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A novel procedure to implement the wavelet transform 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, to meet low-power low-voltage requirements, we optimize the state-space description of the filter with respect to dynamic range, sensitivity and sparsity. The filter design that follows is based on an orthonormal ladder structure and employs log-domain integrators as main building blocks. Measurements demonstrate that it approximates the required wavelet base (i.e. Morlet) in an excellent way. The tenth-order log-domain filter operates from a 1.5-V supply voltage and a total bias current of 4.3μA.