Custom Fast Binary Matrix Multiplication Processor Design自定义快速二进制矩阵乘法运算的处理器的设计
快速傅里叶变换处理稀疏矩阵-概述说明以及解释
快速傅里叶变换处理稀疏矩阵-概述说明以及解释1.引言1.1 概述快速傅里叶变换（Fast Fourier Transform, FFT）是一种重要的信号处理技术，广泛应用于图像处理、语音识别、数据压缩等领域。
它通过将时域信号转换到频域来实现信号的分析和处理，具有高效、快速的特点。
稀疏矩阵是一种具有大部分元素为零的矩阵。
由于其特殊的结构，稀疏矩阵在存储和计算的效率上具有很大优势。
在实际应用中，大量的数据都可以表示为稀疏矩阵的形式，例如图像数据、网络数据等。
本文将探讨如何利用快速傅里叶变换处理稀疏矩阵。
首先，我们将介绍快速傅里叶变换的原理，包括离散傅里叶变换（Discrete Fourier Transform, DFT）和快速傅里叶变换的基本概念。
然后，我们将详细介绍稀疏矩阵的定义和特点，包括稀疏矩阵的存储方式以及如何对稀疏矩阵进行表示和计算。
接着，我们将探讨快速傅里叶变换在处理稀疏矩阵中的应用，包括如何利用快速傅里叶变换提高稀疏矩阵的计算效率和压缩存储等方面的优势。
通过本文的研究和分析，我们可以得出结论：快速傅里叶变换在处理稀疏矩阵中具有重要的应用价值。
它不仅可以提高稀疏矩阵的计算效率和存储效率，还可以在图像处理、语音识别等领域中发挥重要作用。
因此，在实际应用中，我们可以充分利用快速傅里叶变换的优势，更好地处理和分析稀疏矩阵的数据。
文章结构部分的内容可以参考以下例子：1.2 文章结构本文将分为三个主要部分进行讨论：引言、正文和结论。
在引言部分，我们将提供对快速傅里叶变换处理稀疏矩阵的概述，介绍本文的目的和重要性。
通过该部分，读者将对文章的主要内容有一个整体的了解。
正文部分包括两个小节：2.1 快速傅里叶变换的原理和2.2 稀疏矩阵的定义和特点。
在2.1小节中，我们将详细介绍快速傅里叶变换的原理和算法，以及其在信号处理领域的应用。
在2.2小节中，我们将定义稀疏矩阵，并讨论稀疏矩阵的特点和常见表示方法。
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数学名词英文
数学mathematics, maths(BrE),math(AmE) 公理axiom 定理theorem 计算calculati on 运算operati on 证明prove 假设hypothesis, hypotheses(pL) 命题propositi on 算术arithmetic力卩plus(prep.), add(v.), additi on(n.)被加数auge nd, summa nd 加数adde nd 和sum减minu s(prep.), subtract(v.), subtracti on(n.) 被减数minuend 减数subtrahe nd 差rema in der乘times(prep.), multiply(v.), multiplicati on(n.) 被乘数multiplica nd, faciend 乘数multiplicator积product除divided by(prep.), divide(v.), division(n.) 被除数divide nd 除数divisor 商quotie nt等于equals, is equal to, is equivale nt to 大于is greater tha n 小于is lesser tha n大于等于is equal or greater than 小于等于is equal or lesser than 运算符operator 平均数mean算术平均数arithmatic mean 几何平均数geometric mean n个数之积的n次方根倒数(reciprocal )x的倒数为1/x 有理数rational nu mber 无理数irrati onal nu mber 实数real nu mber 虚数imag inary nu mber 数字digit 数nu mber自然数n atural nu mber 整数in teger 小数decimal 小数点decimal point 分数fracti on 分子nu merator 分母denomin ator 比ratio 正positive 负n egative 零n ull, zero, no ught, nil 十进希9 decimal system 二进希9 binary system 十六进希9 hexadecimal system 权weight, sig nifica nee 进位carry 截尾trun catio n四舍五入round 下舍入round dow n 上舍入round up 有效数字sig nifica nt digit 无效数字in sig nifica nt digit 代数algebra 公式formula, formulae(pl.) 单项式mono mial 多项式polyno mial, multi no mial 系数coefficie nt 未知数unknown, x-factor, y-factor, z-factor 等式，方程式equation 一次方程simple equati on 二次方程quadratic equati on 三次方程cubic equati on 四次方程quartic equati on 不等式in equati on 阶乘factorial 对数logarithm 指数，幕exp onent 乘方power二次方，平方square 三次方，立方cube 四次方the power of four, the fourth powern 次方the power of n, the nth power 开方evoluti on, extract ion 二次方根，平方根square root 三次方根，立方根cube root 四次方根the root of four, the fourth rootn 次方根the root of n, the nth rootsqrt(2)=1.414 sqrt(3)=1.732 sqrt(5)=2.236 常量con sta nt 变量variable 坐标系coord in ates 坐标轴x-axis, y-axis, z-axis 横坐标x-coordi nate 纵坐标y-coordi nate 原点orig in 象限quadra nt 截距(有正负之分)intercede (方程的)解solution 几何geometry 点poi nt 线line 面pla ne 体solid 线段segme nt 射线radial 平行parallel 相交in tersect 角an gle 角度degree 弧度radia n 锐角acute an gle 直角right an gle 钝角obtuse an gle 平角straight an gle 周角perig on 底base 边side 高height 三角形tria ngle锐角三角形acute triangle 直角三角形right triangle 直角边leg 斜边hypote nuse 勾股定理Pythagorea n theorem钝角三角形obtuse triangle 不等边三角形scalene triangle 等腰三角形isosceles triangle 等边三角形equilateral triangle 四边形quadrilateral 平行四边形parallelogram 矩形recta ngle 长len gth 宽width 周长perimeter 面积area 相似similar 全等con grue nt 三角trig ono metry 正弦si ne 余弦cos ine 正切tangent 余切cota ngent 正割seca nt 余割coseca nt 反正弦arc si ne反余弦arc cos ine 反正切arc tangent 反余切arc cota ngent 反正割arc seca nt 反余割arc coseca nt 集合aggregate 元素eleme nt 空集void 子集subset 交集in tersect ion 并集union 补集compleme nt 映射mappi ng 函数fun cti on定义域domain, field of definition 值域range单调性mono to ni city 奇偶性parity周期性periodicity 图象image 数列，级数series 微积分calculus 微分differe ntial 导数derivative 极限limit 无穷大infin ite(a.) infin ity (n.) 无穷小infini tesimal 积分in tegral 定积分defi nite in tegral 不定积分indefinite integral 复数complex nu mber 矩阵matrix 行列式determ inant 圆circle 圆心centre(BrE), cen ter(AmE) 半径radius 直径diameter 圆周率pi 弧arc 半圆semicircle 扇形sector 环ring 椭圆ellipse 圆周circumfere nee 轨迹locus, loca(pl.) 平行六面体parallelepiped 立方体cube七面体heptahedr on 八面体octahedro n 九面体enn eahedro n 十面体decahedr on 十面体hendecahedron 十二面体dodecahedron 二十面体icosahedron 多面体polyhedro n 旋转rotati on 轴axis 球sphere 半球hemisphere 底面un dersurface 表面积surface area 体积volume空间space 双曲线hyperbola 抛物线parabola 四面体tetrahedro n 五面体pen tahedr on 六面体hexahedr on 菱形rhomb, rhombus, rhombi(pl.), diam ond 正方形square 梯形trapezoid 直角梯形right trapezoid 等腰梯形isosceles trapezoid 五边形pen tag on 六边形hexag on 七边形heptag on 八边形octag on 九边形enn eag on 十边形decag on 十边形hen decago n 十二边形dodecagon 多边形polyg on 正多边形equilateral polygon 相位phase 周期period 振幅amplitude 内心incentre(BrE), i ncen ter(AmE) 夕卜心exce ntre(BrE), exce nter(AmE) 旁心esce ntre(BrE), esce nter(AmE) 垂心orthoce ntre(BrE),orthoce nter(AmE)重心baryce ntre(BrE), baryce nter(AmE)内切圆in scribed circle 夕卜切圆circumcircle 统计statistics 平均数average 力卩权平均数weighted average 方差varia nee标准差root-mea n-square deviatio n, sta ndard deviati on 比例propoti on 百分比perce nt 百分点perce ntage 百分位数perce ntile排列permutati on 组合comb in ati on 概率，或然率probability 分布distributio n 正态分布normal distribution 非正态分布abnormal distribution 图表graph 条形统计图bar graph 柱形统计图histogram 折线统计图broken line graph 曲线统计图curve diagram代数ALGEBRA1. 