| Wavelet transform (WT) is a key breakthrough in the methods of mathematical analysis after the Fourier transform. The WT is an ideal tool to analyze non-stationary signal thanks to its excellent localization characteristics both in the time-domain and frequency-domain. The WT has been widely used in the field of signal processing. Usually, the WT is realized by algorithms based on computer software. In order to achieve real-time signal processing performance, people had began to study the methods of the WT based on circuits in the past few years, and mainly using the digital circuits to replace the computer to realize the WT algorithms. Associated with the requirement of analog to digital (A/D) converter, the realization of WT by digital circuits have been shortcomings in large circuit volumes and high power consumptions. So it is unable to meet the low power requirements of some special applications and incompatible with the trend of modern WT devices developing to low voltage, low power and miniaturization direction. And it hinders the application of the WT theory in specific occasions. As compared with digital circuits, analogue circuits have the characteristics of low power dissipation, and WT using it has been a hot research topic in recent years. Switched-current (SI) circuit is a kind of current mode analog sampled data processing system, which has the advantages of low voltage, low power consumption, wide frequency band and large dynamic range. When the WT is realized by SI current circuits, the wavelet scales can be precisely tuned by changing the working frequency of the switches. In addition, SI circuit is fully compatible with standard digital CMOS process, so the WT circuits can be ultra large scale integrated.The primary task of design WT filter by SI circuit is the construction of basic wavelet filter function, i.e. approximation of an analog filter function to a wavelet which can not realized by circuits. The key content is the realization of the basic wavelet filter using SI circuits. It has made many achievements in the above two aspects, however, there still exists some problems. It can be summarized as follows:(1) Firstly, the construction methods of basic wavelet filter function is not rich enough; secondly, the time-domain construction model is still not perfect; thirdly, the frequency-domain construction methods are not perfect and with poor effect.(2) In the process of present methods, the basic SI circuit modules are used to implement WT and the circuit power concumptions and influence of non-ideal factors are almost not considered. The traditional analog filter structures are used to realize WT but the modern digital filter structures are ignored.(3) The research of construction and implementation mainly focuses on the SI real wavelet filter but rarely on SI complex wavelet filter.(4) The single wavelet filters have been researched mainly, but the multiple wavelet filters’realization by sharing SI circuits is almost blank.Under this background, this dissertation has conducted the research about the theory and methods of SI wavelet filters. In response to the above problems, some improved methods have been proposed. The main content of this dissertation are listed as follows:1. The basic theory and methods of the WT by analogue filter circuits have been studied. Firstly, the background and significance of this research topic, the research status and problems were introduced. Then, the principle of the WT’s implementation using analog filter circuits and the key steps of the WT’s realization by SI circuits were introduced. Finally, the key issues and the time-domain optimization model about constructing a wavelet filter were introduced.2. The approximation theory and methods for basic wavelet filter construction in time-domain have been investigated. Firstly, the real wavelet bases approximation model in time-domain with initial constraint was designed. Based on it a general time-domain construction method for real-valued wavelet basic filter function was proposed by using an improved Hybrid Particle Swarm (PSO) algorithm. Further more, a novel construction method for poles-shared analog complex wavelet filter function was proposed, in which the calculation can be simplified by using the periodic feature of sinusoidal signals. Finally, considering the differential or integral relationship between some general wavelets, a time-domain construction method for poles-and zeros-shared multi-wavelet filter functions was put forward. The experimental results show that the proposed construction methods have good approximation accuracy and system stability.3. The approximation theory and methods for basic wavelet filter construction in frequency-domain have been studied. The time-domain construction and optimization methods were extended to frequency-domain. Firstly, the approximation and optimization model in frequency-domain for real wavelet bases was designed, based on which a general construction method for real-valued wavelet filter was proposed. Further more, by improving this model a novel direct construction method for poles-shared analog complex wavelet filter was put forward. What’s more, an indirect construction method was proposed based on the characteristics of Gauss envelope for some complex wavelets and the sinusoidal signal’s periodic feature. The proposed direct and indirect methods were compared. Finally, a frequency-domain construction method for poles-and zeros-shared multi-wavelet basic filters was put forward based on the differential or integral relationship between some general wavelets. Simulation results verified the effectiveness of the proposed construction methods.4. The wavelet filter circuit’s network structure has been studied. A synthesis method of SI wavelet filter based on infinite-impulse-response (IIR) digital network was proposed. Firstly, the impulse invariant transformation was used to design SI wavelet filter network. Then, the cascode and class AB circuit technologies were occupied to improve the basic SI signal sample and hold unit. Based on the improved SI unit, the SI first-and second-order section modules were designed. Finally, the synthesis method was illustrated by designing a real wavelet filter and a complex wavelet filter. Simulation results show that the SI IIR wavelet filter circuit has merits of small transmission error, little influence of non-ideal factors, less circuit parameters and which can be realized easily.5. The realization of circuit-shared SI multi-wavelet filters was studied. To expand the applicability of the WT and satisfy the requirements of different occasions, a synthesis method for circuit-shared SI multi-wavelet filters was presented. Firstly, the circuit-shared structures were designed. Then, two realization schemes based on integrator and differentiator were put forward, respectively. Finally, the circuit-shared SI Gauss-Marr wavelet filters was toke as an example to illustrate the method. The circuit-shared schemes were compared by simulation and analysis. A conclusion was draw that the differential share scheme is better than the integral share scheme. |
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