Analog Wavelet Filters: The Need for Approximation
- 1.3k Downloads
From its definition, we stated that the implementation of the wavelet transform is based on the design of a bandpass filter that presents an impulse response equal to the desired wavelet base. In order to obtain a synthesizable transfer function of a particular wavelet filter, mathematical approximation techniques are required. In Chapter 4, we present several methods to obtain good approximations in the time domain of wavelet bases functions. One important objective of the introduced approaches is that the resulting approximated function should be rational and stable in the Laplace domain. This entails that the approximating function leads to a physically realizable network. Nevertheless, due to limitations in chip area, power consumption and coefficient matching, there is a trade-off between the approximation accuracy versus the order of the filter to be implemented. Thus, the design challenge is to obtain a low-order system while preserving a good approximation to the intended function.
KeywordsTransfer Function Mean Square Error Impulse Response Wavelet Base Morlet Wavelet
Unable to display preview. Download preview PDF.
- K. L. Su, Time Domain Synthesis of Linear Networks, Prentice-Hall, Englewood Cliffs, NJ, 1971. Google Scholar
- H. Kamada and N. Aoshima, Analog Gabor transform filter with complex first order system, in: Proc. SICE, Tokushima, Japan, pp. 925-930, Jul 1997. Google Scholar
- N. Aoshima, Analog realization of complex first order system and its application to vowel recognition, in: Proc. SICE, Hokkaido, Japan, pp. 1239-1244, 1995. Google Scholar
- S. A. P. Haddad, R. P. M. Houben and W. A. Serdijn, Analog wavelet transform employing dynamic translinear circuits for cardiac signal characterization, in: Proc. ISCAS, Bangkok, Thailand, vol. 1, pp. I-121-124, May 25-28, 2003. Google Scholar
- S. A. P. Haddad, N. Verwaal, R. Houben and W. A. Serdijn, Optimized dynamic translinear implementation of the Gaussian wavelet transform, in: Proc. IEEE Int. Symp. Circuits and Systems, Vancouver, Canada, vol. 1, pp. 145-148, May 23-26, 2004. Google Scholar
- J. M. H. Karel, R. L. M. Peeters, R. L. Westra, S. A. P. Haddad and W. A. Serdijn, Wavelet approximation for implementation in dynamic translinear circuits, in: Proc. IFAC World Congress 2005, Prague, July 4-8, 2005. Google Scholar
- J. M. H. Karel, R. L. M. Peeters, R. L. Westra, S. A. P. Haddad and W. A. Serdijn, An L 2 -based approach for wavelet approximation, in: Proc. CDC-ECC 2005, Seville, Spain, December 12-15, 2005. Google Scholar
- J. M. H. Karel, R. L. M. Peeters, R. L. Westra, S. A. P. Haddad and W. A. Serdijn, Optimal discrete wavelet design for cardiac signal processing, in: Proc. EMBC 2005, Shanghai, China, September 1-4, 2005. Google Scholar
- R. Schaumann and M. V. Valkenburg, Design of Analog Filters, Oxford University Press, London, ISBN: 0-19-511877-4. Google Scholar