Interpretability and Equivalence in Quantified Equilibrium Logic

毕 业 设 计（论 文）外 文 参 考资 料 及 译 文译文题目： CIC MegaCore Function 学生姓名： 高佳 学 号： 1021129024 专 业： 通信工程 所在学院： 龙蟠学院 指导教师： 姜志鹏 职 称： 讲师2013年11月06日CIC MegaCore Function----From DescriptionThis document describes the Altera CIC MegaCore function. The Altera CIC MegaCore function implements a cascaded integrator-comb filter with data ports that are compatible with the Avalon Streaming interface. CIC filters (also known as Hogenauer filters) are computationally efficient for extracting baseband signals from narrow-band sources using decimation, and for constructing narrow-band signals from processed baseband signals using interpolation.CIC filters use only adders and registers, and require no multipliers to handle large rate changes. Therefore, CIC is a suitable and economical filter architecture for hardware implementation, and is widely used in sample rate conversion designs such as digital down converters (DDC) and digital up converters (DUC).The Altera CIC MegaCore function supports the following features:■Support for interpolation and decimation filters with variable rate change factors (2 to 32,000), a configurable number of stages (1 to 12), and two differential delay options (1 or 2).■Single clock domain with selectable number of interfaces and a maximum of 1,024 channels.■Selectable data storage options with an option to use pipelined integrators.■Configurable input data width (1 to 32 bits) and output data width (1 to full resolution data width).■Selectable output rounding modes (truncation, convergent rounding, rounding up, or saturation) and Hogenauer pruning support.■Optimization for speed by specifying the number of pipeline stages used by each integrator.■Compensation filter coefficients generation.■Easy-to-use MegaWizard interface for parameterization and hardware generation.■IP functional simulation models for use in Altera-supported VHDL and Verilog HDL simulators.■DSP Builder ready.Cascaded Integrator Comb (CIC) filters are widely used in modern communication systems. As the signal processing in all aspects of requirements are constantly improve, in digital technology, the design of the filter appears increasingly important.Those who have signal processing ability of device can be referred to as a filter.In the modern telecommunications equipment and all kinds of control system, filter is widely used.Of all the electronic devices, using the most, the most widely used, technology is the most complex filter.Filter quality directly decides the product quality, good performance of filter can make the system more stable, so the filter of the countries all over the research and production has always been highly valued.With the wide application of digital technology, field programmable gate array (FPGA) has been the rapid development, integration and speed is growing.FPGA has high integration and reliability of the gate array (FPGA), and programmable resistance, maximum limit reduces the design cost, shorten the development cycle.Using CIC filters provides a silicon efficient architecture for performing sample rate conversion. This is achieved by extracting baseband signals from narrow-band sources using decimation, and constructing narrow-band signals from processed baseband signals using interpolation. The key advantage of CIC filters is that they use only adders and registers,and do not require multipliers to implement in hardware for handling large rate changes.A CIC filter (also known as a Hogenauer filter) can be used to perform either decimation or interpolation. A decimation CIC filter comprises a cascade of integrators (called the integrator section), followed by a down sampling block (decimator) and a cascade of differentiators (called the differentiator or comb section). Similarly an interpolation CIC filter comprises a cascade of differentiators, followed by an up sampling block (interpolator) and a cascade of integrators .In a CIC filter, both the integrator and comb sections have the same number of integrators and differentiators. Each pairing of integrator and differentiator is called a stage. The number of stages ( N ) has a direct effect on the frequency response of a CIC filter. The response of the filter is determined by configuring the number of stages N , therate change factor R and the number of delays in the differentiators (called the differential delay) M . In practice, the differential delay is set to 1 or 2.The MegaWizard interface only allows you to select legal combinations of parameters, and warns you of any invalid configurations .For high rate change factors, the maximum required data width for no data loss is large for many practical cases. To reduce the output data width to the input level, quantization is normally applied at the end of the output stage. In this case, the following rounding or saturation options are available:■Truncation : The LSBs are dropped. (This is equivalent to rounding to minus infinity.)