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Construction of Analog Wavelet Base and Log-domain Circuit Implementations of Wavelet Transform and Its Applications

Author: LiHongMin
Tutor: HeZuoGang
School: Hunan University
Course: Electrical Engineering
Keywords: Continuous wavelet transforms Wavelet construction Particle swarm optimization Log-domain circuits Analog VLSI Cardiac signal Harmonic detection Speech signal
CLC: TN911
Type: PhD thesis
Year: 2008
Downloads: 268
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As a new time-frequency analyzing method appeared in recent years, wavelet transform (WT) has been shown to be a powerful mathematical tool for local analysis of nonstationary and fast transient signals, due to its good properties of multiresolution and mathematical microscope. So far, WT has been widely applied in many fields such as image processing, quantum mechanics, radar, speech analysis, pattern recognition, earthquake exploration, data compact, fault diagnosis, orientation, and so forth. Usually, the WT is implemented using numerical computation on PC or digital signal processor (DSP). However, in ultra low-power and high-speed applications such as biomedical implantable devices, radar etc, it is not suitable to implement the WT by means of digital circuitry due to the high power consumption associated with the required A/D converter and the heavy computational cost. Consequently, it is difficult to operate the algorithm of WT in real time and wide frequency range on PC or DSP. To widen the application fields of WT, analog VLSI hardware implementation of continuous wavelet transform has been one of the research focuses that attract many researchers. Instantaneous companding circuit theory is a crucial technology in developing low voltage and low power analog VLSI in international disciplinary research, it offers the possibility of wide dynamic range and high frequency operation on low voltage with low distortion. In this thesis, by combining the Instantaneous companding circuit technology with the WT theory, the log-domain analog VLSI implementations of continuous wavelet transform are studied systematically, which is on the application background such as cardiac signal analysis, power system harmonics detection, the extraction of speech signal envelops. The purpose of this research is to implement the WT using an analog chip instead of numerical computation to satisfy low-power and real-time applications such as implantable medical instruments as well as portable electric equipments, etc. This thesis achieves innovative results as follows:1. According to the principle of implementing the WT in an analog way, a kind of novel wavelet base functions named analog wavelets are defined. Using these functions as mother wavelets, the WT can be implemented by the analog VLSI facilely. The optimization mathematical model of constructing analog wavelet base function is presented. 2. The mathematical models of constructing analog wavelet base function are multidimensional variable and multi-modal constrained nonlinear function optimization problems, which are had to solve with traditional means. For solving the nonlinear optimization problems, a hybrid optimization algorithm integrating chaos particle swarm optimization (PSO) and sequential quadratic programming (SQP) .The PSO based on chaos searching is introduced to solve the optimization problem so as to achieve an initial estimation of the global solution. Then, based on the initial estimation, the SQP optimizer is employed to search the accurate global optimal solution with rapid convergent rate. Number simulation results on benchmark complex functions with high dimension demonstrate that the hybrid optimization algorithm is effective and efficient, and performances are fairly superior to similar methods.3. Using the hybrid optimization algorithm to solve the optimization problems on constructing analog wavelet base functions , five kinds of wavelet functions, including the first derivation of the Gaussian analog wavelet, Marr analog wavelet, Morlet analog wavelet, complex Gaussian analog wavelet and complex Morlet analog wavelet, are constructed. Those constructed analog wavelets are fairly similar to common wavelets such as Gaussian wavelet, Marr wavelet, Morlet wavelet, complex Gaussian wavelet and complex Morlet wavelet, respectively, as a result, preserve the excellent performances of common wavelets. Thereinto, the mathematical model of constructing complex Morlet analog wavelet is a multi-objective optimization problem, and to solve it, a new hybrid optimization algorithm based multi-objective optimization algorithm is developed.4. To characterize cardiac signal, the log-domain WT analog circuits are designed, which implement the first derivation of the Gaussian analog wavelet transform of cardiac signal. QRS complex of cardiac signal is detected by using the modulus maxima in the WT implemented by analog VLSI. This method can meet low-power low-voltage and real-time applications need, and is easy to be integrated on a chip. It is especially suitable to implantable devices such as pacemakers as well as mobile ECG telemonitoring system. Simulations indicate that the log-domain WT analog circuits can successfully distinguish QRS complex of cardiac signal, and is equal to the software method in effect.5. The wavelet-based power system harmonic detection algorithm is implemented using digital signal processing. However, because of the heavy computational cost as well as the required analog-digital converter, harmonic detection instrument is difficult to operate in real time and wide frequency range with high power consumption. A novel method for harmonic detection based on low-power low-voltage log-domain continuous wavelet transform circuits is presented. To measure harmonics, the wavelet transform of harmonic signal is realized by analog CMOS VLSI composed of analog filter bank, whose impulse response is the constructed Morlet analog wavelet. CMOS log-domain integrators are the main building blocks of wavelet filters. By changing the values of the integrators bias currents, this circuit can realize various scales wavelet transform of harmonic signal. The validity of the proposed method is confirmed by SPICE simulation. Results demonstrate that this method can precisely and speedily separate the integer and non-integer harmonics with different frequencies from power harmonics signal.6. For applications requiring low-power and real-time,an analog implementation of complex continuous WT using log-domain VLSI is investigated. A new orthonormal ladder structure for the design of log-domain high order filter is presented, which has the properties of low sensitivity and optimum dynamic range. Employing orthonormal ladder structure, the complex Morlet analog wavelet transform log-domain circuits are designed, which consist of complex wavelet filters, modulus circuit and phase circuit. By sharing the implementing circuits of state space matrix A and B of complex wavelet filters, the area of WT chip is saved, which is useful to improve the degree of system integration, and the power consumption is cut down. The modulus circuit and phase circuit are designed on the static translinear principle. For the first time, the complex Morlet analog wavelet transform log-domain circuits are used in extracting and analyzing the envelop of speech signal. Simulation results show that the complex WT circuits can realize accurate extraction of speech signal envelops in real-time.

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