Enhance Your Signal Processing Toolbox with Complex Notation
|
|
- Darren Logan
- 5 years ago
- Views:
Transcription
1 Enhane Your Signal Proessing Toolbox with Complex Notation Barry L. Dorr, P.E. Dorr Engineering, In. At first glane this notation seems lie an unneessary ompliation rather than an aid, and has aused many a good engineer to wal away from valuable signal proessing information. As the speed of DSP's and digital hardwa eeps inasing, softwa and digital hardwa a plaing traditional analog hardwa, maing today's gizmos and gadgets smarter, mo liable, less expensive, and mo power effiient than ever befo. As an embedded systems engineer, you may have found yourself doing mo signal proessing than you originally bargained for! This artile about omplex notation is a survival guide to some of the most portant basis of signal proessing. Begin ading nearly any artile on signal proessing and you will quily enounter omplex notation. Signals that ould be easily psented as sine s or osines beome Re(e j( ωt-φ and we often minded that j is the squa root of -1. It gets worse a sple sinusoid atually ontains both positive and negative fquenies, but fquently only positive fquenies a used. We also see modulated signals ferd to as "omplex envelopes." At first glane this notation seems lie an unneessary ompliation rather than an aid, and has aused many a good engineer to wal away from valuable signal proessing information. Most signal proessing textboos provide an exellent view of omplex notation, but these desriptions a sometes mo general and involved than the woring engineer wants. This artile psents the basis of omplex numbers as used in signal proessing, and will provide you with the tools for using them. Through the examples used in this artile you will gain a lear understanding of AC iruit analysis using phasors, and also get introdued to some of the ey omponents of a QPSK eiver. THE BASICS OF COMPLE NUMBERS Figu 1 shows a omplex number. The al part of the number, Re(C, is psented by the horizontal omponent and the aginary part of the number, Im(C, is psented by the vertial omponent. The omplex number appears mediately useful beause, lie a sine wave, it has both a magnitude and an angle. If we hange the sign of the aginary part we obtain the omplex onjugate of the number, and we designate the omplex onjugate with the overbar symbol.
2 C a +b C b Φ a Figu 1- Complex number The omplex number an be psented various ways: C a + j b Equation 1 [ os( φ + sin( φ ] C C j whe : C a + b and φ tan 1 b a Equation The Euler identity shown below forms the basis of omplex notation. C jφ C e Equation 3 Note that the tangular forms of equations 1 and allow onvenient addition and subtration of omplex numbers. The polar form of equation 3 allows onvenient multipliation and division. If Φ is a phase angle whih inases linearly with te then the omplex number in Figu 1 rotates in a ounter-lowise irle. Letting the magnitude of the omplex number be unity, equation beomes C os( ωt + j sin( ωt Equation 4 and it s evident that the al part of this expssion is a sple osine wave. Furthermo, equations 1 through 4 an be easily manipulated to yield other useful forms Page of 11
3 e j ω t os( ωt + j sin( ωt Equation 5 e os( ωt j sin( ωt Equation 6 e os( ωt e sin( ωt e j + e Equation 7 Equation 8 Several things a adily appant from equations 5 through 8. First they a lated - equation 7 is the sult of adding equations 5 and 6, and equation 8 is the sult of subtrating equation 6 from equation 5. Equations 5 and 6 an also be viewed as two ounter-rotating vetors in whih the omplex parts always anel theby aounting for the al sult. Equation 6 an be viewed as two ounter-rotating vetors whe the al parts anel. Equations 1 through 8 an also be used to derive useful identities suh as: x + x Re( x Equation 9 x y x y Equation 10 But the most signifiant observation is that if we wish to tae advantage of omplex exponentials, we must either use the abstration of omplex numbers (equations 5 and 6 or the abstration of negative fquenies (equations 7 and 8. LINEAR FILTERING AND PHASORS The problem of determining the steady state sponse of a linear networ to a sinusoidal input is an exellent appliation of omplex notation. However, woring the problem one will show that steady-state analysis an be done virtually by inspetion using the phasor tehnique. This setion will infore what we ve oved so far by showing why the phasor tehnique wors. Digital and analog filters an be desribed by omplex fqueny domain transfer funtions. For example the lowpass RC filter shown in Figu has the transfer funtion: V H ( ω V Out in ( ω 1 ( ω ( 1+ jωrc Equation 11 This transfer funtion an be evaluated at diffent fquenies. At DC (ω0 the sult is 1 + j0. At ω1/rc the sult is j0.707, at ω the sult is 0. Page 3 of 11
