Wavelet analysis is a perfect fruit of functional analysis、 Fourier analysis、 spline analysis、 harmonic analysis and numerical analysis. It has an application in signal processing, image processing, speech analysis, pattern recognition, quanta physics and many nonlinearity science field, and has a lot of applicable fruits of wavelet analysis in signal detection, feature abstraction, abort diagnosis and orientation, data compact, etc. While lots of computing work during the wavelet transform is a main obstacle to a wide application of wavelet synthesis and arithmetic. To overcome the obstacle and promote greatly the application of wavelet theory and get a real time characteristic of wavelet application, the study in hardware application of wavelet transform, i.e. the development of wavelet transform quick arithmetic and its hardware application appears a special important theoretical and disciplinary meaning.The hardware application research of wavelet transform has not a long history, and still in a beginning stage. In 1993, R.T.Edwards and M.D.Godfrey developed the first analog auditory wavelet transform chip. Thereafter the appearance of the chips of auditory continuous wavelet transform by using switch- capacitor network and a analog CMOS high-frequency continuous wavelet transform has an important impact in promoting the application of wavelet theory.Study the development of hardware implementation of wavelet transform, the predominant technology is VLSI which develops to low voltage low power application. Study the international research in the field, it has used surface acoustic wave device or switched-capacitor circuits to realize wavelet transform and its reconstruction devices. How to excogitate LV/LP VLSI wavelet transform chip has a good foreground in the VLSI realization of wavelet transform. Instantaneous Companding circuit theory is a crucial technology in developing low voltage low power analog VLSI in international disciplinary research, where signal is logarithm compacted before processing and exponential expanded after processing to recover the initial dynamic range. Their application is based on the large-signal exponential characteristic of bipolar junction transistors. Although the internal system is nonlinear, the output of the whole system remains linear. The companding processing is of a small internal voltage amplitude so that it potentially offerhigh-frequency operation, low distortion and low disturbance. Instantaneous companding technology resolves effectively the contradiction of low power supply voltage, noise and high-frequency capability and obtains an optimal dynamic range and low power under a lowest power supply voltage. The research in the paper appears a special important theoretical and disciplinary meaning in promoting the application of the companding circuit theory and design technique in wavelet transform and its network application, and in establishing and developing new study, and in promoting the development of wavelet theory and its wide real-time application.The realization of wavelet transform includes two sides: the Discrete Wavelet Transform and the Continuous Wavelet Transform. So far as achievements in study, it is successful in realizing the CWT using digital circuits, and a lot of applied chips had appeared. But the developments of study in using analog circuits to realize the CWT are slowly and only few system architectures and applied chips had been given. There have a lot of aspects need to be improved, such as system integration, analysis precision and power dissipation.So far as the circuits devising methods and the manufacture technics, the devising project and implementing technics of analogy circuits are more complex than digital circuits'. As a new analogy circuit, log-domain circuits work in current-mode, and have a characteristic of low-voltage, low-power. This kind of circuit has a feature of systematism and blocking, which fit for the large size implementation of the continuous wavelet transform system.The theories and the methods of VLSI implementation of one-dimension continuous wavelet transform(CWT) ,which bases on log-domain system, are developed in the paper. At first, the fundamental principles on wavelet transform(WT) and its reconstruction by using log-domain companding circuits, specially its research context, applied domain, purpose and international developments, are summarized. Next, the basic theories of wavelet analysis are expounded.In this paper, the principles on VLSI realization of CWT are set forth, and the relevant methods of the implementation are classified and compared with each other. The implementation of continuous wavelet transform by using log-domain circuits is a new theory and method of instantaneous companding synthesis of wavelet functions and wavelet transform. It includes four sides. One, An analogue CMOS high-frequency continuous wavelet transform circuit proposed in this paper performs