Log-domain wavelet bases

A procedure to approximate wavelet bases using analog circuitry is presented. First, an approximation is introduced to calculate the transfer function of the filter, whose impulse response is the required wavelet. Next, for low-power low-voltage applications, we optimize dynamic range, minimize sensitivity and fulfil sparsity requirements. The filter design that follows is based on an orthonormal ladder structure with log-domain integrators as main building blocks. Simulations demonstrate an excellent approximation of the required wavelet base (i.e. Morlet). The circuit operates from a 1.2-V supply and a bias current of 1.2μA.