4 Figu - RC filter A property of this filter is that its transfer funtion has onjugate odd symmetry. This means that H ω H ω Equations 7 and 8 show that the sinusoidal exitation also has odd symmetry. ( ( We will use the superposition property of linear networs to determine the output of the filter. Stated mathematially: f ( a + b f ( a + f ( b Equation 1 In other words, the output due to the sum of two input signals is equal to the sum of the outputs due to the individual inputs. A qui glane at equations 5 through 8 suggests that this property should ome in handy. The input to the networ is the osine from equation 7. Using superposition, the output signal is sply the sum of the outputs due to the two omponents in equation 7. e e Equation 13 Vo ( ω, t H ( ω + H ( ω Applying the identity in equation 10 yields: e e V ( ω, t H ( ω + H ( ω o Equation 14 Then apply the identity from equation 9: { e H ( } V ( ω, t Re ω Equation 15 o o jφ { ( ( ω e H ω e } V ( ω, t Re Equation 16 j { ( ωt + φ ( ( ω H ω e } V ( ω, t Re Equation 17 o V o ( ω, t H( ω os( ωt + φ( ω Equation 18 Page 4 of 11
5 Beause of the onjugate symmetry of both the input signal and the transfer funtion, the operations in equations 13 through 18 a idential for any networ. As a sult, to find the sponse of a networ due to a sine wave, you sply need to now the magnitude and phase sponse of the networ at the desid fqueny. In iruit analysis omplex numbers a psented using shorthand alled phasor notation as shown below. C C e C φ j ( ωt + φ Equation 19 Setting the angular fqueny to 1/RC, the steady state problem above is solved quily using phasors as follows: Equation 0 V o ( t os( ω t 45 Equation 1 NARROWBAND SIGNALS AND COMPLE NOTATION In signal proessing we fquently wor with narrowband signals as shown in Figu 3. A narrowband signal has its energy onentrated around a fqueny usually near the enter of the signal's bandwidth alled the arrier. Channelized signals an usually be tated as narrowband signals. Complex notation allows us to fous only on the bandwidth ontaining the signal rather than the bandwidth ontaining both the signal and the arrier. It also suggests hardwa and softwa strutus that aid proessing of lowpass signals. Figu 3 - Narrowband signal To illustrate, onsider the signal proessing used for QPSK data transmission shown in Figu 4. Page 5 of 11
6 si Lowpass Filter si os(ωt + m(t Bandpass Filter os(ωt G Complex Equalizer sq -sin(ωt -sin(ωt Lowpass Filter G e -j(ωtφ From arrier overy From adaptive equalizer sq Loal Osillator (T Loal Osillator (R Figu 4 - QPSK transmission system QPSK, or Quadratu Phase Shift Keying is a data transmission tehnique whe groups of two bits of data a enoded into one of four phase shifts of a sinusoidal arrier. The phase shift is held for the symbol te, and then it is updated based on the next pair of bits in the input bit stam. Sine the symbol rate is usually muh lower than the arrier fqueny, the sult is a narrowband signal. It is natural to use omplex notation to psent the two bits omprising eah symbol. The index is used to indiate that the signal psents a pair of bits in a serial bit stam. Signals s i and s q a the th in phase and quadratu signal omponents that tae values of ±1, and s denotes the omplex signal s i + j s q. The omplex baseband signal ould also be psented as e j φ whe φ is 45, 135, 5, or 315 deges. Mapping these signals on the omplex plane sults in the onstellation shown in Figu 5. q i-1 q1 i1 q1 i i-1 q-1 i1 q-1 Figu 5 - QPSK onstellation The two multipliers at the left of Figu 4 up-onvert the omplex baseband signal to the arrier fqueny. This is shown graphially in Figu 6 whe multipliation by e j ω t shifts the omplex baseband spetrum to the right, and taing the al part adds the negative fqueny omponent. Page 6 of 11