数论n atural nu mber 自然数positivenu mber 正数n egative nu mber 负数odd in teger, odd nu mber 奇数eve n in teger, eve n nu mber 偶数in teger, whole number 整数positive whole nu mber 正整数n egative whole number 负整数consecutive number 连续整数real number, rational number 实数,有理数irrational(number)无理数inverse 倒数composite number 合数e.g.4.6.8.9.10.12.14.15 …prime nu mber 质数e.g.2.3.5.7.11.13.15 …reciprocal 倒数com mon divisor 公约数multiple 倍数(minimum) commormultiple (最小)公倍数(prime) factor( 质)因子com mon factor 公因子ordinary scale, decimal scale 十进制nonnegative 非负的tens 十位units 个位mode众数mean平均数media n 中值com mon ratio 公比2. 基本数学概念arithmetic mea n 算术平均值weighted average 力卩权平均值geometric mean 几何平均数exponent 指数，幕base 乘幕的底数, 底边cube 立方数，立方体square root 平方根cube root 立方根commonogarithm 常用对数digit 数字con sta nt 常数variable 变量inv erse fun cti on 反函数compleme ntary fun cti on 余函数lin ear 一次的，线性的factorization 因式分解absolute value 绝对值，e.g. | -32 | =32 round off四舍五入数学3. 基本运算add, plus 力卩subtract 减differe nee 差multiply, times 乘product 积divide 除divisible 可被整除的divided evenly被整除divide nd 被除数，红利divisor 因子,除数，公约数quotient 商rema in der 余数factorial 阶乘power 乘方radical sign, root sign 根号round to 四舍五入to the nearest 四舍五入4. 代数式，方程，不等式algebraic term 代数项like terms, similar terms 同类项nu merical coefficient 数字系数literal coefficie nt 字母系数in equality 不等式tria ngle in equality 三角不等式range 值域original equation 原方程equivale nt equati on 同解方程，等价方程linear equation 线性方程(e.g.5x+6=22) 5. 分数，小数proper fractio n 真分数improper fraction假分数mixed number 带分数vulgar fracti on ，com monfracti on 普通分数simple fractio n简分数complex fractio n 繁分数numerator 分子denominator 分母(least)com mon denomin ator (最小)公分母quarter 四分之一decimal fracti on 纯小数infinite decimal无穷小数recurri ng decimal 循环小数ten ths unit 十分位6. 集合、、union 并集proper subset 真子集soluti on set 解集7. 数列arithmetic progressi on（ seque nee）等差数歹U geometric progressi on（ seque nee）等比数歹U8. 其它approximate 近似（anti）eloekwise （逆）顺时针方向eardinal 基数ordinal 序数direet proportio n 正比disti net 不同的estimati on 估计，近似parentheses 括号proporti on比例permutatio n 排列eomb in ati on 组合table 表格trigono metric fun etio n 三角函数unit 单位,位几何GEOMETRY1. 角alter nate an gle 内错角eorresp onding an gle 同位角vertieal angle 对顶角eentralangle 圆心角interior angle 内角exterior an gle 夕卜角suppleme ntaryangles 补角eomplementary angle 余角adjaeent angle 令B角aeute angle 锐角obtuse angle 钝角right angle 直角round an gle 周角straight an gle 平角in eluded an gle 夹角2. 三角形equilateral tria ngle 等边三角形seale ne tria ngle 不等边三角形soseeles tria ngle 等腰三角形right triangle 直角三角形oblique 斜三角形inseribed triangle 内接三角形3. 收敛的平面图形，除三角形外semieirele 半圆concen trie eireles 同心圆quadrilateral 四边形pen tag on 五边形hexag on 六边形heptagon 七边形oetagon 八边形nonagon九边形deeagon十边形polygon 多边形parallelogram 平行四边形equilateral 等边形plane 平面square 正方形，平方recta ngle 长方形regular polyg on 正多边形rhombus菱形trapezoid 梯形4. 其它平面图形are 弧line, straight line 直线line segme nt 线段parallel li nes平行线segme nt of a circle 弧形5. 立体图形cube立方体，立方数rectangular solid 长方体regular olid/regularpolyhedro n正多面体circular eylinder 圆柱体cone 圆锥sphere 球体solid 立体的6. 图形的附属概念pla ne geometry 平面几何trigo no metry 三角学bisect 平分ireumseribe 夕卜切in scribe 内切in terseet 相交perpe ndicular 垂直Pythagorea n theorem 勾股定理（毕达哥拉斯定理）eongruent全等的multilateral 多边的altitude 高depth深度side 边长eireumfere nee, perimeter 周长adian 弧度surface area 表面积volume体积arm直角三角形的股cross section 横截面een ter of a circle 圆心chord 弦diameter 直径radius 半径an gle bisector 角平分线diagonal 对角线edge 棱face of a solid 立体的面hypotenuse 斜边in eluded side 夹边leg 三角形的直角边median （三角形的）中线base 底边，底数（e.g. 2的5次方，2就是底数）opposite 直角三角形中的对边midpoint 中点endpoint 端点vertex （复数形式vertices）顶点tangent 切线的transversal 截线in tercept 截距7. 坐标coordi nate system 坐标系rectan gular coordi nate 直角坐标系origi n 原点abscissa 横坐标ordi nate纵坐标nu mber line 数轴quadra nt 象限slope 斜率complex plane复平面8. 计量单位cent 美分penny —美分硬币nickel 5 美分硬币dime 一角硬币dozen 打（12 个）score 廿（20 个） Cen tigrade 摄氏Fahre nheit 华氏quart 夸脱gall on 力口仑（1 gall on =4 quart） yard 码meter 米micron 微米inch 英寸foot 英尺mi nute 分（角度的度量单位，60分=1 度）square measure 平方单位希9 cubic meter 立方米pi nt 品脱（干量或液量的单位）基本规律1所有的质数（2除外）都是奇数，但奇数不一定是质数2 若b>a,则b/a > （b+1）/（a+1）;若 b < a>其它1. 单位类cent 美分penny —美分硬币nickel 5 美分硬币dime 一角硬币dozen 打（12 个）score 廿（20 个） Cen tigrade 摄氏Fahre nheit 华氏quart 夸脱gall on 力口仑（1 gall on =4 quart） yard 码meter 米micron 微米inch 英寸foot 英尺mi nute 分（角度的度量单位，60分=1度） square measure 平方单位希9 cubic meter立方米pint 品脱（干量或液量的单位）2. 有关文字叙述题，主要是有关商业in tercalary year（leap year）闰年（366 天）common year 平年（365 天） depreciation 折旧down payment 直接付款discount 打折margin 利润profit 禾U润in terest 禾U息simple in terest 单禾U compo un ded in terest复禾U divide nd 红禾U decrease to 减少至U decrease by 减少了in crease to 增加到in crease by 增加了denote 表示list price 标价markup 丫张价per capita 每人ratio 比率retail price 零售价tie 打。
big.matrix参数
big.matrix参数在R语言中，`big.matrix` 是`bigmemory` 包提供的一个用于处理大矩阵（大数据集）的数据结构。
`big.matrix` 对象提供了对大型数据集的高效存储和操作。
