Some Things On Symmetric Wavelet's Filter

The experts in Engineering, especially in Engineering expect that the compact support wavelets are real, orthogonal and symmetric. In fact, no such a wavelet, except the wavelet Haar, is found.The low frequencies in MRA are in good resolution, but the high ones are not. however, the wavelet packet can overcome the shortcomes in high frequencies and it can make the width of each frequency-band same.However,the calculations are large as the decomposed layer is much high. for example ,from the layer four to the layer five, thirty-two two scale equations must be calculated and much time is spared .therefore, wavelet packet is stopped in Engineering . Signal irregular sampling is great progress relative to signal regular sampling, and it gives the theory of information something new.The focus of the paper is divided into two parts:the part one where the compact supported orthogonal wavelet about symmetry is discussed and a new method about symmetrizing wavelet is put. The compact support wavelet which is real and orthogonal isdivided into two parts:symmetrical part and anti-symmetrical one. It proves that both the two parts are still made into compact orthogonal wavelet base which are symmetrical and anti-symmetrical respectively. It proves that symmetrical part and anti-symmetrical one of scale function are scale function and wavelet function in some subspace respectively. The part two where the irregular sampling under the frame is discussed.