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The question of designing the best wavelet for a given signal is discussed from the perspective of orthogonal filter banks. Two performance criteria are proposed to measure the quality of a wavelet, based on the principle of maximization of variance. The method is illustrated and evaluated by means of a worked example from biomedicine in the area of cardiac signal processing. The experimental results show the potential of the approach.

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 2 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 2 -approximated orthonormal Gaussian wavelet filter using -C integrators is presented.

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A novel 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 fulfill 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.