以下是一些`big.matrix` 的常见参数和相关操作：创建`big.matrix` 对象：```Rlibrary(bigmemory)# 创建一个大矩阵，参数为行数、列数和数据类型bm <- big.matrix(nrow = 1000, ncol = 100, type = "double")````big.matrix` 的常见参数：1. nrow：矩阵的行数。
2. ncol：矩阵的列数。
3. type：数据类型，可以是"double"、"integer"、"character" 等。
4. init：初始值，可选参数，可以设置所有元素的初始值。
5. shared：是否允许多个`big.matrix` 共享相同的内存。
`big.matrix` 对象的基本操作：```R# 获取矩阵的维度dim(bm)# 获取矩阵的行数nrow(bm)# 获取矩阵的列数ncol(bm)# 获取矩阵的数据类型typeOf(bm)# 获取矩阵的第一行bm[1, ]# 获取矩阵的第一列bm[, 1]# 修改矩阵的某个元素bm[1, 1] <- 10````big.matrix` 的高级操作：```R# 从数据框创建big.matrixdf <- data.frame(a = c(1, 2, 3), b = c(4, 5, 6))bm_from_df <- as.big.matrix(df)# 从文件读取数据创建big.matrixfilename <- "path/to/your/file.csv"bm_from_file <- read.big.matrix(filename, type = "double", header = TRUE, separator = ",")# 写入big.matrix 数据到文件write.big.matrix(bm, filename, type = "double", separator = ",")# 向big.matrix 添加新的行或列new_row <- c(11, 12, 13)bm <- rbind(bm, new_row)new_col <- c(21, 22, 23)bm <- cbind(bm, new_col)```请注意，`big.matrix` 主要用于处理大型数据集，特别是当数据无法一次性加载到内存时。
智能融合cSoC：多通道FFT共享处理器使用FPGA纤维说明书
Application Note AC381February 20121© 2012 Microsemi Corporation SmartFusion cSoC: Multi-Channel FFT Co-Processor Using FPGA FabricTable of ContentsIntroductionThe SmartFusion ® customizable system-on-chip (cSoC) device integrates FPGA technology with a hardened ARM ® Cortex™-M3 processor based microcontroller subsystem (MSS) and programmable high-performance analog blocks built on a low power flash semiconductor process. The MSS consists of hardened blocks such as a 100 MHz ARM Cortex-M3 processor, peripheral direct memory access (PDMA), embedded nonvolatile memory (eNVM), embedded SRAM (eSRAM), embedded FlashROM (eFROM), external memory controller (EMC), Watchdog Timer, the Philips Inter-Integrated Circuit (I 2C),serial peripheral interface (SPI), 10/100 Ethernet controller, real-time counter (RTC), GPIO block, fabric interface controller (FIC), in-application programming (IAP), and analog compute engine (ACE).The SmartFusion cSoC device is a good fit for applications that require interface with many analog sensors and analog channels. SmartFusion cSoC devices have a versatile analog front-end (AFE) that complements the ARM Cortex-M3 processor based MSS and general-purpose FPGA fabric. The SmartFusion AFE includes three 12-bit successive approximation register (SAR) ADCs, one first order sigma-delta DAC (SDD) per ADC, high performance signal conditioning blocks, and comparators. The SmartFusion cSoCs have a sophisticated controller for the AFE called the ACE. The ACE configures and sequences all the analog functions using the sample sequencing engine (SSE) and post-processes the results using the post processing engine (PPE) and handles without intervention of Cortex-M3 processor.Refer to the SmartFusion Programmable Analog User’s Guide for more details.This application note describes the capability of SmartFusion cSoC devices to compute the Fast Fourier Transform (FFT) in real time. The Multi Channel FFT example design can be used in medical applications, sensor network applications, multi channel audio Spectrum analyzers, Smart Metering, and sensing applications (such as vibration analysis).This example design uses the Cortex-M3 processor in the SmartFusion MSS as a master and the FFT processor in the FPGA fabric as a slave. All three of the SmartFusion cSoC A2F500’s ADCs are used for data acquisition. The example design uses Microsemi’s CoreFFT IP and the advanced peripheral bus interface (CoreAPB3). A custom-made APB3 interface has been developed to connect CoreFFT with the MSS via CoreAPB3. The Cortex-M3 processor uses the PDMA controller in the MSS for the data transfer and thus helps to free up the Cortex-M3 processor instruction bandwidth.A basic understanding of the SmartFusion design flow is assumed. Refer to Using UART with SmartFusion - Microsemi Libero ® SoC and SoftConsole Flow Tutorial to understand the SmartFusion design flow.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Design Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Design Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Implementing Multi Channel FFT on EVAL KIT BOARD . . . . . . . . . . . . . . . . . . . . . . . . . 7Running the Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Appendix A – Design Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10SmartFusion cSoC: Multi-Channel FFT Co-Processor Using FPGA Fabric2Design OverviewThis design example demonstrates the capability of the SmartFusion cSoC device to compute the FFT for multiple data channels. The FFT computation is a complex task that utilizes extensive logic resources and computation time. In general, for N number of channels, N number of FFT IP’s are needed to be instantiated, which in turn utilize more logic resources on the FPGA. A way to avoid this limitation is to use the same FFT logic for multiple input channels.This design illustrates the implementation of a Multichannel FFT to process multiple data channels through a single FFT