7 Step 1 - Multiplying the omplex baseband signal by e shifts the omplex baseband spetrum to the arrier fqueny ω -ω DC Step - Retaining only the al part adds the negative fqueny omponent. The sult is a al signal. ω Figu 6 - Up-onverter operations Equations to 5 desribe the operation of the up-onverter. The output is the al modulated signal m(t 1. m t Re jω {( s + j s e t } ( Equation i q {( s + j s ( os( ω t + j sin( ω } m( t Re t Equation 3 i q { s os( ω t s sin( ω t + j ( s os( ω t + s sin( ω } m( t Re t i q Eq. 4 m( t s os( ω t s sin( ω t Equation 5 i q q i At the eiver the signal enounters a bandpass filter used for jeting out-of-band signals. The bandpass filter sponse is not symmetri about the arrier fqueny and it distorts the signal slightly. The two multipliers and lowpass filters after the bandpass filter a used to down onvert the signal to its lowpass psentation. We'll elaborate on the down onverter sine it is a ommonly enounted signal proessing operation. One way to explain the operation of the down onverter is to begin with the signal as desribed by equation 5, multiply the sines and osines and note that the lowpass filter moves the double fqueny terms sulting from the multipliations. But instead of using sines and osines, we'll use our newfound sills with omplex notation. For the top arm we have: jω { s e t } os( ω t + φ Re Equation 6 The identities in equations 9 and 10 and the Euler identities allow us to write this as: 1 This expssion for m(t is valid for the th symbol only. Refer to the fenes for an aurate desription of a modulated data signal. Page 7 of 11
8 s e jω t + s e jω t ( j ( ωt+ φ j ω + φ e t + e Equation 8 1 s e ( ω φ ( ω φ ( ω + ω + φ ( ω + ω + φ + 1 t t j t j t j j t t s e s e + s e + Equation 9 Whe: ω ω ω Re 1 1 Equation 30 { } j ( ω t φ j (( ω + ω t + φ { s e } + Re s e The lowpass filter moves the double fqueny term on the right. Multiplying by yields the final sult: Re j ( ω φ { t s e } Equation 31 Silarly the sult for the bottom arm is: j ( ω φ { t } Im s e Equation 3 The I and Q branhes at the output of the down-onverter a lowpass signals and an be sampled at a muh lower rate than the modulated signal, whih dues both power onsumption and hardwa ost. Figu 4 shows the I and Q branhes ombined into a single heavy line indiating that the signal is omplex. A lear advantage of omplex notation is that the fqueny and phase diffenes between the transmit and eive osillators a maintained by equations 31 and 3. The next step for the QPSK eiver to over the transmitted data bits s i and s q is to ort for the fqueny offset ( ω and phase offset ( φ between transmitter and eiver. The proess of moving these offsets is alled arrier overy, and the eiver has the means to detet them and internally generate the signal e j( ωt-φ The proess of applying the ortion is often ferd to as de-rotation beause the fqueny offset auses the baseband phasor to rotate at the diffene fqueny. However this is sply omplex multipliation as shown by equation 33 and plemented in Figu 7. Though the strutu appears formidable, it an be done in just a few lines of DSP ode. ( x x ( y + y x y x y + j( x y + x y + Equation 33 Page 8 of 11
9 - + xy y + xy y Figu 7 - Complex multiplier The final step for overing the transmitted data bits is to move the distorting effets of the bandpass filter at the eiver input. The modem has the means for identifying the distortion based on statistial harateristis of the distorted input or orted output. This proess is alled adaptive equalization, and the sult of the equalization proess is the omplex filter shown in Figu 4 at the right of the de-rotator. Befo desribing the omplex filter, observe the signal spetrum shown in Figu 8. The operation of the down onverter an be viewed as shifting the positive portion of the spetrum left by ωˆ and disarding the negative fqueny term. The de-rotator further shifts the signal so that the overall shift pisely mathes the fqueny (and phase of the up-onverter. However the shifted signal is not symmetrial about DC. The i and q signals from the de-rotator a al signals. But when viewed as i + j*q, the sult is omplex and the asymmetrial spetrum is perfetly aeptable. The negative fqueny omponent is disarded. The positive fqueny omponent is shifted left by ω -ω DC ω Figu 8 - Bandpass and lowpass spetrums The oversplifiation is for the sae of larity. In this example, the output from the arrier overy would have a slight phase error beause its input has been distorted by the bandpass filter. Modern demodulators fquently perform arrier overy and equalization jointly. Page 9 of 11
10 Equalization of the asymmetrial signal spetrum quis an asymmetrial filter for the equalizer. To see how this wors note that when a signal is passed through a linear filter, the sulting signal spetrum is equal to the spetrum of the input signal multiplied by the fqueny sponse of the filter. If both the spetrum and the filter a omplex we have: ( S ( f + j S ( f ( H ( f + j H ( S( f H ( f f Equation 34 S [ S ( f H ( f + S ( f H ( ] ( f H ( f S ( f H ( f + j f Equation 35 Figu 9 shows an plementation of the omplex equalizer. The i and q signals from the equalizer pisely math those at the transmitter. Figu 9 - Complex filter ANOTHER TOOL IN THE TOOLBO! As engineers, we strive to avoid unneessary omplexity, and