Very large scale integration (VLSI) word size and precision analysis of the discrete wavelet transform

An important consideration in the design of VLSI architectures is that of word size and the consequent data precision it confers. The word size affects the dimension of the final circuit as well as the machine's performance, power consumption, I/O requirement, production costs, and so on; while issues concerning the precision relate to how the data words are interpreted -- as integers, fixed-point numbers, standard or custom floating point numbers. In existing architectural designs for the discrete wavelet transform (DWT), little consideration has been given to word size and precision. In this paper we address this problem, showing how the word size expectations can be calculated for a specific problem (based on the range of the input data and the wavelet used). As the depth of the DWT filtering increases the data-word requirements increase, so it is important to investigate how this can affect the potential of the resulting hardware. Although the theory of wavelets is based on perfect reconstruction filters, in a digital implementation there are rounding errors associated with the word size selected and so this must be analyzed to be sure the signal processing benefits of the DWT are not compromised. We present example cases for this analysis, showing the one-dimensional analysis of speech data and two-dimensional analysis of images. Our studies show the tradeoffs involved with respect to precision and perfect reconstruction, and we show simulation results using fixed-point arithmetic with varying word size and precision.