Implementing Wavelets in Continuous-Time Analog Circuits With Dynamic Range Optimization

Signal processing by means of analog circuits offers advantages from a power consumption viewpoint. A method is described to implement wavelets in analog circuits by fitting the impulse response of a linear system to the time-reversed wavelet function. The fitting is performed using local search involving an L₂ criterion, starting from a deterministic starting point. This approach offers a large performance increase over previous Padé-based approaches and allows for the circuit implementation of a larger range of wavelet functions. Subsequently, using state-space optimization the dynamic range of the circuit is optimized. Finally, to illustrate the design procedure, a sixth-order L₂-approximated orthonormal Gaussian wavelet filter using G_m-C integrators is presented.