DSP_lect06_sampling2

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DSP实验报告6

DSP第六、七次实验报告1. 实验目的:（1）进一步熟悉Matlab实验环境和语言。

（2）熟悉各种滤波器的结构及Matlab实现语言。

（3）掌握用冲击响应不变法和双线性变换法设计IIR滤波器的方法。

（4）掌握用窗函数法和频率抽样法设计FIR滤波器的方法。

2. 实验内容及总结:1.滤波器结构:（1）IIR滤波器各种结构1、直接型结构例如直接型滤波器系统函数, 则有系数向量a=[1,a1,a2,a3],b=[b0,b1,b2], 利用:Y=filter[b,a,x]求信号x(n)通过此滤波器的输出。

2、由系统函数或差分方程求系统的二阶分式（含一阶分式）的级联结构将例如的系统函数重写为二阶分式节的级联型, 利用:[sos,G]=tf2sos(b,a)3、由二阶分式的级联结构转换成系统函数的直接结构是第二步的逆运算, 调用函数:[b,a] = sos2tf(sos)可以求得系数向量a,b, 从而得到H(z)4、由系统函数求部分分式展开（留数及其极点计算）即求z反变换的部分分式展开法, 利用:[r,p,c]=residuez(b,a)其中极点为p, 留数为r, 直接项系数为c。

5、由r,p,c求系统函数即第4步的逆运算, 利用:[b,a]=residuez(r,p,c)6、由直接型结构转换为并联型结构需开发函数:[C,B,A]=tf2par(b,a)其中, b,a为直接型的系数向量, C,B,A为并联型实系数向量, 基本思想是: 1.反复调用[r,p,c]=residuez(b,a)求出极点及留数；2.利用cplxpair函数把极点、留数对按复共轭极点-留数对, 实极点-留数对的顺序排列；3.开发cplxcomp函数, 保证极点和留数相互对应；4.调用[b,a]=residuez(r,p,c)计算并联二阶节的分子分母。

