Generalized High-Level Synthesis of Wavelet-Based Digital Systems via Nonlinear I/O Data Space Transformations Dongming Peng and Mi Lu Electrical Engineering Department, Texas A&M University, College Station, TX77843, USA 1 Introduction In this paper, we systematically present the high-level architectural synthesis for general wavelet-based algorithms via a model of I/O data space and the nonlin- ear transformations of the I/O data space. The parallel architectures synthesized in this paper are based on the computation model of distributed memory and distributed control. Several architectural designs have been proposed for the Discrete Wavelet Transform (DWT) [4]-[11]. None of these architectural designs for computing the DWT follows a systematic data dependence and localiza- tion analysis of general wavelet-based algorithms, and thus they only serve as particular designs and cannot be extended to other complicated wavelet-based algorithms such as MultiWavelet Transform (MWT)[1,13,14], Wavelet Packet Transform (WPT)[2,15] or Spacial-Frequential Quantization (SFQ) [12]. Using the WPT as a representative example of complex wavelet-based algortihms, this paper fully describes the theory and methodology used in synthesizing parallel architectures for general wavelet-based algorithms. 2 I/O Data Space Modeling of Wavelet-Based Algorithms The basic equation for any discrete wavelet-based algorithms is generally repre- sented by X j+1 [t]= ∑ k∈L C[k]X j [Mt − k] (Eq.1) where C[k] are taps of a wavelet filter, X j and X j+1 are the sequence of input data and output data respectively at the (j + 1) th level transform, L is a set that corresponds to the size of the wavelet filter, and M is a constant scalar in the algorithm. Generally, the algorithm is termed as M-ary wavelet transform for M ≥ 2. There are M wavelet filters for M-ary wavelet transform. If X j and X j+1 are scalar data and C is scalar-valued taps of the wavelet filter, the algo- rithm is a classical scalar wavelet transform; if X j and X j+1 are vector-valued data and C is matrix-valued taps of the multiwavelet filter, it is an MWT. If t and k are scalars, the algorithm is a 1-D transform; if t and k are n-D vectors, it is an n-D transform. Wavelet-based algorithms are multiresolution algorithms, i.e., the output data at a level of transform can be further transformed at the next level. V.N. Alexandrov et al. (Eds.): ICCS 2001, LNCS 2073, pp. 884–893, 2001. c  Springer-Verlag Berlin Heidelberg 2001