and store FFT points in a buffer. The FFT computes the input data read from each channel and stores the N-point result in the respective channel’s allocated buffer. The channel multiplexing is done once each channel buffer has been loaded with the FFT length.Computing frequency components for a real time data of six channels is described in this application note. For sampling the input signals the AFE is used and the complex FFT computation is implemented in the fabric of the SmartFusion cSoC device. The Cortex-M3 processor in the MSS of the SmartFusion cSoC handles the buffer management and channel muxing.Figure 1 depicts the block diagram of six channel FFT co-processor in FPGA fabric.Design DescriptionThe design uses CoreFFT for computing the FFT results. You can download the core generator for CoreFFT at /soc/portal/default.aspx?r=4&p=m=624,ev=60.The design example uses a 512-point and 16-bit FFT. A custom-made APB3 interface has been developed to connect CoreFFT IP with the MSS’s FIC. The CoreFFT output data is stored in a 512x32FIFO within the fabric. The FIFO status signals are given in Table 1 on page 3. The status signals indicate that FFT is ready to receive data and data is available in the output of FIFO. These status signals are mapped to the GPIOs in the MSS. The Cortex-M3 processor can read the GPIOs to handle flow control in the data transfer process from the MSS to CoreFFT.Figure 1 • Multi Channel FFT Block DiagramDesign Description3Figure 2 shows the block diagram of logic in the fabric with custom-made APB3 bus.The data valid signal (ifiD_valid) is generated in custom logic whenever the master needs to write data into the input buffer of the FFT to process through the APB3 interface. The FFT_IP_RDY signal indicates the status of the input buffer of the FFT. If the input buffer is full, the FFT_IP_RDY goes low. The master can read the FFT_IP_RDY signal to get the FFT input buffer status. The FFT generates the processed data with a data valid signal (ifoY_valid). The processed data is stored in the FIFO. When FIFO is not ready to receive output data, it can stop the data fetching from the FFT by pulling down the ifiRead_y signal. The status signal FFT_OP_RDY is used to indicate to the master that processed data is available in the FIFO. FFT_OP_RDY goes High whenever processed data is available in the FFT output buffer.The master can use AEMPTY_OUT or EMPTY_OUT to determine whether the FIFO is empty and all the processed data has been read. Refer to the CoreFFT Handbook for more details on architecture and interface signal descriptions.Three ADCs are configured to have two channels, each channel with 100 ksps sampling rate. The external memory is used for input and output buffers. For each channel, one input buffer having length double to the length of FFT i.e. 1024 words and one output buffer having length equal to the length of FFT i.e. 512 words are used. After each channel's input buffer has 512 points required for the full length of the FFT, each channel, one after the other, streams its points from the FIFO through the FFT. During the FFT computational period, the sampled data values of each channel are stored in the second half of the input buffer. Once the FFT computations for the First half of input buffer completes then the points in the second half of the input buffer will be streamed to FFT. This operation utilizes a ping-pong method. The Cortex-M3 processor is used for data management, that is, buffering the sampled points and data routing or muxing of these values to the FFT computation block. Sampling of the real time data is done by the ACE. The PDMA handles the data transfer between the external SRAM (eSRAM) buffers and CoreFFT logic in FPGA fabric.Figure 2 • CoreFFT with APB Slave InterfaceTable 1 • FIFO Status Signals with DescriptionsSignalDescription FFT_IP_RDYFFT is ready to receive the Input from the master processor FFT_OP_RDYProcessed data is ready in output buffer of FFT AEMPTY_OUTOutput FIFO is almost empty EMPTY_OUT Output FIFO is emptySmartFusion cSoC: Multi-Channel FFT Co-Processor Using FPGA Fabric4Figure 3 shows the implementation of multi channel FFT on the SmartFusion cSoC device.Hardware ImplementationThe MSS is configured with an FIC, clock conditioning circuit (CCC), GPIOs, EMC and a UART. The CCC generates 80 MHz clock, which acts as the clock source. The FIC is configured to use a master interface with an AMBA APB3 interface. Four GPIOs in the MSS are configured as inputs that are used to handle flow control in data transfer from MSS to FFT coprocessor. The EMC is configured for Region 0as Asynchronous RAM and port size as half word. The UART_0 is configured for printing the FFT values to the PC though a serial terminal emulation program.ADC0, ADC1, and ADC2 are configured with 12-bit resolution, two channels and the sampling rate is set to approximately 100 KHz. Figure 4 on page 5 shows the ACE configuration window.Figure 3 • Implementation of