■Convergent rounding . Also known as unbiased rounding . Rounds to the nearest even number . If the most significant deleted bit is one, and either the least significant of the remaining bits or at least one of the other deleted bits is one, then one is added to the remaining bits.■Round up: Also known as rounding to plus infinity. Adds the MSB of the discarded bits for positive and negative numbers via the carry in.■Saturation: Puts a limit value (upper limit in the case of overflow, or lower limit in the case of negative overflow) at the output when the input exceeds the allowed range. The upper limit is+2n-1 and lower limit is –2n.These rounding options can only be applied to the output st age of the filter. The data widths at the intermediate stages are not changed. The next section describes cases where the data width at the intermediate stages can be changed.Hogenauer pruning [Reference ] is a technique that utilizes truncation or rounding in intermediate stages with the retained numb er of bits decreasing monotonically from stage to stage, while the total error introduced is still no greater than the quantization error introduced by rounding the full precision output. This technique helps to reduce the number of logic cells used by the filter and gives better performance.The existing algorithms for computing the Hogenauer bit width growth for large N and R values are computationally expensive.For more information about these algorithms, refer to U. Meyer-Baese, Digital Signal Processing with Field Programmable Gate Arrays, 2nd Edition, Spinger, 2004.The CIC MegaCore function has pre-calculated Hogenauer pruning bit widths stored within the MegaCore function. There is no need to wait for Hogenauer pruning bit widths to be calculated if Hogenauer pruning is enabled for a decimation filter. Hogenauer pruning is only available to decimation filters when the selected output data width is smaller than the full output resolution data width.There are often many channels of data in a digital signal processing (DSP) system that require filtering by CIC filters with the same configuration. These can be combined into one filter, which shares the adders that exist in each stage and reduces the overall resource utilization. This combined filter uses fewer resources than using many individual CIC filters. For example, a two-channel parallel filter requires two clock cycles to calculate two outputs. The resulting hardware would need to run at twice the data rate of an individual filter. This is especially useful for higher rate changes where adders grow particularly large.To minimize the number of logic elements , a multiple input single output (MISO) architecture can be used for decimation filters, and a single input multiple output (SIMO) architecture for interpolation filters as described in the following sections.In many practical designs, channel signals come from different input interfaces. On each input interface, the same parameters including rate change factors are applied to the channel data that the CIC filter is going to process. The CIC MegaCore function allows the flexibility to exploit time sharing of the low rate differentiator sections. This is achieved by providing multiple input interfaces and processing chains for the high rate portions, then combining all of the processing associated with the lower rate portions into a single processing chain. This strategy can lead to full utilization of the resources and represents the most efficient hardware implementation. These architectures are known as multiple input single output (MISO) decimation filters.Single input multiple output (SIMO) is a feature associated with interpolation CIC filters. In this architecture, all the channel signals presented for filtering come from a single input interface.Like the MISO case, it is possible to share the low sampling rate differentiator section amongst more channels than the higher sampling frequency integrator sections. Therefore, this architecture features a single instance of the differentiator section, and multiple parallel instances of the integrator sections.After processing by the differentiator section, the channel signals are split into multiple parallel sections for processing in a high sampling frequency by the integrator sections. The