discrete Wavelet Transform (DWT) and its Inverse (IDWT). The wavelet and scaling function coefficients at each level are computed by successive convolutions and the computation of transform coefficients at all levels is performed in parallel. Adopting the principle of polyphase splitting, the input sequence and filter coefficients at each level ’j’ are divided into 2j subsequences, incorporating additional parallelism within levels. Expressions for the computational complexity are derived and a comparison of complexity against the popular filter-bank tree structure is made, for variations of signal length, order of wavelet and the number of levels. The Parallel Multiple Subsequence (PMS) structure suggested here, involves much less computation than state-of-the-art algorithms up to 6 levels of processing for Haar wavelet and 3 levels for others, for any data length. For higher decomposition levels and for real-time applications, the proposed algorithm is made superior by optimal selection of processing frame size.