One-dimensional Continuous Wavelet Functions And Wavelet Transform, Frequency Domain Synthesis

The theories and the methods of VLSI implementation of one-dimension continuous wavelet transform(CWT) .which bases on state-space log-domain filter, are developed in the paper. At first, the fundamental principles on wavelet transform(WT) and its reconstruction, specially on one-dimension CWT, binary discrete a,# CWT and their reconstruction, are provided. Next, the principles on VLSI realization of one-dimension CWT are expounded, and the relevant methods of the implementation are classified and compared with each other. A systematic algorithm for approximating the wavelet function and a example of calculation are gived.It is demonstrated by the example that the algorithm is simple, effective,low erroneous and can be applied to approximating the wavelet function with analytic expression or equal interval samples in time-domain. Then, the fundamental principles on log-domain integrator, the influences of relevant non-ideal factors and the ways of compensation are discussed in detai1, simultaneously,Pspice simulation results are presented, the results are in accord with theoretical analysis.Base on above discussions, the state-space synthesis method of log-domain filter is introduced in length, it is showed that the method has a advantage, i. e there is one-to-one map between the mathematical formulation and circuit realization, and that the method is systematic and suited for designing the network function with zeros and high-order filter.At last, the limitation and applied fields of the methods for realizing one-dimension CWT based on state-space log-domain filter are pointed out, it is also proved by the theoretical analysis and calculation results that the methods are suited for synthesizing the wavelet functions with very small scale or the frequence-transloction version of the mother wavelet (with much translocation in frequence-domain). Based on that, the paper proposes a method of implementating one-dimension CWT which is based on log-domain state-space filter. The circui t construct ion and the relevant schemes of the realization of the circuit are also provided,simultaneously, the source of errors and the compensation methods are discussed.All of analysises, calculation results and simulations demonstrate that the methods presented in the paper are feasible, the algorithm is effective, the realization of circuit is simple, the procedures of the design are standard, the circuit is easy to be fabricated on a monolithic, and the system can be used for processing middle-high frequence signal and be applied in low-voltage,low-power and at high speed.