7、由并联型结构转换成直接型结构开发函数:[b,a]=par2tf(C,B,A)为[C,B,A]=tf2par(b,a)的逆函数。

Atlas Sound DSP8807 自包含、紧凑的多区域数字控制的声音掩蔽处理器说明书

©2012 A t l a s S o u n d L .P . A l l r i g h t s r e s e r v e d . A t l a s S o u n d a n d S t r a t e g y S e r i e s a r e t r a d e m a r k s o f A t l a s S o u n d L .P . A l l o t h e r t r a d e m a r k s a r e t h e p r o p e r t y o f t h e i r r e s p e c t i v e o w n e r s . A T S 004406 R e v A 5/12DSP8807Self Contained, Compact Multi-Zone Digital Controlled Sound Masking ProcessorGeneral DescriptionThe Atlas Sound DSP8807 is a self-amplified, sound masking controller with extensive digital signal processing (DSP) and telephony interface capabilities. All aspects of signal routing, processing and prioritization are administered through an intuitive Graphic User Interface (GUI) managed via a local Windows ® based laptop or desktop computer. The software has the ability to expand up to (253) systems with over 2,000 zones (2,048) with primary and secondary assignment in a zone paging dialing plan. It also provides the ability to set up “All zone” page, “Group zone“ page (up to 32 groups) and “Single zone“ page with an architectural dialing plan (2-digit DTMF) set up in the GUI. AVB (Audio Video Bridge) audio networking allows distribution of paging, BGM and line level inputs between multiple DSP8807 and/or DSP2212 units across TCP/IP data networks.The DSP8807 has 8 channels of independent on-board digital class-D amplifiers capable of delivering 50W RMS per 70.7V output. Additionally, a simultaneous line level output rated at 1V/600Ω (nominal) per zone is available for driving higher power amplifiers. The DSP8807 includes two independent, uncorrelated pink noise generators, which are random and non-repeating up to 215 hours with 1⁄3-octave EQ adjustments programmable on a per zone basis.Each DSP8807 is capable of managing remote ambient level sensing microphones (ALM-1) for each zone (x8), via a single CAT5e cable up to 1,000 feet from the DSP8807. These microphones can provide automatic adjustment of the masking level based on real- time noise levels with set up and control via the GUI.Features• A VB (Audio Video Bridge) Audio Networking Allows Distribution of Paging, BGM and Line Level Inputs Between Multiple DSP8807 and/or DSP2212 Units Across TCP/IP Data Networks • User Friendly GUI and Easy Network Setup• Built-In Amplification for Each Output (50W @ 70.7V x 8)• Line Level Outputs (x8) for Expansion to External Amplifiers • Expandable - Up to 256 Units (2048 Zones) • Non Repeating Pink Noise Sources • Front Panel Visual Status LED’s for All I/O • Parametric EQ for All Paging / Line Sources • 1⁄3 Octave EQ for All Masking Zones• C omprehensive Telco Interface Facilitates Complex Paging Scenarios for Multi Floor Buildings • Paging Mic Input for Evacuation or General Announcements • Optional Ambient Sensing Microphones for Automatic System Adjustment • UL / CUL and FCC Listed DSP8807 FrontDSP8807 Back238751461. A mplifier Outputs (50 Watts x8 @ 70.7V)2. Line Level Outputs for Expansion to External Amplifiers (x8)3. R J45 Inputs for Optional Ambient Sensing Microphones (x8)4. T elco Page Input (Loop Start). Use with 2-5 Digit GUI Defined DTMF Dial Plan5. B GM, and Line Inputs6. Paging Mic Input with 32VDC Switchable Phantom Power7. Contact Closure Inputs (x4)8. TCP/IP Network Input (Parallel Input Also on Front Panel)©2012 A t l a s S o u n d L .P . A l l r i g h t s r e s e r v e d . A t l a s S o u n d a n d S t r a t e g y S e r i e s a r e t r a d e m a r k s o f A t l a s S o u n d L .P . A l l o t h e r t r a d e m a r k s a r e t h e p r o p e r t y o f t h e i r r e s p e c t i v e o w n e r s . A T S 004406 R e v A 5/12SpecificationsSystem Performance / DSP ProcessorsDynamic Range >102dB A-Weighted Frequency Response 80Hz–20kHz (±3dB) at Rated Output Distortion THD+N.001% Typical at +4dBu, 1kHz, 0dB GainInput Sensitivity ≤ 1.0% at 1kHz at Rated Output Interchannel Crosstalk > 80dB Typical Crosstalk Input To Output > 80dBChannel Separation > 100dB at 1kHz (In Thru Out) Common Mode Rejection Ration (CMRR) >50dB, 80Hz – 20kHz Typical > 55dB at 1kHzProcessor Capacity 264 MIPS, 528MFLOPS, Continuous OperationSample Rate Audio Conversion 48kHz D/A Converter Type (Audio) 24-bit Sigma Delta D/A Performance Dynamic Range (Converter) > 100dB A-Weighted A/D Performance Dynamic Range > 110dB A-WeightedNon-Volatile MemoryMemory Storage For All Programs And Set Up Protected For 24 Hours In Power Brown Out, Interruption, or Computer Shut Down. Data Settings Good for Ten Years W/O Refresh DSP Manual RestartFront Restart Manual Button To Reload DSP’sCODEC – DSP Protection All I/O Protected With Buffers From Spikes and Transients or Sneak CurrentsSystem Inputs (Unless Noted Located On Rear Panel)Power AC MainsIEC 3-pin with Ground, 100VAC-240VAC, 50Hz-60kHz with ON/OFF Manual Switch With Replaceable FuseNetwork – Data RJ45 Module Jack (EIA 568B)Telco Loop Start2-Pin Dockable Keyed Connector Input Transformer 600ΩRing Voltage 105V – 14V (POTS – VoIP) DTM F Dial Plan Single, Group, or All Page Microphone3-Pin Dockable Keyed Connector Background MusicR CA Connector 10k Ω (Sum to Mono)Master Override2-Pin Dockable Keyed Connector (1V – 70.7V nominal)Ambient Sensing Microphones (x8)R J45 Modular Jack (EIA 568B) No Polarity System Outputs (Unless Noted Located On Rear Panel)Speakers (x8)2-Pin Dockable Keyed Connector(70.7V at 50 Watts RMS)Audio Line