| The design of waveform matched wavelet and the compression of one-dimension and two-dimension certain signals is researched in this paper. Three aspects of work is completed as follows.1. A waveform matching method which find the wavelet filter matched the given signal is studied. At present, there are many types of wavelet possessed many sorts of properties. Furthermore, new wavelets will be designed continually. However, the design of optimized wavelet bases matched some types of given signal is a problem which has not been solved. Waveform matching is included in the matching between the signal and wavelet function. Compared with the energy matching, it has its own characters and is used in some specific domains. Based on the basic conceptions of wavelet transform, the realization of waveform matching and find the optimized wavelet filter is presented in this paper.2. An algorithm of waveform matching which is used to design the wavelet filter matched a given one-dimension signal is proposed. The 9/7 wavelet is one of popular wavelets. Its corresponding 9/7 filter has many advantages as: biorthogonality, linear phase, short length, simple realization and wide using realms. So it is advocated by many authors. Based on the conception of waveform matching, this paper presents an algorithm which is fit for finding a waveform matching 9/7 wavelet to a given one-dimension signal. At the same time, the simulation is shown in this paper.3. An algorithm of waveform matching which is used to design the wavelet filter matched a given two-dimension signal is presented. Two-dimension signal has its own characters compared with one-dimension signal. The conception of waveform matching is used in two-dimension signal and three types of simplicities from the match between wavelet function and two-dimension signal to one-dimension signal are shown. Its algorithm of waveform matching can confirm the 9/7 wavelet which is matched with a given two-dimension signal.
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