abstrations suh as aginary numbers and negative fquenies sometes fall into this ategory and end up on the hopping blo. In ality, omplex notation is a valuable tool for any engineer woring with signal proessing beause: Woring with exponentials is muh less tedious than woring with sines and osines. Signal proessing artiles and tehnial papers use omplex notation extensively. Complex notation suggests hardwa and softwa strutus for plementing signal proessing funtions. The intent of this artile has been to provide a set of tools for understanding and woring with omplex notation. Most signal proessing textboos (see fenes below inlude a hapter or setion dediated to narrowband signals. These a exellent fenes, and most inlude muh of the mathematial rigor not inluded he. The information in this artile should allow you to beze through the basis and get the most out of that next signal proessing artile. Page 10 of 11
11 REFERENCES [1] J. Proais, Digital Communiations, MGraw Hill, 1983, Chapter 3 [] H. Meyr, M. Moenelaey, A. Fehtel, Digital Communiation Reeivers, Wiley Intersiene, Chapter 1. [3] M. Shwartz, W. Bennett, S. Stein, Communiation Systems and Tehniques, MGraw Hill, 1966, Chapter 1. About the author: Barry Dorr is the owner/psident of Dorr Engineering Servies, In., a onsulting firm loated in San Maros, CA. DESI speializes in signal proessing, modem development, and embedded servos. He holds a BSEE from California Polytehni State University and an MSEE dege from San Diego State University, and is a gisted Professional Engineer in the state of California. Outside of wor he enjoys his hildn and playing the trombone. Mr. Dorr has also teahes a ourse in Embedded Servo Systems: He an be ahed at bdorr@dorngineering.om. Page 11 of 11
EE (082) Chapter IV: Angle Modulation Lecture 21 Dr. Wajih Abu-Al-Saud
EE 70- (08) Chapter IV: Angle Modulation Leture Dr. Wajih Abu-Al-Saud Effet of Non Linearity on AM and FM signals Sometimes, the modulated signal after transmission gets distorted due to non linearities
More informationModule 5 Carrier Modulation. Version 2 ECE IIT, Kharagpur
Module 5 Carrier Modulation Version ECE II, Kharagpur Lesson 5 Quaternary Phase Shift Keying (QPSK) Modulation Version ECE II, Kharagpur After reading this lesson, you will learn about Quaternary Phase
More information6. Amplitude Modulation
6. Amplitude Modulation Modulation is a proess by whih some parameter of a arrier signal is varied in aordane with a message signal. The message signal is alled a modulating signal. Definitions A bandpass
More informationEE140 Introduction to Communication Systems Lecture 7
3/4/08 EE40 Introdution to Communiation Systems Leture 7 Instrutor: Prof. Xiliang Luo ShanghaiTeh University, Spring 08 Arhiteture of a (Digital) Communiation System Transmitter Soure A/D onverter Soure
More informationGenerating 4-Level and Multitone FSK Using a Quadrature Modulator
Generating 4-Level and Multitone FSK Using a Quadrature Modulator Page 1 of 9 Generating 4-Level and Multitone FSK Using a Quadrature Modulator by In a reent olumn (lik on the Arhives botton at the top
More informationANALOG COMMUNICATION (9)
11/5/013 DEARTMENT OF ELECTRICAL &ELECTRONICS ENGINEERING ANALOG COMMUNICATION (9) Fall 013 Original slides by Yrd. Doç. Dr. Burak Kellei Modified by Yrd. Doç. Dr. Didem Kivan Tureli OUTLINE Noise in Analog
More informationChapter 3 Digital Transmission Fundamentals
Chapter 3 Digital Transmission Fundamentals Modems and Digital Modulation CSE 33, Winter Instrutor: Foroohar Foroozan Modulation of Digital Data Modulation of Digital Data Modulation proess of onverting
More informationObjectives. Presentation Outline. Digital Modulation Lecture 04
Digital Modulation Leture 04 Filters Digital Modulation Tehniques Rihard Harris Objetives To be able to disuss the purpose of filtering and determine the properties of well known filters. You will be able
More informationIntroduction to Analog And Digital Communications
Introdution to Analog And Digital Communiations Seond Edition Simon Haykin, Mihael Moher Chapter 9 Noise in Analog Communiations 9.1 Noise in Communiation Systems 9. Signal-to-Noise Ratios 9.3 Band-Pass
More informationIntroductory Notions
Introdutory Notions - he blok diagram of a transmission link, whih onveys information by means of eletromagneti signals, is depited in the figure below. Message Signal aqusition blok Information ransmitter
More informationDigitally Demodulating Binary Phase Shift Keyed Data Signals
Digitally Demodulating Binary Phase Shift Keyed Signals Cornelis J. Kikkert, Craig Blakburn Eletrial and Computer Engineering James Cook University Townsville, Qld, Australia, 4811. E-mail: Keith.Kikkert@ju.edu.au,
