Improved Genetic Agorithms' Application To Wavelet's Filter And DSP

The research of this paper can be divided into three parts. Firstly, we will introduce IGA (Improved Genetic Algorithm) and apply it to choosing the best wavelet's basis. An optimal choice method of an orthogonal wavelet basis through genetic algorithms is presented in paper. By expanding the signal in wavelet series, we get its approximation up to a desired scale. And a cost function for representing the error between the signal and its approximation is established. We then optimize the cost function by Improved Genetic Algorithms in order to obtain the global optimal orthogonal wavelet basis. Secondly, the symmetrical prosperity of wavelet's base is discussed in Chapter 3. This article shows a new method to construct symmetric compacted orthogonal wavelet packet basis :the original compacted orthogonal wavelet basis and scaling function are decomposed into symmetric and anti-symmetric parts respectively ,then we prove that three of four parts is also wavelet basis and another is scale function. we find it simple to process 1-D signal. Finally, By these results above, all the results above are applied to DSP.