| Multirate filter banks theory is an important part of modern signal processing theory and the basis of multirate digital system, and is also the focus and difficult problem in this field. It is appllied not noly in military such as software radio, but also in civil domain such as image processing and wavelet design. A multirate filter bank with linear phase (LP) and perfect reconstruction (PR) is called linear phase perfect reconstruction filter bank (LPPRFB).Linear phase (LP) means the filters in M-channel LPPRFB are all linear phase FIR filters; Perfect reconstruction (PR) condition means no aliasing and no distortion during the signal processing. An M-channel maximally decimated uniform filter bank is to decompose the all signal frequency range into M subbands with the same bandwidth, and then to process the signal in each subband. One of the difficulties of designing M-channel LPPRFB is to find the types and lengths of the 2M linear phase FIRs.Although many researches on the analysis filter banks have been developed, but the research on the filter types and lengths of synthesis banks can be rarely reported. Therefore, it is very important for filter banks design to solve this problem.Based on the perfect reconstruction (PR) condition of multirate filter banks, the method how to choose the types and lengths of the synthesis filters in LPPRFB is proposed in this dissertation. After studying the relationship between 2-channel LPPRFB and 2-channel lattice structure wavelet filter bank, a new design method of one type of symmetric biorthogonal wavelets which are implemented efficiently and quickly is proposed, and examples are given. Finally, a 10-channel LPPRFB is designed to analyse the fault signal on high voltage transmission line, and to find the fault location and realize the transient protection by extracting fault characteristic, constructing and verifying the fault criterion. The main achievements and conclusions are summarized as follows:(1)The type combination of synthesis filters in 2-channel LPPRFB is studied. The 2-channel LPPRFB is a special case of an M-channel LPPRFB, and is also the basis for designing symmetric biorthogonal wavelets. The filter's symmetric coefficients are introduced, and the types and lengths selection conditions of the analysis filters for 2-channel LPPRFB are derivated. And then the derivation about the types and lengths selection conditions of the synthesis filters is given, and the general method for choosing the types and lengths of synthesis filters for 2-channel LPPRFB is obtained in turn. Finally, an example is used to illustrate the proposed method.(2) The symmetry and lengths selection problem of the synthesis filters in M-channel LPPRFB is solved. The signal flow in M-channel LPPRFB is analyzed first and PR condition of LPPRFB is gained. Based on the PR condition and the types and lengths selection conditions of the analysis filters for M-channel LPPRFB,the symmetry selection conditions of synthesis filters is deduced first. And then the filters' odd lengths or even lengths selection frame is derivated in turn, and the type combination rule of synthesis filters is established. As a result, the general selection method of synthesis filters symmetry and lengths for M-channel LPPRFB is proposed finally. It is considered that the problem of selection of symmetry and lengths for M-channel LPPRFB has been solved effectively.(3)Based on 2-channel LPPRFB theory, a new design method of one type of lattice structure symmetric biorthogonal wavelets which can be implemented quickly is proposed. It is indicated that biorthogonality equals PR condition, and the filter bank of biorthogonal wavelet is a type of 2-channel perfect reconstruction filter bank (PRFB), and symmetric biorthogonal wavelets filter bank must satisfy not only PR condition but also linear phase (LP). Let one type of lattice structure filter banks be equivalent to 2-channel LPPRFB, a design method for lattice structure symmetric biorthogonal wavelets which can be implemented quickly is proposed. With this method, the linear phase of lattice structure symmetric biorthogonal wavelet filters is satisfied, and the filters binary real coefficients can be calculated from some equations, and the filters' coefficients are all power of 2, which can be implemented by shift right or left to realize multiplication or division in register of circuit. Therefore, the error from finite word-length effects is reduced. Obviously, this lattice structure symmetric biorthogonal wavelets transform can be accomplished by VLSI easily. Compared with the LPPRFB of tree structure, the lengths of wavelet filters, transmission filters, and crossed filters are all shorter. Furthermore, the parallel channels exchange information via the lattice filters simultaneously. Hence the new discrete wavelet algorithm has more advantages both in time delay and computation efficiency.(4) A 10-channel cosine-modulated filter bank is designed to analyze the current traveling waves on high voltage transmission line when fault appeared, and the analysis includs extracting fault signal characteristic, constructing and verifying the criterion. When faults occur on transmission line, transient current traveling waves will appear in the transmission system and reflect between fault point and overhead line. The research indicates that transient current always declines when they flow through overhead lines because of the capacitor between overhead line and the earth. Furthermore, the higher the current frequency, the more the declining. Based on this characteristic, it is possible to locate the fault which occurred on high voltage transmission lines by means of transient current traveling waves.A 10-channel cosine-modulated filter bank with 100kHz bandwidth is designed to decompose the band of fault signal of current traveling waves on high voltage transmission line. The research indicates that the signals in 6th channel with frequency 50-60 kHz and that in 8th channel with frequency 70-80 kHz are significant. And the ratio of this two channels'signal energy is considered as the protection criterion. With the criterion, we can judge whether the fault has been occurred on high voltage transmission line within the subarea or not, and the relay may act for the subarea protection or not immediately.The Simulations testify that the fault criterion for high voltage transmission line proposed in this dissertation doesn't rely on the happened time of fault, fault type, fault location, and transition impedance of fault. Because of parallel synchronous signal processing, the algorithm has the good characteristic of real-time, and it is significant for actualizing the protection of high voltage transmission line rapidly and exactly. Keywords:linear phase (LP), linear phase perfect reconstruction filter banks (LPPRFB), symmetric biorthogonal wavelets, lattice structure; biorthogonal filter bank, transient current traveling waves...
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