More informationAnalog Transmission of Digital Data: ASK, FSK, PSK, QAM
Analog Transmission of Digital Data: ASK, FSK, PSK, QAM Required reading: Forouzan 5. Garia 3.7 CSE 33, Fall 6 Instrutor: N. Vlaji Why Do We Need Digital-to-Analog Conversion?! ) The transmission medium
More informationBPSK so that we have a discrete set of RF signals. t)cos(
BPSK. BPSK Introdution Reall that the most general modulation has the form s( t) a( t)os[ t ( t)]. We remared earlier that phase modulation was not an effetive way to implement analog ommuniation, one
More informationENSC327 Communications Systems 4. Double Sideband Modulation. Jie Liang School of Engineering Science Simon Fraser University
ENSC327 Communiations Systems 4. Double Sideband Modulation Jie Liang Shool of Engineering Siene Simon Fraser University 1 Outline DSB: Modulator Spetrum Coherent Demodulator: Three methods Quadrature-arrier
More informationEKT358 Communication Systems
EKT358 Communiation Systems Chapter 2 Amplitude Modulation Topis Covered in Chapter 2 2-1: AM Conepts 2-2: Modulation Index and Perentage of Modulation 2-3: Sidebands and the Frequeny Domain 2-4: Single-Sideband
More informationENSC327 Communications Systems 4. Double Sideband Modulation. School of Engineering Science Simon Fraser University
ENSC327 Communiations Systems 4. Double Sideband Modulation Shool of Engineering Siene Simon Fraser University 1 Outline Required Bakground DSB: Modulator Spetrum Coherent Demodulator: Three methods Quadrature-arrier
More informationA Quadrature Downconversion Autocorrelation Receiver Architecture for UWB
A Quadrature Downonversion Autoorrelation Reeiver Arhiteture for UWB Simon Lee, Sumit Bagga, Wouter A. Serdijn Eletronis Researh Laboratory, Faulty of Eletrial Engineering, Mathematis and Computer Siene
More informationLecture 22: Digital Transmission Fundamentals
EE 400: Communiation Networks (0) Ref: A. Leon Garia and I. Widjaja, Communiation Networks, 2 nd Ed. MGraw Hill, 2006 Latest update of this leture was on 30 200 Leture 22: Digital Transmission Fundamentals
More informationTELE3013 Mid-session QUIZ 1
TELE3013 Mid-session QUIZ 1 Week 7 10 th April, 2006 Name: Student No: Instrutions to Candidates (1) Time allowed: 90 minutes or so (2) Answer all questions. Total Marks = 90. (3) Marks are as indiated.
More informationCalculating the input-output dynamic characteristics. Analyzing dynamic systems and designing controllers.
CHAPTER : REVIEW OF FREQUENCY DOMAIN ANALYSIS The long-term response of a proess is nown as the frequeny response whih is obtained from the response of a omplex-domain transfer funtion. The frequeny response
More informationChapter 3 Amplitude Modulation. Wireless Information Transmission System Lab. Institute of Communications Engineering National Sun Yat-sen University
Chapter 3 Amplitude Modulation Wireless Information Transmission System Lab. Institute of Communiations Engineering National Sun Yat-sen University Outline 3.1 Introdution 3.2 Amplitude Modulation 3.3
More informationEE 464 Band-Pass Sampling Example Fall 2018
EE 464 Band-Pass Sampling Example Fall 2018 Summary This example demonstrates the use of band-pass sampling. First, a band-pass signal is onstruted as a osine modulated speeh signal. This is a double sideband
More informationEXPLORATIONS IN COMMUNICATION SYSTEMS USING A VIRTUAL TOOLKIT
EXPLORATIONS IN COMMUNICATION SYSTEMS USING A VIRTUAL TOOLKIT Murat Tanyel Dordt College Session 2320 Abstrat A typial ommuniation systems ourse is rih with proesses that are best desribed by blok diagrams.
More informationELG3175 Introduction to Communication Systems. Conventional AM
ELG317 Introdution to Communiation Systems Conventional AM Disadvantages o DSB-SC The reeiver must generate a replia o the arrier in order to demodulate a DSB-SC signal. Any phase and/or requeny error
More informationEffect of Pulse Shaping on Autocorrelation Function of Barker and Frank Phase Codes
Columbia International Publishing Journal of Advaned Eletrial and Computer Engineering Researh Artile Effet of Pulse Shaping on Autoorrelation Funtion of Barker and Frank Phase Codes Praveen Ranganath
More informationFigure 4.11: Double conversion FM receiver
74 4.8 FM Reeivers FM reeivers, like their AM ounterparts, are superheterodyne reeivers. Figure 4.11 shows a simplified blok diagram for a double onversion superheterodyne FM reeiver Figure 4.11: Double
More informationDr. Md. Farhad Hossain Associate Professor Department of EEE, BUET
