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Analog complex wavelet filters

This paper presents an analog implementation of the complex wavelet transform using both the complex first order system (CFOS) and the Pade approximation. The complex wavelet filter design is based on the combination of the real and the imaginary state-space descriptions that implement the respective transfer functions. In other words, a complex filter is implemented by an ordinary state-space structure for the real part and an extra C matrix for the imaginary part. Several complex wavelets, such as Gabor, Gaussian and Morlet complex wavelets, are obtained and simulations demonstrate excellent approximations to the ideal wavelets.