level (x8)3-Pin Dockable Keyed Connector (1v nominal) M icrophone Frequency Level 80Hz – 18kHz M usic 80Hz – 20kHz Line out 80Hz – 18kHz Telco250Hz – 4kHzNetwork system linkRJ45 Modular Jack (EIA 568B)System Amplifiers (x8)Frequency Response 80Hz – 20kHz, (±.25dB)Total Distortion.001% Typical at +4dB, 1kHz,0dB GainTransformer Output 70.7V and IV Line Level Efficiency 85% or Better Gain Control Adjustable to 34dB Power SupplyUL / CUL /CE RecognizedInput Impedance 50k ΩOutput Impedance 8ΩCarrier Frequency 400kHz Peak Current 1.2A MTBF (Mean Time Between Failure) 100,000 HoursEMC / EMI Radiation F CC Part 15 Class B, EN6100, CISPR 22System Mechanical Data Length 14" (358mm)Width 19" (482.6mm)Height3.5" (88.9mm)Material (Outer Housing) C RS (Cold Roll Steel) 18AWG(.047" Nominal)FinishFlat Black Powder Coat With Zinc Undercoat Corrosion ResistantPrinted Circuit Boards UL Recognized UL94VO Electronic Components RoHS Operating Temperature 0˚ to +50˚C Storage Temperature -40˚ to +85˚CHumidity 95% Non-Condensing (Max.) ©2012 A t l a s S o u n d L .P . A l l r i g h t s r e s e r v e d . A t l a s S o u n d a n d S t r a t e g y S e r i e s a r e t r a d e m a r k s o f A t l a s S o u n d L .P . A l l o t h e r t r a d e m a r k s a r e t h e p r o p e r t y o f t h e i r r e s p e c t i v e o w n e r s . A T S 004406 R e v A 5/12Specification Friendly Text1. D igital Signal Processor (DSP) with Noise Masking and Amplification – DSP shall provide multi-zone digital DSP-GUI controlled processor and digital amplifiers capable of simultaneous distribution of masking, paging, and background music signals. DSP shall include status lights on front panel. DSP shall: a. Be 2RU High. b. I nclude 8x8 I/O with 8 ambient noise sensor connections and 8 channels of 50 Watts class D amplifiers. c. I nclude two independent pink/white noise generators that arerandom and non-repeating over 215 hours. d. D SP shall include parametric EQ, Graphic EQ, Volume, Tonecontrols, Network Volume Control, Telco compressor, Matrix, mixer, and ambient mic monitoring. e. Include telephone interface.f. U tilize Audio Video Bridge AVB Protocols that are IEEE802.1 standards.g. P rovide status indication of Processors running, Mute, Page Active,Masking Active, Mic Active, Amplifier channels, Emergency Audio Inputs, and System Power h. M anufacturer Atlas Sound DSP8807 with ALM-1 Ambient SensingMicrophones or approved equal.ApplicationsThe Atlas Sound DSP8807 digital processor “Privacy” system is a self contained, compact multi-zone digital DSP-GUI controlled processor and digital amplifier capable of simultaneous distribution of masking, paging, and background music signals for use in:• Hospitality• Government Facilities • Education Transportation • Corporate • Industrial • RestaurantsArchitect and Engineer SpecificationsThe Atlas Sound DSP8807 unit shall provide automatic mixing, set up and administration of all 8x8 inputs / outputs per zone (channel) via an intuitive ‘simple to use’ Graphic User Interface (GUI) managed via a local Windows ® based laptop or desktop computer. The DSP8807 shall include 8 channels of independent on-board digital class-D amplifiers that shall deliver 50 Watts RMS at 70.7V output. An audio line level output rated at 1V/600Ω (nominal) per zone shall drive higher power amplifiers. The DSP8807 shall have two (2) independent uncorrelated pink and white noise generators which are random and non-repeating up to 215 hours with EQ adjustments programmable on a per zone basis.The DSP8807 shall provide dynamic control and management based on IEEE802.1 AVB standards (Audio-Video Bridging) with independent 1⁄3 Octave (28) band EQ *(Filter type is Butterworth @ 19dB and Linkwitz-Riley at 24dB) and Parametric EQ for calibration of all PA, ambient level sensing and automatic volume control on a per zone basis. Paging (PA) presets shall be assigned in 10dB increments (10, 20, 30dB) per zone with automatic gain control (AGC) for all Telco and microphone paging inputs. The DSP8807 GUI called the ‘DSP Series Masking ControlSoftware’ shall control system setup. The software shall have the ability to expand up to (253) systems with over 2,000 zones (2,048) withprimary and secondary assignment in a zone paging dialing plan. It shall also provide the ability to set up All zone page, Group zone page (up to 32 groups) and single zone page with an architectural dialing plan (2-digit DTMF) set up in the GUI.Each DSP8807 shall be capable of managing remote ambient level sensing microphones (ALM-1) for each zone (x8) wired via a singleCAT5e cable up to 1,000 feet from the DSP8807 for automatic adjustment of the masking level based on real-time noise levels with set up and control via the GUI. Frequency response shall be 80Hz – 20kHz (±3dB) at rated output with .001% THD typical at 4dBu, 1kHz at 0dB gain and a Dynamic range of 102dB A-weighted. Mechanical dimensions shall be (L x W x H) 14" (358mm) x 19" (483mm) x 3.5" (89mm). All Power Components shall be UL Recognized, Boards Are UL94v0 and RoHS. DSP8807 shall be UL / CUL / FCC and CB (International) Listed.©2012 A t l a s S o u n d L .P . A l l r i g h t s r e s e r v e d . A t l a s S o u n d a n d S t r a t e g y S e r i e s a r e t r a d e m a r k s o f A t l a s S o u n d L .P . A l l o t h e r t r a d e m a r k s a r e t h e p r o p e r t y o f t h e i r r e s p e c t i v e o w n e r s . A T S 004406 R e v A 5/12D S P 8807B l o c k D i a g r a m。