EEE 309 Communiation Theory Semester: January 06 Dr. Md. Farhad Hossain Assoiate Proessor Department o EEE, BUET Email: marhadhossain@eee.buet.a.bd Oie: ECE 33, ECE Building Part 03-3 Single-sideband Suppressed
More informationDSP First Lab 05: FM Synthesis for Musical Instruments - Bells and Clarinets
DSP First Lab 05: FM Synthesis for Musial Instruments - Bells and Clarinets Pre-Lab and Warm-Up: You should read at least the Pre-Lab and Warm-up setions of this lab assignment and go over all exerises
More informationCHAPTER 3 BER EVALUATION OF IEEE COMPLIANT WSN
CHAPTER 3 EVALUATIO OF IEEE 8.5.4 COMPLIAT WS 3. OVERVIEW Appliations of Wireless Sensor etworks (WSs) require long system lifetime, and effiient energy usage ([75], [76], [7]). Moreover, appliations an
More informationELEC 350 Communications Theory and Systems: I. Analog Signal Transmission and Reception. ELEC 350 Fall
ELEC 350 Communiations Theory and Systems: I Analog Signal Transmission and Reeption ELEC 350 Fall 2007 1 ELEC 350 Fall 2007 2 Analog Modulation A large number o signals are analog speeh musi video These
More informationParallel Interference Cancellation in Multicarrier DS-CDMA Systems
N Parallel Interferene Canellation in ultiarrier D-CD ystems K. R. hankar kumar and. Chokalingam Department of ECE Indian Institute of iene Bangalore 50012 INDI bstrat In this paper we present and analyze
More informationA 24 GHz Band FM-CW Radar System for Detecting Closed Multiple Targets with Small Displacement
A 24 GHz Band FM-CW Radar System for Deteting Closed Multiple Targets with Small Displaement Kazuhiro Yamaguhi, Mitsumasa Saito, Takuya Akiyama, Tomohiro Kobayashi and Hideaki Matsue Tokyo University of
More informationConsiderations and Challenges in Real Time Locating Systems Design
Considerations and Challenges in Real Time Loating Systems Design Dr. Brian Gaffney DeaWave Ltd. Email: brian.gaffney@deawave.om Abstrat Real Time Loating Systems (RTLS) are a ombination of hardware and
More informationANALOG COMMUNICATIONS IV Sem. Prepared by Mr. T. Nagarjuna ECE Department
ANALOG COMMUNICAIONS IV Sem Prepared by Mr.. Nagaruna ECE Department UNI I SIGNAL ANALYSIS AND LI SYSEMS Classifiation of Signals Deterministi & Non Deterministi Signals Periodi & A periodi Signals Even
More informationDESIGN AND PERFORMANCE ANALYSIS OF BAND PASS IIR FILTER FOR SONAR APPLICATION
International Journal of Emerging Tehnologies and Engineering (IJETE) ISSN: 238 8 ICRTIET-21 Conferene Proeeding, 3 th -31 st August 21 11 DESIGN AND PERFORMANCE ANALYSIS OF BAND PASS IIR FILTER FOR SONAR
More informationAMPLITUDE MODULATION AND DEMODULATION
Modulation is a tehnique to transit inforation via radio arrier wavefor. It is a non-linear proess that generates additional frequenies, as we will see. Aplitude Modulation (AM) works by varying the aplitude
More informationLayered Space-Time Codes for Wireless Communications Using Multiple Transmit Antennas
Layered Spae-Time Codes for Wireless Communiations Using Multiple Transmit Antennas Da-shan Shiu and Joseph M. Kahn University of California at Bereley Abstrat Multiple-antenna systems provide very high
More informationEFFICIENT IIR NOTCH FILTER DESIGN VIA MULTIRATE FILTERING TARGETED AT HARMONIC DISTURBANCE REJECTION
EFFICIENT IIR NOTCH FILTER DESIGN VIA MULTIRATE FILTERING TARGETED AT HARMONIC DISTURBANCE REJECTION Control Systems Tehnology group Tehnishe Universiteit Eindhoven Eindhoven, The Netherlands Dennis Bruijnen,
More informationANALYSIS OF THE IONOSPHERIC INFLUENCE ON SIGNAL PROPAGATION AND TRACKING OF BINARY OFFSET CARRIER (BOC) SIGNALS FOR GALILEO AND GPS
ANALYSIS OF THE IONOSPHERIC INFLUENCE ON SIGNAL PROPAGATION AND TRACKING OF BINARY OFFSET CARRIER (BOC) SIGNALS FOR GALILEO AND GPS Thomas Pany (1), Bernd Eissfeller (2), Jón Winkel (3) (1) University
More informationRF Link Budget Calculator Manual
RF Link Budget Calulator Manual Author Ivo van Ling for www.vanling.net Software Release RF Link Distane Calulator, Version 1.00, Dated 4 January 2010 Manual Version 1.00 Date 19-01-2010 Page: 1(8) Contents
More informationParameters of the radio channels that affect digital signal transmissions Propagation Environment Attenuation Index, γ
Parameters of the radio hannels that affet digital signal transmissions 1.Free spae attenuation - the signal undergoes an average attenuation that depends on the length of the path and signal s frequeny
More informationHomework: Please number questions as numbered on assignment, and turn in solution pages in order.
ECE 5325/6325: Wireless Communiation Systems Leture Notes, Spring 2010 Leture 6 Today: (1) Refletion (2) Two-ray model (3) Cellular Large Sale Path Loss Models Reading for today s leture: 4.5, 4.6, 4.10.
