Low-power high-accuracy compact implementation of analog wavelet transforms

Implementing wavelet transform using analog circuits is of great interest when low power consumption and chip area become important issues. In this case, the complexity of circuits depends on the accuracy of the wavelet approximation. First, an optimized procedure based on a Hankel-norm model reduction is applied to approximate the transfer function of a linear steady- state system whose impulse response implements the required wavelet. The proposed approach significantly improves the accuracy of approximated wavelet. Next, the approximation result is implemented using a low- power low-voltage second order log domain filter as a design example in 0.18 mum CMOS technology. The implemented filter based on the presented method features compact chip area, improved linearity, and ultra low-power consumption. Moreover, it presents a tunable gain, which allows for filters bands configurability. Finally, the design of a complete log domain filter bank, based on the proposed second order filter as main building block is detailed. The filter bank implements a rational approximation of a Gaussian wavelet function following the presented approximation method.