DSP_Builder用户指南60完整版

DSP Builder 6.0 用户指南1.关于 DSP Builder1.1特性⏹DSP Builder支持以下特性：把MathWorks MATLAB(信号处理工具箱和滤波设计工具箱)和Simulink软件与Altera公司的Quartus II软件连接。

⏹支持以下ALTERA 器件系列：●Stratix®,Stratix GX,Stratix II和Stratix II GX器件●Cyclone和Cyclone II器件●APEX™II，APEX 20KC和APEX 20KE器件●Mercury™器件●ACEX®1K器件●FLEX 10K®和FLEX®6000器件⏹使用Altera DSP开发板快速建立样机。

⏹支持SignalTap®II逻辑分析仪，探测来自DSP上Altera器件嵌入式信号分析仪和把数据转入到MATLAB工作空间，以利用可视化分析。

⏹在AltLib库中支持的HDL转入模块：●VHDL或Verilog HDL设计授权转入●转入在Quartus工程文件中的HDL⏹回路中的硬件模块(HIL)能够使FPGA硬件在Simulink(AltLab library)中加速二次模拟。

⏹在SOPC Builder Link Library中的Avalon Blockset包括了你能用于建立一些定制逻辑的模块，这些定制逻辑和Nios II以及其它的SOPC Builder设计一起工作。

●低级Avalon和辅Avalon接口模块●Avalon Read FIFO和Avalon Write FIFO捆绑模块●全部Avalon模块是用户可以配置的●分离的模块可用来支持Avalon端口●将Avalon接口拖拉进DSP Builder设计模块中，你能建立任何的Avalon SOPC元件●根据Simulink中的仿真，你能验证Avalon接口，用生成的HDL和PTF文件把你的设计输出到SOPE Builder⏹包括状态机模块。

第2次DSP试验内容与步骤-图像平滑试验讲解

第4次DSP试验试验名称：图像平滑试验（有二种方法：邻域平均法与加权平均法，你们挑一种进行实验与写实验报告）试验目的：1. 掌握图像平滑的原理;2. 掌握DSP进行图像平滑的基本方法。

要求：（1）每个同学看懂邻域平均法与加权平均法的基本原理；（2）把程序DSP的编写出来；图像平滑1为什么要进行图像平滑实际获得的图像在形成、传输、接收和处理的过程中，不可避免地存在着外部干扰和内部干扰，如光电转换过程中敏感元件灵敏度的不均匀性、数字化过程的量化噪声、传输过程中的误差以及人为因素等，均会存在着一定程度的噪声干扰。

这样以来，噪声则恶化了图像质量，使图像模糊，特征淹没，给后续对图像的进一步分析带来困难。

因此，去除噪声，恢复原始图像是图像处理中的一个重要内容。

消除图像噪声的工作称之为图像平滑或滤波。

图像平滑的目的有两个，即改善图像质量和突出对象的特征。

2 邻域平均法图像平滑2.1 基本原理对一些图像进行线性滤波可以去除图像中某些类型的噪声，如基于邻域平均法的均值滤波器就非常适用于去除通过扫描得到的图像中的颗粒噪声。

领域平均法是空间域平滑噪声技术，其基本原理是：将原图中每一个像素的灰度值和它周围邻近像素的灰度值相加，然后将求得的平均值作为新图中该像素的灰度值。

在具体实施过程中，它采用模板计算的思想，模板操作实现了一种邻域运算，即某个像素点的结果不仅与本像素灰度有关，而且与其邻域点的像素值有关。

模板运算在数学中的描述就是卷积运算，这里不再赘述。

邻域平均法也可以用数学公式表达：假设待处理的图像为(),f x y ,处理后图像为(),g x y ，领域平均法图像平滑处理的数学表达可表示为：()()(),1,,m n S g x y f x m y n M ∈=--∑ （10-1）式中(),f x y 为N N ⨯的阵列, x , y =0,1,2,…，N -1，S 是以(),x y 点为中心的邻域的集合，M 为邻域S 中的像素点数。

基于DSP的机动车测速雷达双目标检测算法

Abstract：An FSK⁃based algorithm of speed measuring radar of motor vehicle is introduced. The C6713B series DSP is taken as the signal processing system. The speed of the target is measured according to Doppler principle，and its distance is mea⁃
Keywords：speed measuring radar；frequency shift keying；digital signal processing；dual⁃target detection；Doppler princi⁃ ple；phase difference
0引言
目前国内应用于道路交通卡口测速的微波雷达系统，其工作体制大部分为连续波（Continuous Wave，CW）体制，利用多普勒原理对机动车目标进行测速。 [1] 机动车测速雷达主要用于协助交通管理部门对交通进行实时监测，通过相机抓拍超速车辆，但由于受到机动车的大小、外形等因素影响，雷达根据机动车目标反射信号的强弱来判断车辆位置信息并不准确，导致相机无法捕获到超速车辆的全部信息 [2]，例如，车牌信息不完整，大大影响交管部门的管理工作。
行全程识别与跟踪，实现双目标检测。
关键词：测速雷达；FSK；DSP；双目标检测；多普勒原理；相位差
中图分类号：TN958.95⁃34
文献标识码：A
文章编号：1004⁃373X（2018）09⁃0127⁃04