Multi Channel FFT on the SmartFusion cSoCDesign Description5The APB wrapper logic is implemented on the top of CoreFFT and connected to CoreAPB3. A FIFO of size 512*32 is used to connect to CoreFFT output.CoreAPB3 acts as a bridge between the MSS and the FFT coprocessor block. It provides an advanced microcontroller bus architecture (AMBA3) advanced peripheral bus (APB3) fabric supporting up to 16APB slaves. This design example uses one slave slot (Slot 0) to interface with the FFT coprocessor block and is configured with direct addressing mode. Refer to the CoreAPB3 Handbook for more details on CoreAPB3 IP .For more details on how to connect FPGA logic MSS, refer to the Connecting User Logic to the SmartFusion Microcontroller Subsystem application note.The logic in the FPGA fabric consumes 18 RAM blocks out of 24. We cannot use eSRAM blocks for implementing CoreFFT as the transactions between these SRAM blocks and FFT logic are very high and are time critical.Figure 5 on page 6 illustrates the multi channel FFT example design in the SmartDesign.Figure 4 • Configure ACESmartFusion cSoC: Multi-Channel FFT Co-Processor Using FPGA Fabric6Table 2 summarizes the logic resource utilization of the design on the A2F500M3F device.Software ImplementationThe Cortex-M3 processor continuously reads the values from ACE and stores the values into the input buffers. If the first 512 points are filled then the processor initiates the FFT process. In the FFT process,the input buffers are streamed one after other to the CoreFFT with the help of PDMA. Using another channel of PDMA the output of FFT is moved to the corresponding channel output buffers.During the FFT process the Cortex-M3 processor stores the sampled values into the second half of the input buffers. Once the FFT process completes the first half of input buffer, then the second half of the input buffer are streamed to CoreFFT.Figure 5 • SmartDesign Implementation of Multi Channel FFTTable 2 • Logic Utilization of the Design on A2F500M3FCoreFFTOther Logic in Fabric Total Ram Blocks14418 (75%)Tiles 78424718313 (72.1%)Implementing Multi Channel FFT on EVAL KIT BOARD7The CALL_FFT(int *) application programmable interface (API) initiates the PDMA to transfer input buffer data to the FFT in the fabric. Before initiating PDMA it checks for FFT whether or not it is ready to read the data. The CALL_FFT(int *) API also checks if the output FIFO is empty so that all the FFT out values have been already read. When the input buffer has points equal to the full length of FFT, then it will be called.The Read_FFT() API initiates the PDMA for reading the FFT output values from FIFO in fabric to the corresponding output buffer. After reading all the values it calls the CALL_FFT() API with the next channel buffer to compute the FFT for next channel. This is done for all channels. After completion of FFT computation for all channels, if the continuous variable is not defined, it will print the FFT output values on the serial terminal. When FFT_OP_READY interrupt occurs then this API will be called.The GPIO1_IRQHandler() interrupt service routine occurs on the positive edge of FFT_OP_READY signal. It calls Read_FFT() API. This interrupt mechanism is used to read the sample values continuously while computing the FFT.If continuous variable is defined, then the FFT is computed without any loss of data samples. If #define continuous line is commented then after every completion of FFT computation of all channels the FFT output is printed on serial terminal. The printed values are in the form of complex numbers.The ping-pong mechanism is used for input data buffer to store the samples continuously. For each channel the input buffer length is double of the full FFT length. While computing the FFT for the first half of the buffer, the new sample values are stored in the second half of the input buffer and while computing the FFT for second half of buffer, the new sample values are stored in first half of the input buffer.Customizing the Number of ChannelsYou can change the design depending on your requirement. Configure the ADC (Figure 4 on page 5)with the required number of channels and required sampling rate. In SoftConsole project change the parameter value NUM_CHANNELS according to the ADC configuration. Edit the main code for reading ADCs data into buffers according to ACE configuration.Throughput CalculationsThe actual time to get 512 samples with 100 ksps is 5.12 ms. Each channel is configured to 100 ksps, so for every 5.12 ms we will have 512 samples in the input buffers.The actual time taken to compute the FFT for each channel is the sum of time taken to transfer 512points to CoreFFT, FFT computation time, and time to read FFT output to the output buffer.