模拟小波基构建及开关电流电路实现理论与方法研究
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摘要
小波变换是继傅立叶变换之后在数学分析方法上的一项重大突破。因其在时域和频域同时具有优良的局部化特性而成为分析非平稳信号的理想工具。小波变换已广泛应用于信号处理领域。小波变换的实现以基于计算机软件的算法方式为主。为提高信号处理的实时性,近些年来人们开始致力于基于电路的小波变换方法研究,但主要是采用数字电路代替计算机实现小波算法。由于需要模数转换(A/D)电路,因而小波变换的数字电路实现有着体积大和功耗高的缺点,无法满足功耗要求严格的应用场合需求,不符合现代小波变换器件面向低电压、低功耗和微型化方向发展的趋势,阻碍了小波变换理论在特定场合的实用化进程。由于模拟电路较数字电路在低功耗设计方面具有绝对优势,基于模拟电路的小波变换实现方法成为近年来的研究热点。基于电流模式的开关电流电路是一种模拟取样数据处理系统,具有低电压、低功耗、宽频带和大动态范围的优点。且采用开关电流电路实现小波变换,可通过改变电路开关的工作频率来精确调谐小波尺度。此外,开关电流电路与标准数字CMOS工艺完全兼容,有利于超大规模集成以达到小波变换器件的微型化。
开关电流小波变换电路设计的首要任务是模拟小波基的构建,即用模拟滤波器函数逼近难以用电路直接实现的小波函数；核心内容是基本小波滤波器的开关电流电路实现。虽然现有研究在上述两个方面取得了不少成果,但是仍存在一些问题,可概括为：(1)小波滤波器函数构建方法还不够丰富,且现有的时域构建模型还不够完善,频域构建方法存在缺陷且效果不佳。(2)现有方法都采用基本型开关电流电路模块实现小波变换,鲜有电路功耗和非理想因素影响的研究；现有方法多采用经典模拟滤波器结构实现小波变换,少有基于现代数字滤波器结构实现的研究。(3)现有研究多关注于实小波滤波器的构建和实现,少有开关电流复小波滤波器设计方面的研究。(4)目前方法主要关注于单个小波滤波器的实现,多个小波滤波器共享实现的研究几乎处于空白状态。
在此背景下,本论文主要对基本模拟小波滤波器函数构建及开关电流电路实现的理论及方法进行了研究,对现有方法的不足提出了一些改进措施。全文的主要工作包括以下几个方面：
1、对模拟小波变换的基本理论与方法进行了研究学习。首先,介绍了课题研究的背景与意义,研究现状和存在的问题。然后,阐明了小波变换的模拟滤波器实现原理,归纳了开关电流电路小波变换方法和步骤。最后,介绍了模拟小波基构建的关键问题和时域优化模型。
2、对模拟小波基的时域构建方法进行了研究。首先,设计了具有初值约束的实小波基时域优化模型,提出了基于改进型混合粒子群算法的通用实小波基时域构建方法。进一步地,针对常见复小波具有高斯包络的特点,并利用正弦信号的周期性,提出一种可简化计算的共极点模拟复小波基时域构建方法。最后,基于常见小波基之间的微积分关系,提出了一种共极共零的多小波基时域构建方法。实验结果表明,所提出的小波基时域构建方法在逼近精度和系统稳定性方面都有良好的效果。
3、对模拟小波基的频域构建方法进行了研究,将时域优化构建方法推广到频域。首先,设计了模拟小波基频域逼近优化模型,提出了基于该模型的通用实小波基频域优化构建方法。然后,对实小波基频域构建模型进行改进,提出了一种共极点复小波基的频域直接构建方法。进而针对常见复小波基具有高斯包络的特点,并基于正弦信号的周期性,提出一种共极点复小波基频域间接构建方法。对复小波基频域直接和间接构建方法进行了对比。最后,依据常见小波基之间具有微积分关系的特性,提出了一种共极共零的多小波基频域构建方法。仿真实验验证了方法的有效性。
4、对小波滤波器的网络结构进行了研究。提出了基于IIR数字网络的开关电流模拟小波滤波器综合方法。首先,基于冲激响应不变法设计了开关电流小波滤波器网络。然后,为降低电路传输误差和功耗,采用共源共栅组态和甲乙类电路技术改进基本型开关电流采样保持单元,并设计了开关电流一阶节和二阶节电路模块。最后,分别以实小波滤波器和复小波滤波器为示例阐述了开关电流小波滤波器综合方法。电路仿真结果表明,基于IIR数字网络设计的开关小波滤波器具有电路传输误差小、非理性因素影响小、电路参数少且易于实现等优点。
5、对多个基本小波滤波器的开关电流电路共享实现进行了研究。为拓展小波变换的适用范围,满足不同场合的应用需求,提出了一种共极共零的多小波滤波器开关电流电路实现方法。首先对共享结构进行了设计。然后提出了基于积分器和微分器的多小波滤波器共享实现方案。最后以高斯-Marr基本小波滤波器的共享实现为例,分别基于积分和微分方案进行了电路综合。通过电路仿真理论分析对两种方案进行了对比,得出了微分共享方案优于积分共享方案的结论。
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.