基于DSP的柴油机瞬时转速智能监测节点设计

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基于DSP+FPGA的高速采样系统设计

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基于ＤＳＰ＋ＦＰＧＡ的高速采样系统设计
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制模块输出ｉ次控制信号。飞轮转子每圈耗时０．６ｍｓ，即
从采样开始到输出控制信号，系统的响应时间须小于
ｓｌａｖｅｄｅｓｉｇｎｍｏｄｅ，ａｍｕｌｔｉ—ｃｈａｎｎｅｌ，ｈｉｇｈ—ｓｐｅｅｄｓａｍｐｌｉｎｇｓｙｓｔｅｍｒｅａｌｉｚａｔｉｏｎｍｅｔｈｏｄｂａｓｅｄｏｎＤＳＰａｎｄＦＰＧＡｉｓｐｒｏｐｏｓｅｄ．Ｍｏｄｕｌｅｆｕｎｃｔｉｏｎ，ｈａｒｄｗａｒｅｌａｙｏｕｔａｎｄｓｏｆｔｗａｒｅｄｅｓｉｇｎｏｆｔｈｅｓｙｓｔｅｍａｓｗｅｌｌａｓｃｏｎｔｒｏｌｍｏｄｅｆｏｒｈｉｇｈ— ｓｐｅｅｄＡＤｃｈｉｐＴＨＳ１２０７ａｒｅｅｌａｂｏｒａｔｅｄ．Ｉｔｉｓｐｒｏｖｅｄｂｙｅｘｐｅｒｉｍｅｎｔｔｈａｔｔｈｅｄｅｓｉｇｅｄｓｙｓｔｅｍｃａｎａｃｈｉｅｖｅｒｅｑｕｉｒｅｍｅｎｔｓｏｆｍｕｌｔｉ—ｃｈａｎｎｅｌａｎｄｈｉｇｈ—ｓｐｅｅｄｓａｍｐｌｉｎｇ．
摘要：对飞轮转子位移信息的采样检测是保证飞轮储能系统（ＦＥＳＳ）高速、稳定运行的关键。利用数字信号处理器（ＤＳＰ）的计算能力和现场可编程门阵列（ＦＰＧＡ）的并行处理能力，采用主从设计方式，提出了一种基于ＤＳＰ和ＦＰＧＡ的多通道、高速采样系统的实现方法；阐述了系统的模块功能、硬件布局、软件设计以及对高速ＡＤ芯片ＴＨＳ１２０７的控制方式。实验证明了设计的系统能够实现多通道、高速采样的要求。关键词：数字信号处理器；现场可编程门阵列；ＴＨＳ１２０７芯片；高速采样中图分类号：ＴＰ３９３文献标识码：Ａ文章编号：１０００－９７８７（２０１８）０９－００４７－０３

Model 7265 DSP Lock-in Amplifier 信号恢复仪说明书

Dual Reference In this mode the instrument can make simultaneous measurements on two signals at different reference frequencies, which is ideal, for example, for use in source compensated optical experiments
Graphical Display
The model 7265 is extremely easy to use. All instrument controls are adjusted using soft-touch, front panel push-buttons, with the present settings and measured outputs being displayed on the centrally located, cold fluorescent backlit dot-matrix LCD. A particularly convenient feature is the pop-up keypad which is
External control of the unit is via either the RS232 or GPIB interfaces, using simple mnemonic-type ASCII commands. A second RS232 port allows up to sixteen 7265 or compatible instruments to be operated from a single RS232 computer port by connecting them in a “daisy-chain” configuration.

DSP C67x lab2

ቤተ መጻሕፍቲ ባይዱ
List of Figures
Fig1-1 C67x DSP Architecture .......................................................................................................4 Fig1-2 C6x internal buses .............................................................................................................5 Fig1-3 Processing Unit Structure...................................................................................................5 Fig 1-4 C6713 DSK Memory Map ..................................................................................................8 Fig1-5 C6000 Peripheral ...............................................................................................................9 Fig1-6 Pipeline Stages..................................................................................................................9 Fig1-7 Instruction Decode ..........................................................................................................10 Fig1-8 Simple Computing ..........................................................................................................10 Fig1-9 Compare Non-Pipelined and Pipelined .............................................................................11 Fig1-10 Interrupt Process ...........................................................................................................11 Fig1-11 Interrupt Selection .........................................................................................................12 Fig1-12 DSP/BIOS Thread Types..................................................................................................15 Fig1-13 SWI States.....................................................................................................................16 Fig1-14 Task States....................................................................................................................16 Fig1-15 DSP/BIOS API Modules ...................................................................................................17 Fig2-1 Add the include and library search path ............................................................................19 Fig 2-2 Modify the source code...................................................................................................19 Fig 2-3 FFT result .......................................................................................................................19 Fig 2-4 FFT result by MATLAB .....................................................................................................20 Fig 2-5 Second kind of signal ......................................................................................................20 Fig 2-6 Result in program and in MATLAB...................................................................................20 Fig 2-7 Set Hardware Interrupt ...................................................................................................21 Fig 2-8 Create a Software Interrupt.............................................................................................22 Fig 2-9 SetSoftware Interrupt .....................................................................................................22