More informationDesign and Performance of a 24 GHz Band FM-CW Radar System and Its Application
Frequeny Design and Performane of a 24 GHz Band FM-CW Radar System and Its Appliation Kazuhiro Yamaguhi, Mitsumasa Saito, Kohei Miyasaka and Hideaki Matsue Tokyo University of Siene, Suwa CQ-S net In.,
More informationRevision: April 18, E Main Suite D Pullman, WA (509) Voice and Fax
Lab 9: Steady-state sinusoidal response and phasors Revision: April 18, 2010 215 E Main Suite D Pullman, WA 99163 (509) 334 6306 Voie and Fax Overview In this lab assignment, we will be onerned with the
More informationAnalysis and Design of an UWB Band pass Filter with Improved Upper Stop band Performances
Analysis and Design of an UWB Band pass Filter with Improved Upper Stop band Performanes Nadia Benabdallah, 1 Nasreddine Benahmed, 2 Fethi Tari Bendimerad 3 1 Department of Physis, Preparatory Shool of
More informationA Study on The Performance of Multiple-beam Antenna Satellite Receiving System Dezhi Li, Bo Zeng, Qun Wu*
16 nd International Conferene on Mehanial, Eletroni and Information Tehnology Engineering (ICMITE 16) ISBN: 978-1-6595-34-3 A Study on The Performane of Multiple-beam Antenna Satellite Reeiving System
More informationAverage Current Mode Interleaved PFC Control
Freesale Semiondutor, n. oument Number: AN557 Appliation Note ev. 0, 0/06 Average Current Mode nterleaved PFC Control heory of operation and the Control oops design By: Petr Frgal. ntrodution Power Fator
More informationPrediction Method for Channel Quality Indicator in LEO mobile Satellite Communications
Predition Method for Channel Quality Indiator in LEO mobile Satellite Communiations Yadan Zheng *, Mingke Dong *, Wei Zheng *, Ye Jin *, Jianjun Wu * * Institution of Advaned Communiations, Peking University,
More informationDate: August 23,999 Dist'n: T1E1.4
08/0/99 1 T1E1.4/99-49 Projet: T1E1.4: VDSL Title: Filtering elements to meet requirements on power spetral density (99-49) Contat: G. Cherubini, E. Eleftheriou, S. Oeler, IBM Zurih Researh Lab. Saeumerstr.
More informationMultilevel PWM Waveform Decomposition and Phase-Shifted Carrier Technique
Multilevel PWM Waveform Deomposition and Phase-Shifted Carrier Tehnique R. Naderi* and A. Rahmati* Abstrat: Multilevel PWM waveforms an be deomposed into several multilevel PWM omponents. Phase-shifted
More informationTransmission Adaptation for Broadband Wireless MIMO-OFDM Systems with Limited Feedback
Transmission Adaptation for Broadband Wireless MIMO-OFDM Systems with Limited Feedba Harri Pennanen and Jouo Leinonen Centre for Wireless Communiations P.O. Box 4500, 90014 University of Oulu, Finland
More informationANALOG COMMUNICATION (8)
/5/3 DEPARTMENT OF ELECTRICAL &ELECTRONICS ENGINEERING ANALOG COMMUNICATION (8) Fall 3 Original slides by Yrd. Doç. Dr. Burak Kellei Modified by Yrd. Doç. Dr. Didem Kivan Tureli OUTLINE Random Variables
More informationLimitations and Capabilities of the Slanted Spectrogram Analysis Tool for SAR-Based Detection of Multiple Vibrating Targets
Limitations and Capabilities of the Slanted Spetrogram Analysis Tool for SAR-Based Detetion of Multiple Vibrating Targets Adebello Jelili, Balu Santhanam, and Majeed Hayat Department of Eletrial and Computer
More informationAbstract. 1. Introduction. 2. Fading
An Interative Simulation for Flat Fading P.Marihamy*, J.Senthilkumar and V.Vijayarangan ECE Dept., National Engineering College Kovilpatti -68 503, India. * Nizwa College of Tehnology, Sultanate of Oman
More informationLocation Fingerprint Positioning Based on Interval-valued Data FCM Algorithm
Available online at www.sienediret.om Physis Proedia 5 (01 ) 1939 1946 01 International Conferene on Solid State Devies and Materials Siene Loation Fingerprint Positioning Based on Interval-valued Data
More informationMetrol. Meas. Syst., Vol. XVIII (2011), No. 2, pp METROLOGY AND MEASUREMENT SYSTEMS. Index , ISSN
METROLOGY AND MEASUREMENT SYSTEMS Index 330930, ISSN 0860-8229 www.metrology.pg.gda.pl DAC TESTING USING MODULATED SIGNALS Pavel Fexa, Josef Vedral, Jakub Svatoš CTU Prague, Faulty of Eletrial Engineering
More informationAFRL-RY-WP-TP
AFRL-RY-WP-P-009-307 A MODULAION BASED APPROACH O WIDEBAND- SAP (PREPRIN) Ke Yong Li, Unnirishna S. Pillai, Peter Zulh, and Mihael Callahan C & P ehnologies, In. OCOBER 007 Approved for publi release;
More informationand division (stretch).