•Total time for computing FFT = (time taken to receive 512 data + computational latency for 512points + time taken to store 512 data) = 512*5 + 23292 + 512*5 =28412 clks •Time to compute FFT for 6 channels = 28412*6 = 170472 clksTime to compute FFT for six channels is 2.1309 ms (If CLK is 80 MHz). It is less than half the sample rate of 5.12 ms.If only one channel is configured with maximum sampling rate (600 ksps) then time to get 512 samples with 600 ksps is 0.853 ms. Time to compute FFT for these 512 samples is 0.355 ms. If you configure three ADCs with maximum sampling rate (1800 ksps) then time to compute the FFT for these three channels will be 1.065 ms which is higher than the sampling time. In this there is a loss of some samples.The design works fine up to 1440 ksps.Implementing Multi Channel FFT on EVAL KIT BOARDTo implement the design on the SmartFusion Evaluation Kit Board the FFT must be 256 point and 8 bit because the A2F200 device has less RAM blocks and logic cells. The ADC channels must be selected for only ADC0 and ADC1. Figure 6 on page 8 shows the implementation of multi channel FFT on the SmartFusion cSoC (A2F200M3F) device.SmartFusion cSoC: Multi-Channel FFT Co-Processor Using FPGA Fabric8Table 3 summarizes the logic resource utilization of the design with 256 points 8-bit FFT on A2F200M3F device.Running the DesignProgram the SmartFusion Evaluation Kit Board or the SmartFusion Development Kit Board with the generated or provided *.stp file (refer to "Appendix A – Design Files" on page 10) using FlashPro and then power cycle the board.For computing continuous FFT values for the all six signals sampled through the ADCs, uncomment the line #define continuous in the main program. The FFT output values are stored in the rdata buffer. This buffer is updated for every computation of FFT.For printing the FFT values on serial terminal (HyperTerminal or PuTTy), comment the line #define continuous in the main program.Figure 6 • Implementation of Multi Channel FFT on the SmartFusion Evaluation Kit BoardTable 3 • Logic Utilization of the Design on A2F200M3F DeviceCoreFFTOther Logic in Fabric Total Ram Blocks718 (100%)Tiles 3201853286 (66%)Conclusion9Connect the analog inputs to the SmartFusion Kit Board with the information provided in Table 4.Invoke the SoftConsole IDE, by clicking on Write Application code under Develop Firmware in Libero ®System-on-Chip (SoC) project (refer to "Appendix A – Design Files") and launch the debugger. Start HyperTerminal or PuTTY with a baud rate of 57600, 8 data bits, 1 stop bit, no parity, and no flow control.If your PC does not have the HyperTerminal program, use any free serial terminal emulation program such as PuTTY or Tera Term. Refer to the Configuring Serial Terminal Emulation Programs Tutorial for configuring the HyperTerminal, Tera Term, or PuTTY .ConclusionThis application note describes the capability of the SmartFusion cSoC devices to compute the multi channel FFT. The Cortex-M3 processor, AFE, and FPGA fabric together gives a single chip solution for real time multi channel FFT system. This design example also shows the 6-channel data acquisition system.Table 4 • SettingsChannelEvaluation Kit Development Kit Channel 173 of J21 (signal header)ADC0 of JP4Channel 274 of J21 (signal header)ADC1 of JP4Channel 377 of J21 (signal header)77 of J21 (signal header)Channel 478 of J21 (signal header)78 of J21 (signal header)Channel 585 of J21 (signal header)Channel 686 of J21 (signal header)Figure 7 • FFT Output Data for 1 kHz Sinusoidal Signal on PUTTYSmartFusion cSoC: Multi-Channel FFT Co-Processor Using FPGA Fabric10Appendix A – Design FilesThe Design files are available for download on the Microsemi SoC Product Groups website:/soc/download/rsc/?f=A2F_AC381_DF.The design zip file consists of Libero SoC projects and programming file (*.stp) for A2F200 and A2F500.Refer to the Readme.txt file included in the design file for directory structure and description.51900249-0/02.12© 2012 Microsemi Corporation. All rights reserved. Microsemi and the Microsemi logo are trademarks of Microsemi Corporation. All other trademarks and service marks are the property of their respective owners.Microsemi Corporation (NASDAQ: MSCC) offers a comprehensive portfolio of semiconductor solutions for: aerospace, defense and security; enterprise and communications; and industrial and alternative energy markets. Products include high-performance, high-reliability analog and RF devices, mixed signal and RF integrated circuits, customizable SoCs, FPGAs, and complete subsystems. Microsemi is headquartered in Aliso Viejo, Calif. Learn more at .Microsemi Corporate HeadquartersOne Enterprise, Aliso Viejo CA 92656 USAWithin the USA: +1 (949) 380-6100Sales: +1 (949) 380-6136Fax: +1 (949) 215-4996。
Summa Scalable universal matrix multiplication algorithm
These are the special cases implemented as part of the widely used sequential Basic Linear Algebra Subprograms 11]. We will assume that each matrix X is of dimension mX nX , X 2 fA; B; C g. Naturally, there are constraints on these dimensions for the multiplications to be well de ned: We will assume that the dimensions of C are m n, while the \other" dimension is k.