TMS320C66x DSP CPU和指令集参考指南说明书

TMS320C66x DSPCPU and Instruction Set Reference GuideLiterature Number:SPRUGH7November 2010 Release HistoryRelease Date Chapter/Topic Description/CommentsNovember 2010All Initial release based on TMS320C674x CPU and Instruction Set Reference Guide(SPRUFE8)ø-ii TMS320C66x DSP CPU and Instruction Set Reference Guide SPRUGH7—November 2010Submit Documentation FeedbackContents SPRUGH7—November 2010TMS320C66x DSP CPU and Instruction Set Reference Guide ø-iii Submit Documentation Feedback ContentsRelease History. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ø-iiList of Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ø-xviiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ø-xx List of Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .ø-xxivPreface ø-xxvAbout This Manual. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .ø-xxvNotational Conventions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .ø-xxvRelated Documentation from Texas Instruments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ø-xxviTrademarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ø-xxvi Chapter 1Introduction1-11.1DSP Features and Options. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1-21.1.14x Multiply. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1-31.1.2Floating point support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1-31.1.3Vector Processing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1-31.1.4Complex arithmetic and matrix operations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1-41.2DSP Architecture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1-51.2.1Central Processing Unit (CPU) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1-61.2.2Internal Memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1-61.2.3Memory and Peripheral Options. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1-6Chapter 2CPU Data Paths and Control2-12.1Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-22.2General-Purpose Register Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-32.3Functional Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-52.4Register File Cross Paths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-62.5Memory, Load, and Store Paths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-62.6Data Address Paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-72.7Galois Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-72.7.1Special Timing Considerations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-92.8Control Register File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-102.8.1Register Addresses for Accessing the Control Registers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-112.8.2Pipeline/Timing of Control Register Accesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-112.8.3Addressing Mode Register (AMR). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-122.8.4Control Status Register (CSR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-152.8.5Galois Field Polynomial Generator Function Register (GFPGFR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-172.8.6Interrupt Clear Register (ICR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-182.8.7Interrupt Enable Register (IER). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-192.8.8Interrupt Flag Register (IFR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-202.8.9Interrupt Return Pointer Register (IRP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-202.8.10Interrupt Set Register (ISR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-212.8.11Interrupt Service Table Pointer Register (ISTP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-222.8.12Nonmaskable Interrupt (NMI) Return Pointer Register (NRP). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-232.8.13E1 Phase Program Counter (PCE1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-232.9Control Register File Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-242.9.1DSP Core Number Register (DNUM). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-242.9.2Exception Clear Register (ECR). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-242.9.3Exception Flag Register (EFR). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-25Contents ø-iv TMS320C66x DSP CPU and Instruction Set Reference Guide SPRUGH7—November 2010Submit Documentation Feedback2.9.4GMPY Polynomial—A Side Register (GPLYA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-252.9.5GMPY Polynomial—B Side Register (GPLYB) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-262.9.6Internal Exception Report Register (IERR). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-272.9.7SPLOOP Inner Loop Count Register (ILC). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-282.9.8Interrupt Task State Register (ITSR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-282.9.9NMI/Exception Task State Register (NTSR). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-292.9.10Restricted Entry Point Register (REP). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-292.9.11SPLOOP Reload Inner Loop Count Register (RILC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-302.9.12Saturation Status Register (SSR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-302.9.13Time Stamp Counter Registers (TSCL and TSCH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-312.9.13.1Initialization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-312.9.13.2Enabling Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-312.9.13.3Disabling Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-322.9.13.4Reading the Counter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-322.9.14Task State Register (TSR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-332.10Control Register File Extensions for Floating-Point Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-342.10.1Floating-Point Adder Configuration Register (FADCR). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-352.10.2Floating-Point Auxiliary Configuration Register (FAUCR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-372.10.3Floating-Point Multiplier Configuration Register (FMCR). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-40Chapter 3Instruction Set 3-13.1Instruction Operation and Execution Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-23.2Instruction Syntax and Opcode Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-43.2.132-Bit Opcode Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-53.2.216-Bit Opcode Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-53.3Overview of IEEE Standard Single- and Double-Precision Formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-63.3.1Single-Precision Formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-73.3.2Double-Precision Formats. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-83.4Delay Slots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-93.5Parallel Operations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-113.5.1Example Parallel Code. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-133.5.2Branching Into the Middle of an Execute Packet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-133.6Conditional Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-143.7SPMASKed Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-153.8Resource Constraints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-153.8.1Constraints on Instructions Using the Same Functional Unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-153.8.2Constraints on the Same Functional Unit Writing in the Same Instruction Cycle . . . . . . . . . . . . . . . . . . . . . .3-153.8.3Constraints on Cross Paths (1X and 2X) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-163.8.3.1Maximum Number of Accesses to a Register on the Opposite Register File . . . . . . . . . . . . . . . . . . . .3-163.8.4Cross Path Sharing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-163.8.5Cross Path Stalls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-173.8.6Constraints on Loads and Stores. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-173.8.7Constraints on Long (40-Bit) Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-183.8.8Constraints on Register Reads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-183.8.9Constraints on Register Writes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-183.8.10Constraints on AMR Writes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-193.8.11Constraints on Multicycle NOPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-193.8.12Constraints on Unitless Instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-193.8.12.1MFENCE Restrictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-193.8.12.2SPLOOP Restrictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-203.8.12.3BNOP <disp>,n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-203.8.12.4DINT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-203.8.12.5IDLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-213.8.12.6NOP n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-213.8.12.7RINT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-213.8.12.8SPKERNEL(R). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-22ContentsSPRUGH7—November 2010TMS320C66x DSP CPU and Instruction Set Reference Guide ø-v Submit Documentation Feedback 3.8.12.9SPLOOP(D/W). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-223.8.12.10SPMASK(R). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-223.8.12.11SWE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-223.8.12.12SWENR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-233.8.13Constraints on Floating-Point Instructions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-233.9Addressing Modes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-243.9.1Linear Addressing Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-253.9.1.1 LD and ST Instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-253.9.1.2 ADDA and SUBA Instructions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-253.9.2Circular Addressing Mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-253.9.2.1 LD and ST Instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-253.9.2.2ADDA and SUBA Instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-263.9.2.3Circular Addressing Considerations with Nonaligned Memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-263.9.3Syntax for Load/Store Address Generation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-273.10Compact Instructions on the CPU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-293.10.1Compact Instruction Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-293.10.2Header Word Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-303.10.2.1 Layout Field in Compact Header Word. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-303.10.2.2 Expansion Field in Compact Header Word . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-313.10.2.3P-bit Field in Compact Header Word . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-323.10.3Processing of Fetch Packets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-333.10.4Execute Packet Restrictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-333.10.5Available Compact Instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-343.11Instruction Compatibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-35Chapter 4Instruction Descriptions 4-14.1Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-24.2ABS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-44.3ABS2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-74.4ABSDP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-94.5ABSSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-114.6ADD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-134.7ADDAB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-184.8ADDAD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-214.9ADDAH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-234.10ADDAW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-274.11ADDDP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-304.12ADDK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-324.13ADDKPC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-334.14ADDSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-354.15ADDSUB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-374.16ADDSUB2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-394.17ADDU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-414.18ADD2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-434.19ADD4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-464.20AND. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-494.21ANDN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-514.22AVG2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-544.23AVGU4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-564.24B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-584.25B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-604.26B IRP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-624.27B NRP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-644.28BDEC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-66Contents ø-vi TMS320C66x DSP CPU and Instruction Set Reference GuideSPRUGH7—November 2010Submit Documentation Feedback 4.29BITC4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-684.30BITR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-704.31BNOP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-724.32BNOP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-754.33BPOS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-784.34CALLP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-804.35CCMATMPY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-824.36CCMATMPYR1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-854.37CCMPY32R1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-874.38CLR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-904.39CMATMPY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-934.40CMATMPYR1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-954.41CMPEQ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-974.42CMPEQ2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1004.43CMPEQ4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1034.44CMPEQDP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1064.45CMPEQSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1084.46CMPGT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1104.47CMPGT2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1134.48CMPGTDP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1164.49CMPGTSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1184.50CMPGTU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1204.51CMPGTU4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1234.52CMPLT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1264.53CMPLT2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1294.54CMPLTDP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1314.55CMPLTSP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1334.56CMPLTU. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1354.57CMPLTU4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1384.58CMPY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1414.59CMPY32R1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1434.60CMPYR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1464.61CMPYR1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1494.62CMPYSP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1524.63CROT270 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1554.64CROT90 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1564.65DADD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1574.66DADD2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1594.67DADDSP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1614.68DAPYS2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1634.69DAVG2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1654.70DAVGNR2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1674.71DAVGNRU4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1694.72DAVGU4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1714.73DCCMPY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1734.74DCCMPYR1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1744.75DCMPEQ2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1774.76DCMPEQ4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1794.77DCMPGT2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1814.78DCMPGTU4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1834.79DCMPY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1854.80DCMPYR1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1864.81DCROT270 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1884.82DCROT90. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-189。