sampling frequency of the input data is such that it is only possible to time multiplex two channels per bus, therefore the CIC filter must be configured with two input interfaces. Because two interfaces are required, the rate change factor must also be at least two to exploit this architecture. Up to 1,024 channels can be supported by using multiple input interfaces in this way.Single input multiple output (SIMO) is a feature associated with interpolation CIC filters. In this architecture, all the channel signals presented for filtering come from a single input interface. Like the MISO case, it is possible to share the low sampling rate differentiator section amongst more channels than the higher sampling frequency integrator sections.Therefore, this architecture features a single instance of the differentiator section, and multiple parallel instances of the integrator sections.After processing by the differentiator section, the channel signals are split into multiple parallel sections for processing in a high sampling frequency by the integrator sections.The required sampling frequency of the output data is such that it is only possible to time multiplex two channels per bus. Therefore the CIC filter must be configured with four output interfaces. Because four interfaces are required, the rate change factor must also be at least four to exploit this architecture, but in this example a rate change of eight is illustrated.SIMO architecture is applied when an interpolation filter type is chosen and the number of interfaces selected in the MegaWizard interface is greater than one.The total number of input channels must be a multiple of the number of interfaces. To satisfy this requirement, you may need to either insert dummy channels or use more than one CIC MegaCore function. Data is transferred as packets using AvalonStreaming interfaces. CIC filters have a low-pass filter characteristic. There are only three parameters (the rate change factor R , the number of stages N , and the differential delay M ) that can be modified to alter the passband characteristics and aliasing/imaging rejection. However, due to their drooping passband gains and wide transition regions, CIC filters alone cannot provide the flat passband and narrow transition region filter performance that is typically required in decimation or interpolation filtering applications.This problem can be alleviated by connecting the decimation or interpolation CIC filter to a compensation FIR filter which narrows the output bandwidth and flattens the passband gain.You can use a frequency sampling method to determine the coefficients of a FIR filter that equalizes the undesirable passband droop of the CIC and construct an ideal frequency response.The ideal frequency response is determined by sampling the normalized magnitude response of the CIC filter before inverting the response.Generally, it is only necessary to equalize the response in the passband, but you can sample further than the passband to fine tune the cascaded response of the filter chain.The Avalon-ST interface can also support more complex protocols for burst and packet transfers with packets interleaved across multiple channels.The Avalon-ST interface inherently synchronizes multi-channel designs, which allows you to achieve efficient, time-multiplexed implementations without having to implement complex control logic.CIC MegaCore函数----摘自 描述这篇文章对Altera公司的CIC 宏函数作了说明。

1/4波片quarter-wave plateCG矢量耦合系数Clebsch-Gordan vector coupling coefficient; 简称“CG[矢耦]系数”。

X射线摄谱仪X-ray spectrographX射线衍射X-ray diffractionX射线衍射仪X-ray diffractometer[玻耳兹曼]H定理[Boltzmann] H-theorem[玻耳兹曼]H函数[Boltzmann] H-function[彻]体力body force[冲]击波shock wave[冲]击波前shock front[狄拉克]δ函数[Dirac] δ-function[第二类]拉格朗日方程Lagrange equation[电]极化强度[electric] polarization[反射]镜mirror[光]谱线spectral line[光]谱仪spectrometer[光]照度illuminance[光学]测角计[optical] goniometer[核]同质异能素[nuclear] isomer[化学]平衡常量[chemical] equilibrium constant[基]元电荷elementary charge[激光]散斑speckle[吉布斯]相律[Gibbs] phase rule[可]变形体deformable body[克劳修斯-]克拉珀龙方程[Clausius-] Clapeyron equation[量子]态[quantum] state[麦克斯韦-]玻耳兹曼分布[Maxwell-]Boltzmann distribution[麦克斯韦-]玻耳兹曼统计法[Maxwell-]Boltzmann statistics[普适]气体常量[universal] gas constant[气]泡室bubble chamber[热]对流[heat] convection[热力学]过程[thermodynamic] process[热力学]力[thermodynamic] force[热力学]流[thermodynamic] flux[热力学]循环[thermodynamic] cycle[事件]间隔interval of events[微观粒子]全同性原理identity principle [of microparticles][物]态参量state parameter, state property[相]互作用interaction[相]互作用绘景interaction picture[相]互作用能interaction energy[旋光]糖量计saccharimeter[指]北极north pole, N pole[指]南极south pole, S pole[主]光轴[principal] optical axis[转动]瞬心instantaneous