开关电流小波变换电路设计的首要任务是模拟小波基的构建,即用模拟滤波器函数逼近难以用电路直接实现的小波函数；核心内容是基本小波滤波器的开关电流电路实现。虽然现有研究在上述两个方面取得了不少成果,但是仍存在一些问题,可概括为：(1)小波滤波器函数构建方法还不够丰富,且现有的时域构建模型还不够完善,频域构建方法存在缺陷且效果不佳。(2)现有方法都采用基本型开关电流电路模块实现小波变换,鲜有电路功耗和非理想因素影响的研究；现有方法多采用经典模拟滤波器结构实现小波变换,少有基于现代数字滤波器结构实现的研究。(3)现有研究多关注于实小波滤波器的构建和实现,少有开关电流复小波滤波器设计方面的研究。(4)目前方法主要关注于单个小波滤波器的实现,多个小波滤波器共享实现的研究几乎处于空白状态。
在此背景下,本论文主要对基本模拟小波滤波器函数构建及开关电流电路实现的理论及方法进行了研究,对现有方法的不足提出了一些改进措施。全文的主要工作包括以下几个方面：
1、对模拟小波变换的基本理论与方法进行了研究学习。首先,介绍了课题研究的背景与意义,研究现状和存在的问题。然后,阐明了小波变换的模拟滤波器实现原理,归纳了开关电流电路小波变换方法和步骤。最后,介绍了模拟小波基构建的关键问题和时域优化模型。
2、对模拟小波基的时域构建方法进行了研究。首先,设计了具有初值约束的实小波基时域优化模型,提出了基于改进型混合粒子群算法的通用实小波基时域构建方法。进一步地,针对常见复小波具有高斯包络的特点,并利用正弦信号的周期性,提出一种可简化计算的共极点模拟复小波基时域构建方法。最后,基于常见小波基之间的微积分关系,提出了一种共极共零的多小波基时域构建方法。实验结果表明,所提出的小波基时域构建方法在逼近精度和系统稳定性方面都有良好的效果。
3、对模拟小波基的频域构建方法进行了研究,将时域优化构建方法推广到频域。首先,设计了模拟小波基频域逼近优化模型,提出了基于该模型的通用实小波基频域优化构建方法。然后,对实小波基频域构建模型进行改进,提出了一种共极点复小波基的频域直接构建方法。进而针对常见复小波基具有高斯包络的特点,并基于正弦信号的周期性,提出一种共极点复小波基频域间接构建方法。对复小波基频域直接和间接构建方法进行了对比。最后,依据常见小波基之间具有微积分关系的特性,提出了一种共极共零的多小波基频域构建方法。仿真实验验证了方法的有效性。
4、对小波滤波器的网络结构进行了研究。提出了基于IIR数字网络的开关电流模拟小波滤波器综合方法。首先,基于冲激响应不变法设计了开关电流小波滤波器网络。然后,为降低电路传输误差和功耗,采用共源共栅组态和甲乙类电路技术改进基本型开关电流采样保持单元,并设计了开关电流一阶节和二阶节电路模块。最后,分别以实小波滤波器和复小波滤波器为示例阐述了开关电流小波滤波器综合方法。电路仿真结果表明,基于IIR数字网络设计的开关小波滤波器具有电路传输误差小、非理性因素影响小、电路参数少且易于实现等优点。
5、对多个基本小波滤波器的开关电流电路共享实现进行了研究。为拓展小波变换的适用范围,满足不同场合的应用需求,提出了一种共极共零的多小波滤波器开关电流电路实现方法。首先对共享结构进行了设计。然后提出了基于积分器和微分器的多小波滤波器共享实现方案。最后以高斯-Marr基本小波滤波器的共享实现为例,分别基于积分和微分方案进行了电路综合。通过电路仿真理论分析对两种方案进行了对比,得出了微分共享方案优于积分共享方案的结论。
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.
引文
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