## Abstract

Time-domain synthesis is used to design continuous-time filters when their time-domain response for a given excitation is known. A case in point is the design of a continuous-time wavelet filter which requires a chosen wavelet as the filter’s impulse response. A key step in the design of a continuous-time wavelet filter is the approximation of its transfer function to a proper rational function. This approximation problem is addressed using methods that can be broadly categorized as closed-form methods and numerical optimization methods. While optimization methods are very effective, closed-form solutions are attractive because they are easy to design. In this work, we propose variants of nonlinear sequence transformation (a closed-form method) that obtain proper rational approximations of wavelet functions which are stable and also perform better in terms of mean square error when compared to those obtained by other closed-form methods. It is shown that the model-order reduction of the proposed variants leads to either similar or better performance compared to \(L_2\) optimization method. These variants are also shown to act as good starting points for optimization methods that use local search routines.

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Makkena, G., Srinivas, M.B. Nonlinear Sequence Transformation-Based Continuous-Time Wavelet Filter Approximation.
*Circuits Syst Signal Process* **37, **965–983 (2018). https://doi.org/10.1007/s00034-017-0591-9

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DOI: https://doi.org/10.1007/s00034-017-0591-9

### Keywords

- Wavelet filter
- Nonlinear sequence transformation
- Impulse response
- Rational approximation