centre [of rotation][转动]瞬轴instantaneous axis [of rotation]t 分布student's t distributiont 检验student's t testＫ俘获K-captureＳ矩阵S-matrixＷＫＢ近似WKB approximationＸ射线X-rayΓ空间Γ-spaceα粒子α-particleα射线α-rayα衰变α-decayβ射线β-rayβ衰变β-decayγ矩阵γ-matrixγ射线γ-rayγ衰变γ-decayλ相变λ-transitionμ空间μ-spaceχ 分布chi square distributionχ 检验chi square test阿贝不变量Abbe invariant阿贝成象原理Abbe principle of image formation阿贝折射计Abbe refractometer阿贝正弦条件Abbe sine condition阿伏伽德罗常量Avogadro constant阿伏伽德罗定律Avogadro law阿基米德原理Archimedes principle阿特伍德机Atwood machine艾里斑Airy disk爱因斯坦-斯莫卢霍夫斯基理论Einstein-Smoluchowski theory 爱因斯坦场方程Einstein field equation爱因斯坦等效原理Einstein equivalence principle爱因斯坦关系Einstein relation爱因斯坦求和约定Einstein summation convention爱因斯坦同步Einstein synchronization爱因斯坦系数Einstein coefficient安[培]匝数ampere-turns安培[分子电流]假说Ampere hypothesis安培定律Ampere law安培环路定理Ampere circuital theorem安培计ammeter安培力Ampere force安培天平Ampere balance昂萨格倒易关系Onsager reciprocal relation凹面光栅concave grating凹面镜concave mirror凹透镜concave lens奥温电桥Owen bridge巴比涅补偿器Babinet compensator巴耳末系Balmer series白光white light摆pendulum板极plate伴线satellite line半波片halfwave plate半波损失half-wave loss半波天线half-wave antenna半导体semiconductor半导体激光器semiconductor laser半衰期half life period半透[明]膜semi-transparent film半影penumbra半周期带half-period zone傍轴近似paraxial approximation傍轴区paraxial region傍轴条件paraxial condition薄膜干涉film interference薄膜光学film optics薄透镜thin lens保守力conservative force保守系conservative system饱和saturation饱和磁化强度saturation magnetization本底background本体瞬心迹polhode本影umbra本征函数eigenfunction本征频率eigenfrequency本征矢[量] eigenvector本征振荡eigen oscillation本征振动eigenvibration本征值eigenvalue本征值方程eigenvalue equation比长仪comparator比荷specific charge; 又称“荷质比(charge-mass ratio)”。

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表 1 专业学位研究生教育政策文本
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常用数学符号的汉英读法1. 逻辑：Logic∃存在：there exists∀任意：for allp q⇒由p推出q ：p implies q / if p, then q⇔p、q相互推出：p if and only if q /p is equivalent to q / p and q are equivalentp q2.集合：Sets∈x 属于A：x belongs to A / x is an element (or a member) of Ax A∉x 不属于A：x does not belong to A / x is not an element (or a member) of Ax A⊂A真包含B：A is contained in B / A is a subset of BA B⊃A真包含于B：A contains B / B is a subset of AA BA B A 与B的交集：A cap B / A meet B / A intersection BA B A 与B的并集：A cup B / A join B / A union B3. 实数：Real numbersx+x加1：x plus one1x-x减1：x minus one1x±x加或减1：x plus or minus one1xy x乘y：xy / x multiplied by yxx除以y：x over yy=等于：the equals sign5x=x等于5 ：x equals 5 / x is equal to 5≡x恒等于y：x is equivalent to (or identical with) yx y≠x不等于y ：x is not equivalent to (or identical with) yx y>x 大于y：x is greater than yx y≥x 大于或等于y：x is greater than or equal to yx y<x 小于y：x is less than yx y≤x 小于或等于y；x is less than or equal to yx y<<0小于x小于1：zero is less than x is less than 1x01≤≤0小于或等于x小于或等于1：zero is less than or equal to x is less than or equal to 1 01x||x x的模（x的绝对值）：mod x / modulus x2x x的2次方：x squared / x (raised) to the power 23x x的3次方：x cubed4x x的4次方：x to the fourth / x to the power fournx x的n次方：x to the nth / x to the power nnx-x的负n次方：x to the (power) minus nx的2次根式：(square) root x / the square root of xx的3次根式：cube root (of) xx的4次根式：fourth root (of) xx的n次根式：nth root (of) x2+x与y的和的平方：x plus y all squared()x y2()x yx 与y 的商的平方：x over y all squared !n n 的阶乘：n factorialx x 拔：x bari x i x ：i x / x subscript i / x suffix i/ x sub i1n i i a =∑ i a 从1到n 求和：the sum from i equals one to n i a / the sum as i runs from 1 to n of the i a 4.线性代数：Linear algebra OA 向量OA ：OA / vector OAOA 有向线段OA ：OA / the length of the segment OA a b 向量a 与b 平行：vector a parallel to vector ba ⊥b 向量a 与b 垂直：vector a is perpendicular to vector b5. 函数：Functions()f x 函数()f x ： fx / f of x / the function f of x:f S T → f 是从集合S 到T 的函数：a function f from S to Tx y → 从x 到y ：x maps to y / x is sent (or mapped) to y'()f x ()f x 的导数：f prime x / f dash x / the (first) derivative of f with respect to x ''()f x ()f x 的二阶导数：f double-prime x / f double-dash x /the second derivative of f with respect to x'''()f x ()f x 的三阶导数：f triple-prime x / f triple-dash x /the third derivative of f with respect to x()()n f x ()f x 的四阶导数： the nth derivative of f with respect to x1f x ∂∂ f 关于1x 的偏导数：the partial (derivative) of f with respect to 1x 221f x ∂∂ f 关于1x 的二阶偏导数：the second partial (derivative) of f with respect to 1x 0∞⎰ 从0到∞求积分：the integral from zero to infinitylim x → x 趋于0求极限：the limit as x approaches zero 0lim x →+ x 右趋于0求极限：the limit as x approaches zero from above 0lim x →- x 左趋于0求极限：the limit as x approaches zero from belowlog e y 以e 为底数的y 的对数：log y to the base e / log to the base e of y / natural log (of) y ln y y 的自然对数：log y to the base e / log to the base e of y / natural log (of) y。