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Equiv. Equiv ImplementationApplying the downsampling equivalence. equivalencex[k] [ ]2w0w2w4+2+ +y[k]w1w3w5++ This is called a polyphase Filter Critical path improved!21Upsampling22Upsampling NotationxT [n ]n0 1 2 3 4 5 6 7 8 9 10 Sampling period = T/2↑ xT ' [n ]n012345Sampling period = TL ≥ 1 is an integerxT [n ]Sampling period TL⎧ x (kT ), n = kL ↑ xL [ n ] = ⎨ c n ≠ kL ⎩0,Sampling period T’ = T/L⎧ ⎛ T⎞ xc (kT ) = xc ⎜ n ⎟ , n = kL ⎪ ↑ xL [ n ] = ⎨ ⎝ L⎠ ⎪0, n ≠ kL ⎩T T'= L23Upsampling NotationExample: L = 2 a peT = original sampling period T’ = decreased sampling periodT'= T LxT [n ]9T’↑ xT ' [n ]T = LT ' n = 0, ± 1, ± 2, LT T’ 3T’2T 5T’3T 7T’4T“0” sample insertedxT [n ] = xc (nT )↑ xL [ n ]⎧ xT [k ] = xc (kT ), =⎨ ⎩0,n = kL n ≠ kLk = 0, ± 1, ± 2, LNew notationNote that↑ xL [n ] ≠ xT ' [n ]24Two Upsampling SchemesxT [n ]Sampling period TL↑ xL [ n ]Sampling period T’ = T/L T), ⎧ xc ( kT ) n = kL =⎨ n ≠ kL ⎩0,↑ xL [n ]zero insertionn0 1 2 3 4 5 6 7 8 9 10 Sampling period = T/2xT [n ]Sampling period = TWhat’s the difference ??0 1 2 3 4 5nxT ' [n ]direct upsamplingxT [n ]Sampling period T i dLSampling period T’ = T/L T⎛ T⎞ xT ' [n ] = xc ⎜ n ⎟ ⎝ L⎠0 1 2 3 4 5 6 7 8 9 10 Sampling period = T/2n25Upsampling IdentityxT [n ]L⎧ x [k ], =⎨ T ⎩0,∞x [n ]n = kL n ≠ kL↑ xL [n ] e − j Ω ' n ∞↑ L↑ xL [ n ]Example: L = 2 p↑ xL [ n ]T T’ 3T’2T 5T’↑ xL [ n ]3T 7T’4T 9T’T'=T L↑ XL(e ) = ∑jΩ 'n =−∞ = ∞⎛ ∞ ⎞ − jΩ 'n = ∑ ⎜ ∑ xT [ k ]δ [ n − kL ] ⎟e ⎠ n= ∞ ⎝ k = ∞ =−∞ =−∞=k =−∞ ∞∑∞xT [ k ] e − j Ω ' Lk = X T e j Ω ' L()Ω ' = T 'ω =Tω Ω = L L↑ X L ( e j Ω ' ) = XT ( e j Ω ' L ) = X T ( e j Ω )The Upsampling Identity26Upsampling SpectrumX ( jω ) =c∫∞x (t )e dtc −∞− j ωtωB =πT=ωs21X c ( jω )T = sampling period−ωBωB1 TXT (e j Ω )ωXT ( ejΩ1 +∞ 2π ⎛ ⎛Ω = ∑ Xc ⎜ j ⎜ − k ) T T ⎝ ⎝T k =−∞⎞⎞ ⎟⎟ ⎠⎠−2π−ππ2πΩ = ωT↑ X L ( e j Ω ' ) = XT ( e j Ω )L=2Ω scaled down by L y↑ X L (e j Ω ' )1 TT T'= LΩ Ω' = L−2π−π − ππ2π22πΩ ' = ωT '27Frequency Scaling (with aliasing)XT ( ejΩ1 +∞ ) = T ∑ X c ⎛ j ⎛ Ω − k 2π ⎞ ⎞ ⎟ ⎜ ⎜T T ⎠⎟ ⎝ ⎝ ⎠ k =−∞sampling by T li bsampling by T’1 +∞ = ∑ X c ( j (ω − kωT ) ) T k =−∞ωT =2π T1 TωT ' =XT (e j Ω )2π = LωT T'Ω = LΩ '↑ X L e j Ω ' = XT e j Ω +∞()()−2π−π0π↑ X L (e j Ω ' )2πΩ = Tωscale down by LL=31 T1 k ⎛ ⎛ ⎞⎞ = ∑ X c ⎜ j ⎜ ω − ωT ' ⎟ ⎟ T k =−∞ ⎝ ⎝ L ⎠⎠−2π−π−π 2π − 3 30 π 2π π3 32πΩ ' = T 'ωT = T 'LΩ ' = T 'ω28Imaging with Z.I. Upsampling ZIZero Insertion (Z.I.) upsampling causes imaging spectrum. ( ) p p g g g p1 TXT (e j Ω )Original spectrumπ2π−2π−π0Ω = Tω↑ X L (e j Ω ' )L=31 TUpsampling with zero insertion0 π 2π π3 3−2π−π−π 2π − 3 32πΩ ' = T 'ωimaging spectra↑ X L (e j Ω ' )L=31 TDirect Upsampling (without zero insertion)0 π 2π π3 3−2π−π−π 2π − 3 32πΩ ' = T 'ω29Comparison: Compa ison Upsampling1 TXT (e j Ω )imagingT LDownsampling aliasing vs upsampling imaging−ππ0ΩBT'= 2πZI upsampling−2π−Ω BωT2ωTΩ = TωOriginal spectrum width squeezed.L=2−π−2π− L1 TΩB 0↑ X L (e j Ω ' ) = XT (e j Ω L )ωT ' =2π = LωT T'πΩBL(hence not causing aliasing)ωT '22πΩ ' = T 'ωrelative to higher ω If keep the freq axis, upsampling does not change the spectrum.ωT 'change axis h i−π1 TXT (e j Ω )π0ΩB−2π−Ω B2πωT2Ω = Tω30ωTCompasion: D C i Downsampling li1 TXT ( e j Ω )aliasing li iReference spectrumOriginal spectrum width not changed. (hence causing aliasing)31downsa ampling axis c change−2π−π1 MTΩBπ2πΩ = ωTX MT (e j Ω ' )M=2Downsampled spectrumT ' = MT−2π−π1 Tπ M ΩBXT ( e j Ω )2πΩ ' = MΩΩ ' = ωT ' = M Ω Ω = ωTπ2π−2π−πΩBΩ = ωTωs2ωsaliasing to passbandRelative to the higher sampling freqImportant Memo !Upsampling (with zero insertion) cannot remove aliasing. To have upsampled sequence without aliasing, T h l d ith t li i the reference sequence (sampled with period T) must not have aliasing aliasing. But “direct upsampling” (without zero insertion) direct upsampling can avoid aliasing (when sampling freq > Nyquist freq) yq q)32Direct UpsamplingT'= T LTω Ω Ω ' = T 'ω = = L L⎞⎞ ⎟⎟ ⎠⎠ωT =2π TωT ' =2π = LωT T'XT ( ejΩ1 +∞ 2π ⎛ ⎛Ω = ∑ Xc ⎜ j ⎜ − k ) T T ⎝ ⎝T k =−∞ΩB = T ωB ≤ π1 TXT (e j Ω )1 +∞ = ∑ X c ( j (ω − kωT ) ) T k =−∞XT ' ( ejΩ ' +∞ 1 + ⎛ ⎛ ⎞⎞ ) = T ' ∑ X c ⎜ j ⎜ Ω '' − k 2π' ⎟ ⎟ T ⎠⎠ ⎝ ⎝T k =−∞−ππ0ΩB−2π−Ω B2πΩ = TωL +∞ = ∑ X c ( j (ω − kωT ' ) ) T k =−∞ L = ∑ X c ( j (ω − kLωT ) ) T k =−∞+∞L TXT ' (e j Ω ' )−π−2π−Ω B ' 0πΩB '2π≤Ω ' = T 'ωΩB ' = T ' ωB =ΩBLπL33Spectrum Transform (no aliasing) S t T f ( li i )−π1 TXT (e j Ω )π0ΩBΩ'=2πΩL−2π−Ω BΩ = TωXT ' ( ejΩ 'L +∞ ) = T ∑ X c ( j (ω − kLωT ) ) k =−∞ ∞−π1 Tshift in period L2πXT ' (e j Ω / L )L=2still in Ω4ππ0ΩB−4π−2π−Ω B2πΩ = TωΩ scaled down by LL TXT ' (e j Ω ' )now in Ω’2π−ππ−Ω B ' 0−2πΩB 'Ω ' = T 'ω34Spectrum Transform (with aliasing) S t T f ( ith li i )aliasing−π−2π −Ω B1 TXT (e j Ω )π0ΩBΩ'=2πΩLΩ = TωXT ' ( ejΩ 'L +∞ ) = T ∑ X c ( j (ω − kLωT ) ) k =−∞−π1 Tshift in period L2πXT ' (e j Ω / L )L=2still in Ω4ππ0ΩB−4π−2π −Ω B2πΩ = TωΩ scaled down by Lno aliasing!