This work is partially supported by the NASA High Performance Computing and Communications Program's Earth and Space Sciences Project under NRA Grant NAG5-2497. Additional support came from the Intel Research Council. Jerrell Watts is being supported by an NSF Graduate Research Fellowship.
zemax中binary 1 的多项式扩展公式
在 Zemax 中，Binary 1 多项式扩展通常用于描述光学系统中的波面形状。
这是一种用二进制数表示的多项式，其中每个二进制位对应于一个特定的光学表面或操作。
Binary 1 多项式扩展的一般形式如下：
P(x,y)=C0+C1x+C2y+C3x2+C4xy+C5y2+C6x3+C7x2y+C8xy2+⋯
这里，x和y是输入坐标，C i是系数，而指数项表示不同阶数的项。
Binary 1 多项式扩展的特殊之处在于，系数C i可以采用二进制表示。
对于一个给定的二进制表示，仅当相应的二进制位为 1 时，相应的系数项才会被包含在多项式中。
这使得 Binary 1 多项式扩展成为一种灵活的波面形状描述方式，可以精确地表示特定光学系统的形态。
在 Zemax 中，通常可以通过设置系统的多项式扩展（Polynomial Coefficients）来定义 Binary 1 多项式扩展。
这可以通过 Lens Data Editor 中的“Poly”栏目或使用Zemax 的宏语言进行操作。
在实际使用中，具体的 Binary 1 多项式扩展的形式和系数取值将取决于光学系统的需求和设计。
在进行 Zemax 模拟时，工程师通常需要根据系统的特点调整二进制位的状态和系数值。
这种灵活性允许工程师优化系统以满足特定的设计目标。
multi2加密算法原理
multi2加密算法原理Multi2算法的原理分为四个步骤：初始置换、伪随机数生成、混淆和扩散。
在加密之前，需要执行密钥分配和初始化过程。
首先是初始置换（Initial Permutation，IP）步骤。
该步骤通过对输入数据块进行置换，将其转换为与加密有关的格式。
其中，输入数据块被分为4个字节的小块。
接下来是伪随机数生成（Pseudo Random Number Generation，PRNG）步骤。
该步骤使用一个密钥和一个初始化向量来生成伪随机数流。
多重加密技术被用来提高加密强度，生成的伪随机数流用于混淆和扩散过程。
然后是混淆（Confusion）步骤。
在混淆过程中，伪随机数流与输入数据块进行按位异或运算。
这样可以使输入数据块中的每个比特都与伪随机数流的对应比特产生关联。
最后是扩散（Diffusion）步骤。
扩散过程使用单向置换和伪随机数生成器进行数据重排。
这样，原始数据的每个比特都可以影响到输出数据的多个比特，从而增强了加密的强度。
Multi2算法的安全性主要依赖于两个因素：密钥和伪随机数流。
密钥越长，破解难度就越大。
伪随机数流的质量也直接影响加密强度，伪随机数流应具有高级别的不可预测性。
Multi2算法还可以应用于各种通信场景，如移动通信、数据网等。
它具有快速、高效和可扩展性等优点。
同时，Multi2算法也存在一些安全风险和局限性，如密钥管理、远程密钥分发等问题。
但总体来说，Multi2算法仍然是一种相对安全和可靠的加密算法。
总结起来，Multi2加密算法采用分组密码和公钥密码体制，通过初始置换、伪随机数生成、混淆和扩散四个步骤来保护通信数据的安全性。
它兼具高强度、高效率和可扩展性等特点，并在各种通信场景中得到广泛应用。
然而，随着计算机技术的不断进步，可能会出现更先进的破解方法，因此安全性的保证仍然需要不断加强和改进。
基于改进ORB_的无人机影像拼接算法
第 22卷第 4期2023年 4月Vol.22 No.4Apr.2023软件导刊Software Guide基于改进ORB的无人机影像拼接算法张平，孙林，何显辉（山东科技大学测绘与空间信息学院，山东青岛 266590）摘要：针对传统图像拼接算法在无人机遥感影像拼接过程中速度慢、效率低、无法满足实时准确拼接要求的问题，提出一种改进ORB的图像拼接算法。
首先构建尺度金字塔并利用ORB算法提取特征点，利用BEBLID描述符对特征点进行特征描述，采用最近邻比值（NNDR）算法进行粗匹配；然后基于特征点投票构建最优化几何约束对特征点进一步优化，利用随机采样一致性（RANSAC）算法计算变换矩阵，获取高精度变换矩阵；最后利用改进的渐入渐出加权融合算法实现图像拼接。
实验结果表明，所提算法配准精度最高达到100%，配准耗时低于0.91s，拼接图像信息熵达到6.807 9。
相较于传统算法，所提算法具有更高的拼接效率，在降低图像拼接时间的同时能够获取更高质量的拼接图像，性能显著提升。
关键词：图像拼接；多尺度FAST检测；BEBLID特征；最优化几何约束DOI：10.11907/rjdk.222267开放科学（资源服务）标识码（OSID）：中图分类号：TP391.41 文献标识码：A文章编号：1672-7800（2023）004-0156-06UAV Image Mosaic Algorithm Based on Improved ORBZHANG Ping， SUN Lin， HE Xian-hui（College of Geodesy and Geomatics， Shandong University of Science and Technology， Qingdao 266590， China）Abstract：Aiming at the problems of slow speed and low efficiency of traditional image stitching algorithm in UAV remote sensing image stitching process， which cannot meet the requirements of real-time and accurate stitching， an improved ORB image stitching algorithm is pro‐posed. Firstly， the scale pyramid is constructed and the feature points are extracted by ORB algorithm， and then the feature points are de‐scribed by BEBLID descriptor； The nearest neighbor ratio （NNDR） algorithm is used for rough matching， and then the optimal geometric con‐straints are constructed based on the feature point voting to further optimize the feature points. The random sampling consistency （RANSAC）algorithm is used to calculate the transformation matrix and obtain the high-precision transformation matrix； Finally， the improved gradual in and gradual out weighted fusion algorithm is used to realize image mosaic. The experimental results show that the registration accuracy of the proposed algorithm reaches 100% at the highest， the registration time is less than 0.91s， and the information entropy of mosaic image reaches 6.807 9. Compared with the traditional algorithm，the algorithm in this paper has higher splicing efficiency，and can obtain higher quality splicing images while reducing the image splicing time. The algorithm performance is significantly improved.Key Words：image mosaic； multi scale FAST detection； BEBLID feature； optimal geometric constraint0 引言近年来，无人机航拍摄影技术越来越成熟，在遥感监测［1］、电力巡检［2］、灾害勘察［3］、军事侦察［4］等领域均有广泛应用。
