Log-domain wavelet bases

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