−π−Ω B 'L TXT ' (e j Ω ' )now in Ω’2ππ0ΩB '−2πΩ ' = T 'ω35Upsampling vs Di U li Direct Upsampling tU liXT ( e j Ω ) = 1 ∑ X c ( j (ω − kωT ) ) T k =−∞ reference spectrumjΩ ' +∞−π−2π−Ω B1 TXT (e j Ω )Ω = LΩ '2ππ0ΩBΩ = TωXT ' ( eL +∞ ) = T ∑ X c ( j (ω − kωT ' ) ) k =−∞T ' ωT ' = 2πL=2L TXT ' (e j Ω ' )directdirect upsampling↑ XL e jΩ ' =()ω ⎞⎞ 1 ⎛ ⎛ Xc ⎜ j ⎜ ω − k T ' ⎟ ⎟ ∑ T k =−∞ ⎝ ⎝ L ⎠⎠+∞−2π−π −Ω B ' 0ΩB ' π2πΩ ' = T 'ωL=2with zero insertion1) 2) Magnitudes differ by “L”; Periods differ by “L”.−2π1 T↑ X L (e j Ω ' )zero insertion−π −Ω B ' 0 Ω B 'π2πΩ ' = T 'ω36Upsampling in axis of ωXc ( jω )continuous1“Z.I.” upsampled by T’ = T/LXT ( jω )ω1 Tsampled by TXT ( jω )1 T−ωT '−ωT0ωTωT 'ω Ω ' = 2π−ωTωTωΩ = 2πωT =2π Tstill in period of ωTdirect upsampled by T’ = T/L1 L = T' TXT ( jω )XL=2↑ L(e )jΩ '1 +∞ = ∑ X c ( j (ω − kωT ) ) T k =−∞Ω ' = ωT '−ωT '−ωTωTωT 'ωωT ' =2π = LωT T'37in period of ωT’Low-Pass Low Pass FilteringXT ' ( ejΩ ') H (e ) = X (e ) H (e ) ⋅ LjΩ ' ↑ L jΩ ' jΩ 'H (e j Ω )1H (e j Ω ' )1Ω−ππL TXT ' (e j Ω ' )−πLπLΩ'XT ' ( e j Ω ' ) =L ∑ X c ( j (ω − kωT ' ) ) T k =−∞ direct+∞L=2directH (e j Ω ' )ΩB ' πX↑ L(e )jΩ '1 +∞ = ∑ X c ( j (ω − kLωT ' ) ) T k =−∞−2π−π −ΩB ' 02πΩ ' = T 'ωL=2with zero insertionΩB ' = T ' ωB = ΩBL ≤1 T↑ X L (e j Ω ' )zero insertionH (e j Ω ' )πL−2π−π −ΩB ' 0 ΩB 'π2πΩ ' = T 'ω38T ' ωT ' = 2πSummary on UpsamplingFundamental Sampling IdentityXT e j Ω()1 +∞ 2π ⎞ ⎛ Ω = ∑ Xc ⎜ j − k ⎟ T k =−∞ T ⎠ ⎝ TωT =2π TΩ = ωTΩ ' = ωT 'T T'= LΩ' =Ω LUpsampling Identity↑ X L ( e j Ω ' ) = XT ( e j Ω ' L )Direct UpsamplingSpectrum = XT ' ( e j Ω ' )↑ XT ' ( e j Ω ' ) H ( e j Ω ' ) = X L ( e j Ω ' ) H ( e j Ω ' ) ⋅ LRelationship39Time-Frequency Time Frequency PerspectivejΩ x (t ) ↔ X ( jω ) ↔ XT (e jΩ )Time domain Time-domain stretching squeezingFreq domain Freq-domaintωstretchsqueezetω40Interpretation of Sampling Ratex (t )TSampling the original signal by T. tx (t / 2)stretchStretch the signal by 2 in time; but still sample signal by T.txT / 2 [n ]squeezeOversampling by 2Squeeze th signal back S the i lb k by 2 in time. n41Time-scaling of di Ti li f discrete sequence txT [n ] TSampling the original signal by T. nS { x (t / 2);2T } 2TstretchStretch the sequence by 2 in index; fill in with zeros. n↑ x L [n ]squeezeUpsampling by 2Squeeze the sequence back by 2 in index. nS { x (t );T }sample function x(t) with period T42Time-Scaling Time Scaling PerspectiveUnderstand upsampling from time-scaling point of view ...xc ( t ) ↔ X c ( j ω )Time-scaled (stretched) signal( xcL ) (t )X c ( jω )1⎛t ⎞ = xc ⎜ ⎟ ⎝L⎠Time-domain scaling−ωBωBωdoes not change areaMagnitude scaled up by LX(L ) c⎛t ⎞ ( jω ) = xc ⎜ ⎟e − jωt dt −∞ ⎝L⎠∫ =L ∫∞L( X cL ) ( j ω )∞= L X c ( jLω )Frequency-domain scaling−∞xc (τ )e − jLωτ dτ−ωBLωBLωBandwidth scaled down by L 43Direct U Di t Upsampling b time-scaling li by ti lixT ' [n ]Direct Di t upsampling li−LωBL( X cL ) ( j ω )ωBLtime-scaled spectrumωn0 1 2 3 4 5 6 7 8 9 10 Direct upsampling is equiv to sampling (in T) the time-stretched signal:( xcL ) (t )−πTπT⎛t ⎞ = xc ⎜ ⎟ ⎝L⎠⎛ nT ( xcL ) (nT ) = xc ⎜ ⎝ LL T⎞ ⎟ = xc (nT ') = xT ' [n ] ⎠( XTL ) (e j Ω )T T'= L−2 π−π Ω B − LΩB πL2πΩ = ωT44Upsampling by time scaling time-scalingxT ' [n ]TUpsampling U li−LωBL( X cL ) ( j ω )ωBLtime-scaled spectrumωn0 1 2 3 4 5 6 7 8 9 10 Upsampling is equiv to sampling (in LT) the time-scaled (stretched) signal:−πTπT⎛t ⎞ ( xcL ) (t ) = xc ⎜ ⎟ ⎝L⎠⎛ nLT ( xcL ) (nLT ) = xc ⎜ ⎝ L1 T( XTL ) (e j Ω )⎞ ⎟ = xc (nT ) = xT [n ] ⎠Ω' =Ω LT T'= LL 1 = LT T−2 πSqueeze by L to get axis for Ω’45−π Ω B − LΩB πL2πΩ = ωLTUpsampling ComparisonUpsampling ( ith zero i U li (with insertion) ti ) Directly down scaling the frequency by L. Cannot remove “aliasing”! aliasing ! Direct Upsampling (without zero insertion) Place the spectrum in period of L*2π Then scale down the frequency by L times Or equivalently Then scale down the original spectrum by g p y L times Place the spectrum in period of 2π Can remove “aliasing”!46Upsampling Equivalence↑ xL [n ]zero insertion−LπLH (e j Ω )πLΩ = ωT 'n0 1 2 3 4 5 6 7 8 9 10xT [n ]L↑ xL [ n ]LPF Gain = L Cutoff = π/LH(ejΩ)scale up lxc (t )reconstructedxT ' [n ]xT ' [n ]T T'= LDirect upsamplingLPF H’(ejΩ) H( Gain = 1 Cutoff = π/L 1n−xc (t )H '(e j Ω )πLπL0 1 2 3 4 5 6 7 8 9 10Ω = ωT '47Upsampling + LPFxT [n ]L↑ xL [ n ]LPF H(ejΩ) ( Gain = L Cutoff = π/Lxc (t )LH (e j Ω )L=3[ ] xu[0] xu[3] x[6] xu[9] xu[12] [12] xu15]−πLπLxu[0]Ω = ωT 'xu[3] x[6] xu15]xu[9]xu[12]tT1 T2tZero samples interpolated by low-pass filteringUpsampling by LT2 =T1 L48Equivalent Upsampler PlacementY (z) = V (z L )Use the Upsampling Identity:X(z)H(z)V(z)LY(z)Y (e j Ω ) = V (e j Ω L )U.S.Y (e j Ω ) = V (e j Ω L )X(z)LU(z)H(zL)Y(z)= H (e j Ω L ) X (e j Ω L ) = H (e j Ω L )U (e j Ω )U.S.U (z) = X (z L )ORY (z) = H (z L ) X (z L )49Upsampling in z Domain z-Domainxu[n]Y (z ) =n0 1 2 3 4 5 6 7 8 9 10 Sampling period = T/2∑ y [ k ]zk =0∞−kxu[2k] = x[k] xu[2k+1] = 0 Upsampling by LFor L = 2XT2 ( z ) = ∑ xT [k ]z − kk =02∞= ∑ xT [k ]z −2 k = XT1 (z 2 )k =01∞T2 =T1 LX T2 ( z ) = X T1 ( z L )50。