Research On Realization Theory And Method For Analogue Wavelet Transform Based On Switched-Current Technique

Wavelet transform (WT) has found a wide range of applications in signal processing, particularly for local analysis of non-stationary signals, thanks to its time-frequency localization characteristics. In order to achieve real-time performance, hardware implementations of WT have been investigated over the past few years, which often employ digital circuitry. Associated with the required analogue-digital (A/D) converter, the wavelet implementations using digital circuits have the shortcoming of high power consumption, which is incompatible with the trend for WT device towards low-volume low-power and has impeded the application of wavelet analysis theory. As analogue circuits have the characteristics of low power dissipation compared with digital circuits, wavelet implementations using analogue circuits have attracted much attention. Switched-current (SI) circuit is the analogue sampled-data technique operating in current mode. It offers greater ease for lower voltage operation, algebraic manipulation of signals, and precise tuning of dilation. Also, the feature that SI circuit does not require linear floating capacitors enables it to be compatible with standard digital CMOS process, making the technique ideally suitable for VLSI implementation. Therefore, realization of wavelet transform using SI technique is very suitable for low-voltage low-power VLSI implementation of multi-scale analogue WT circuit.As of now, the core task for SI implementation of WT circuits is the construction of SI wavelet filter, mainly involving the rational function approximation of wavelet bases and the design of SI filters whose impulse responses are the approximated wavelet bases (i.e. SI wavelet filters). In recent years, the design methods for the above two steps have been improved, but still have some shortcomings as below:(1) As for the SI implementation of real-valued WT, the Pade approximation used in the existing literatures has the limitations in increasing approximation accuracy, guaranteeing system stability and reducing design complexity. Meanwhile, the magnitude sensitivity of the adopted cascade connection is relatively high. (2) As for the SI implementation of complex WT, there have been no literatures related to this issue so far.Under this background, this dissertation has conducted the research about the design theory and methods of SI WT circuits. The involved design procedure has been summarized detailed in this dissertation, based on which some improved design methods have been proposed. The main content of this dissertation are listed as follows:1. The approximation method for real-valued wavelet bases (RVWB) has been investigated, in which a novel approximation approach using hybrid genetic algorithm (HGA) has been proposed. Firstly, the advantages of time-domain approximation methods and the affection of the wavelet base's shift value are discussed, based on which the mathematical model for the approximation procedure is constructed. Secondly, according to the characteristics of the constructed optimization model, the genetic algorithm (GA) is utilized to solve the optimization problem and quickly obtain initial estimation of the global optimal solution. And then, the quasi-newton method is employed to seek for global optimal solution of RVWB approximation using the obtained initial estimation. Experimental results indicate that the proposed method have the advantages at approximation accuracy, system stability and design complexity over Pade approximation.2. The approximation method for complex wavelet bases (CWB) has been investigated, in which two novel approximation approaches have been proposed. (1) On the basis of RVWB approximation, a novel method for approximating CWB using multi-objective GA is presented, in which the mathematical model for the approximation procedure of CWB is constructed, and the NSGAII algorithm is employed to solve the optimization problem and search for the optimal approximation of CWB. The proposed method is universal, and can be used for any kind of CWB approximation. (2) Another approximation method for CWB, which is called pole-share approximation (PSA), has been presented. The HGA approximation approach and the Laplace transform are used in this method to construct the rational approximation of CWB, whose real part and imaginary part have the same poles. The proposed PSA method can greatly simplify the WT circuit's structure, and is ideally suitable for the construction of commonly-used analogue CWB. Experimental results show that the proposed methods have the advantages at approximation effect and system stability.3. The design of SI wavelet filter'structure has been investigated. The wavelet filter's performances not only rely on the approximation accuracy, but also strongly on the filter structure. To enhance the performance of the wavelet filter, a novel SI wavelet filter structure is proposed. Using bilinear transform theory and "second generation" SI technique, two multiple-loop feedback (MLF) SI filter structures are presented to synthesize the obtained rational approximation to wavelet bases (RAWB). Also, the parameters calculation formulas are deduced mathematically. The theoretical analysis indicates that the proposed SI wavelet filter structure can synthesize arbitrary RAWB, and has the merits of low magnitude sensitivity, simple topology and parameters calculation formulas.4. The design of SI real-valued wavelet transform (RVWT) circuits has been investigated. An improved method of realizing RVWT using SI filters is proposed, in which the HGA based RVWB approximation method is utilized to construct the analogue RVWB and then the MLF SI filter structure is employed to synthesize the approximation function. The real-valued Gaussian wavelet is selected as the example, in order to illustrate the construction procedure of the proposed SI RVWT circuit. Theoretical analysis and simulation result show that the proposed method is superior at approximation precision, system stability and circuit sensitivity.5. The realization of complex wavelet transform (CMWT) using SI circuits has been investigated, in which a method of designing SI complex wavelet filters (CMWF) is proposed. Firstly, the PSA method is used to construct the rational approximation of CWB, whose real part and imaginary part have the same denominator. And then, a structure-shared SI CMWF is designed, which enables the approximated CWB to share the realizing circuit of denominators. The feature that shares part of the WT circuit can greatly simplify the circuit architecture. The complex Morlet wavelet is utilized as the example to elaborate the design procedure of the proposed SI CMWT circuit. Theoretical analysis and simulation results indicate that the proposed method has the merits of low circuit complexity, minimum component realization, high approximation accuracy and strong stability.