【摘要】：數(shù)字信號(hào)處理作為一個(gè)科學(xué)與工程交叉的學(xué)科,是現(xiàn)代科技發(fā)展最重要的基石之一,已經(jīng)被廣泛應(yīng)用于科學(xué)研究和生產(chǎn)實(shí)踐的各個(gè)領(lǐng)域。作為數(shù)字信號(hào)處理系統(tǒng)的核心部分之一:數(shù)字濾波器,其設(shè)計(jì)與實(shí)現(xiàn)方法一直是該學(xué)科重要的研究領(lǐng)域�；谙到y(tǒng)的狀態(tài)空間理論,對(duì)于一個(gè)給定傳輸函數(shù)的數(shù)字濾波器,存在著許多種等價(jià)的實(shí)現(xiàn)結(jié)構(gòu)。數(shù)字濾波器的無(wú)限精度設(shè)計(jì)注重找到可行解的效率和系統(tǒng)的穩(wěn)定性;有限精度設(shè)計(jì)還要進(jìn)一步考慮實(shí)現(xiàn)結(jié)構(gòu)的低復(fù)雜度和減少有限字長(zhǎng)(finite word length-FWL)效應(yīng)。另一方面,數(shù)字濾波器可以用兩種方法實(shí)現(xiàn),當(dāng)采用計(jì)算機(jī)軟件實(shí)現(xiàn)時(shí),特別注重算法的高吞吐率;當(dāng)采用專用或通用集成電路等硬件方法實(shí)現(xiàn)時(shí),則更注重綜合結(jié)果的高速率和低成本。本文以如何提高數(shù)字系統(tǒng)性能為背景,基于系統(tǒng)結(jié)構(gòu)理論研究數(shù)字濾波器的參數(shù)化設(shè)計(jì)方法與高效實(shí)現(xiàn)問(wèn)題,主要工作和成果如下:1.基基于JSS結(jié)結(jié)構(gòu)的IIR數(shù)數(shù)字濾波器參數(shù)化方法:設(shè)計(jì)無(wú)限沖激響應(yīng)(infinite impulse response-IIR)數(shù)字濾波器的代價(jià)函數(shù)一般是高度非線性的,而且還與濾波器的穩(wěn)定性有關(guān)。由于模擬濾波器的JSS結(jié)構(gòu)對(duì)于一個(gè)N階濾波器,只含有2N+1個(gè)參數(shù),且具有l(wèi)2-scaling特性,本文基于JSS結(jié)構(gòu)和廣義雙線性變換,提出一種設(shè)計(jì)IIR濾波器的參數(shù)化方法,該方法是完備和緊凸的,具有較好的收斂性能,同時(shí)優(yōu)化模型建立為成熟的無(wú)約束非線性規(guī)劃問(wèn)題。該方法能更高效地設(shè)計(jì)穩(wěn)定的IIR濾波器,且通帶波動(dòng)、阻帶衰減、群遲延等性能更好。2.基基于遺傳算法的格型結(jié)構(gòu)參數(shù)離散化設(shè)計(jì):分子注入式和分子抽頭式相結(jié)合的格型濾波器結(jié)構(gòu)具有自由度,可以對(duì)節(jié)點(diǎn)信號(hào)功率比等FWL性能進(jìn)行優(yōu)化,且該結(jié)構(gòu)只有2N+1個(gè)乘法器,參數(shù)靈敏度很低,特別適用于IIR濾波器離散化設(shè)計(jì)。但傳統(tǒng)的梯度優(yōu)化方法已經(jīng)不再適用,且參數(shù)的搜索空間較大,窮舉法也并非為有效方法。本文利用基于格雷碼的遺傳算法解決該非線性優(yōu)化問(wèn)題,在濾波器低階時(shí)采用全局優(yōu)化,高階時(shí)采用分步優(yōu)化,有效解決了IIR濾波器參數(shù)離散化問(wèn)題中效率和性能的矛盾,有利于IIR濾波器的實(shí)用化。3.并并行計(jì)算的全通數(shù)字濾波器結(jié)構(gòu):輸入平衡實(shí)現(xiàn)具有低參數(shù)敏感度和很小的舍入噪聲增益�；谝活愝斎肫胶夂Ｉ駥�(shí)現(xiàn)和歸一化格型結(jié)構(gòu),提出兩類并行計(jì)算的全通數(shù)字濾波器結(jié)構(gòu)。基于狀態(tài)空間分析方法論述并行處理原理,并推導(dǎo)了舍入噪聲增益的表達(dá)式,對(duì)于一個(gè)N階全通濾波器,其舍入噪聲增益僅為4N。所提結(jié)構(gòu)由于具備并行處理能力,更加適合低復(fù)雜度高吞吐率的數(shù)字系統(tǒng)實(shí)現(xiàn)。4.基基于集成電路的低成本FIR數(shù)數(shù)字濾波器實(shí)現(xiàn):子項(xiàng)空間技術(shù)利用有限沖激響應(yīng)(finite impulse response-FIR)數(shù)字濾波器系數(shù)之間的子項(xiàng)共享可以有效減少實(shí)現(xiàn)時(shí)加法器的個(gè)數(shù);外推補(bǔ)償技術(shù)利用FIR濾波器沖激響應(yīng)的準(zhǔn)周期特性可以有效降低多常系數(shù)乘法的復(fù)雜度�；谶@兩種技術(shù),利用硬件描述語(yǔ)言編程在集成電路上對(duì)FIR濾波器進(jìn)行了實(shí)現(xiàn),并結(jié)合集成電路綜合特點(diǎn),通過(guò)硬件結(jié)構(gòu)的改進(jìn)得到高速率低成本FIR濾波器的實(shí)現(xiàn)方法,有利于進(jìn)一步推動(dòng)FIR濾波器的實(shí)用化。
[Abstract]:As an interdisciplinary subject of science and engineering, digital signal processing is one of the most important cornerstones of the development of modern science and technology, and has been widely used in various fields of scientific research and production practice. Fields. Based on the state space theory of systems, there are many equivalent implementation structures for a digital filter with a given transfer function. Infinite precision design of digital filters focuses on the efficiency of finding feasible solutions and the stability of the system. Finite precision design also considers the low complexity and the limited reduction of the implementation structure. On the other hand, digital filters can be implemented in two ways, with special emphasis on the high throughput of algorithms when implemented by computer software, and with more emphasis on the high speed and low cost of