matlab信源二进制赫夫曼编码
信源二进制赫夫曼编码是一种常见的数据压缩算法，它可以有效地降低数据传输和存储的成本。
在本文中，我将深入探讨matlab中的信源二进制赫夫曼编码的原理、实现和应用，并共享我的个人观点和理解。
让我们来了解一下信源编码的基本概念。
信源编码是一种将离散或连续信号转换为离散符号的过程，其目的是尽量减少信号的冗余度，以便更高效地传输和存储。
在数字通信和数据存储领域，信源编码起着至关重要的作用。
而二进制赫夫曼编码是一种常见的无损数据压缩算法，其核心思想是通过对出现频率较高的符号赋予较短的编码，而对出现频率较低的符号赋予较长的编码，从而实现数据的压缩。
在matlab中，我们可以利用赫夫曼树和编码表来实现信源二进制赫夫曼编码。
接下来，我将详细介绍matlab中的信源二进制赫夫曼编码的实现过程。
在matlab中，我们可以使用`huffmandict`函数来创建赫夫曼编码字典，该函数需要输入符号和它们对应的概率作为参数。
我们可以使用`huffmanenco`函数来对输入的符号序列进行赫夫曼编码，得到压缩后的二进制码字。
我们可以使用`huffmandeco`函数来对压缩后的二进制码字进行解码，得到原始的符号序列。
通过这些函数的组合，我们可以在matlab中轻松实现信源二进制赫夫曼编码。
具体的实现细节和示例代码我将在下文中进行详细讲解。
信源二进制赫夫曼编码的应用非常广泛，特别是在无线通信、图像压缩和音频处理等领域。
通过使用赫夫曼编码，我们可以大大减小数据传输和存储的成本，提高系统的效率和可靠性。
赫夫曼编码也是信息论中的重要概念，它为我们理解信息压缩和编码提供了重要的思路和方法。
从个人观点来看，信源二进制赫夫曼编码作为一种经典的数据压缩算法，具有重要的理论意义和实际应用价值。
在matlab中，我们可以利用现成的函数库来实现赫夫曼编码，同时也可以根据具体的应用场景进行定制化的优化。
通过不断深入研究和实践，我们可以进一步发掘赫夫曼编码的潜力，为数据压缩和信息传输领域带来更多的创新和突破。
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If 100 K x 10 M matrix, there are ONE Trillion possible intersections.
Motivation
As can be seen from example, a very large matrix can emerge:
1 Trillion intersections would require potentially up to 31 Billion 32 bit instructions in the worst case.
A co-processor design would be built on an add-on board such that the whole database is loaded onto the board at startup, and thereafter, queries are sent to the board, and results are returned, thus requiring a lot less machine main memory accesses.
Custom Fast Binary Matrix Multiplication Processor Design
Tim Pevzner () CSE237A 6/12/2019
Outline
Introduction
Use case example Design Design Process Future Work Conclusion
Also, storing that matrix would require a lot of memory and a lot of disk accesses.
Even with a lot of main memory, the memory is not dedicated wholly for this task.
Use Case Example Analysis
The matrix was very small, therefore, results are not very interesting
Interesting when matrix is on the order of 110 million data items and 100 thousand selectors.
Introduction
Fast binary matrix multiplication custom processor
An exercise in ISA design
Custom instructions Custom design
Outline
Introduction
Billion operations, or half of the operations required for 32 bit instructions.
Outline
Introduction Use case example Design
Design Process
Future Work Conclusion
Use case example
Design Design Process Future Work Conclusion
Use Case Example
Rows represent “Selectors”
Columns represent “Data Items”
Want to find correlation between different data items as a binary number:
1 == there is a correlation 0 == there is no correlation
In this example, there are only nine selectors and 11 data items, a very small example!
Blond Brown White Short Tall Female Male Old Young
Blond Brown White Short Tall Female Male Old Young
1 0 0 1 1 1 11 1 0 1 0 1 1 1 11 1 0 0 1 1 1 1 11 0 1 1 1 1 0 1 11 1 1 1 1 0 1 1 11 1 1 1 1 1 1 1 01 1 1 1 1 1 1 0 11 1 1 1 1 1 1 1 11 0 1 1 0 1 1 1 10 1
Outline
Introduction Use case example
Design
Design Process Future Work Conclusion
Design
A new design is proposed as a co-processor model:
00000101100 01101010011 10010000000 10101001100 01010110011 01011000100 10100111011 10111001010 01000110101
Use Case Example (cont’d)
Blond Brown White Short Tall Female Male Old Young