synthesis results when implemented by hardware methods such as special purpose or general purpose integrated circuits. The main work and achievements are as follows: 1. Based on the JSS junction structure, the IIR number digital filter parameterization method: The cost function of designing infinite impulse response-IIR digital filter is generally used. Because the JSS structure of an analog filter contains only 2N+1 parameters for a N-order filter and has l2-scaling property, a parametric method for designing IIR filters is proposed based on the JSS structure and generalized bilinear transform. The method is complete, compact and convex, and has the property of l2-scaling. This method can design stable IIR filters more efficiently, and has better performances such as passband fluctuation, stopband attenuation, group delay and so on. 2. Based on genetic algorithm, the discrete design of lattice structure parameters: the combination of molecular injection and molecular tapping The lattice filter structure has the degree of freedom and can optimize the FWL performance such as node signal power ratio. The structure has only 2N+1 multiplier, and the parameter sensitivity is very low. It is especially suitable for the discrete design of IIR filter. In this paper, the genetic algorithm based on Gray code is used to solve the nonlinear optimization problem. The global optimization is used in the low-order filter, and the step-by-step optimization is used in the high-order filter. The contradiction between efficiency and performance in the discretization of IIR filter parameters is effectively solved, which is conducive to the practicality of IIR filter. 3. All-pass digital filter with parallel computation is used. Structure: Input balancing implements low parametric sensitivity and low rounding noise gain. Based on a class of Heisenberg implementations and normalized lattice structures, two types of all-pass digital filters for parallel computation are proposed. Parallel processing principle is discussed based on state space analysis method, and rounding noise gain expression is derived. For a N-order all-pass filter, the rounding noise gain is only 4N. The proposed architecture is more suitable for low-complexity and high-throughput digital systems because of its parallel processing capability. 4. Low-cost FIR digital filter implementation based on integrated circuits: subspace technology uses finite impulse response-FI R) Subitem sharing among the coefficients of digital filters can effectively reduce the number of adders for implementation; extrapolation compensation technique can effectively reduce the complexity of multiplication of multiple constant coefficients by utilizing the quasi-periodic characteristics of impulse response of FIR filters. Based on these two techniques, FIR filters are programmed on integrated circuits using hardware description language. Combining with the integrated circuit characteristics, the implementation method of high-speed and low-cost FIR filter is obtained by improving the hardware structure, which is helpful to further promote the practicality of FIR filter.
【學(xué)位授予單位】：浙江工業(yè)大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：TN713.7

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