Filterg AC signals Topi areas Eletrial and eletroni engeerg: AC Theory. Resistane, reatane and impedane. Potential divider an AC iruit. Low pass and high pass filters. Mathematis: etor addition. Trigonometry.
More informationTRANSISTORS: DYNAMIC CIRCUITS. Introduction
TRANSISTORS: DYNAMIC CIRCUITS Introdution The point of biasing a iruit orretly is that the iruit operate in a desirable fashion on signals that enter the iruit. These signals are perturbations about the
More informationAnalog Communications
1 Analog Communiations Amplitude Modulation (AM) Frequeny Modulation (FM) 2 Radio broadasting 30-300M Hz SOURCE Soure Transmitter Transmitted signal Channel Reeived signal Reeiver User Analog baseband
More informationResearch on Blanket Jamming to Beidou Navigation Signals Based on BOC Modulation
Int. J. Communiations, Network and System Sienes, 6, 9, 35-44 Published Online May 6 in SiRes. http://www.sirp.org/ournal/ins http://dx.doi.org/.436/ins.6.95 Researh on Blanket Jamming to Beidou Navigation
More informationREET Energy Conversion. 1 Electric Power System. Electric Power Systems
REET 2020 Energy Conversion 1 Eletri Power System Eletri Power Systems An Eletri Power System is a omplex network of eletrial omponents used to reliably generate, transmit and distribute eletri energy
More informationPerformance of Random Contention PRMA: A Protocol for Fixed Wireless Access
Int. J. Communiations, Network and System Sienes, 2011, 4, 417-423 doi:10.4236/ijns.2011.47049 Published Online July 2011 (http://www.sirp.org/journal/ijns) Performane of Random Contention PRMA: A Protool
More informationIntroduction to signals and systems
CHAPTER Introduction to signals and systems Welcome to Introduction to Signals and Systems. This text will focus on the properties of signals and systems, and the relationship between the inputs and outputs
More informationEstimation and Compensation of IQ Imbalance in Millimeter-Wave OFDM UWB System
Journal of Computers Vol. 8, No. 4, 07, pp. 79-88 doi:0.3966/99559070880409 Estimation and Compensation of I Imbalane in Millimeter-Wave OFDM UWB System Zhan Xu *, Ya-Bing Cheng, and Shi-Jie Ren 3,4 Shool
More informationAdaptive RAKE Receiver Structures for Ultra Wide-Band Systems
Adaptive RAE Reeiver Strutures for Ultra Wide-Band Systems A Thesis Submitted to the College of Graduate Studies and Researh n Partial Fulfillment of the Requirements For the Degree of Master of Siene
More informationCopyright Blind Selected Mapping Techniques for Space-Time Block Coded Filtered Single-Carrier Signals
Blind Seleted Mapping Tehniques for Spae-Time Blok Coded Filtered Single-Carrier Signals IEEE VTS AWCS 6 6 August 6 @ Tokyo, Japan Amnart Boonkaay Fumiyuki Adahi Wireless Signal roessing Researh Group
More informationFully Joint Diversity Combining, Adaptive Modulation, and Power Control
Fully Joint Diversity Combining, Adaptive Modulation, and Power Control Zied Bouida, Khalid A. Qaraqe, and Mohamed-Slim Alouini Dept. of Eletrial and Computer Eng. Texas A&M University at Qatar Eduation
More informationSinusoids and Phasors (Chapter 9 - Lecture #1) Dr. Shahrel A. Suandi Room 2.20, PPKEE
Sinusoids and Phasors (Chapter 9 - Lecture #1) Dr. Shahrel A. Suandi Room 2.20, PPKEE Email:shahrel@eng.usm.my 1 Outline of Chapter 9 Introduction Sinusoids Phasors Phasor Relationships for Circuit Elements
More informationConsidering Capacitive Component in the Current of the CSCT Compensator
Proeedings of the World Congress on Engineering and Computer Siene 8 WCECS 8, Otober - 4, 8, San Franiso, SA Considering Capaitive Component in the Current of the CSCT Compensator Mohammad Tavakoli Bina,
More informationCommunication Systems Lecture 7. Dong In Kim School of Info/Comm Engineering Sungkyunkwan University
Communiation Systems Leture 7 Dong In Kim Shool o Ino/Comm Engineering Sungkyunkwan University 1 Outline Expression o SSB signals Waveorm o SSB signals Modulators or SSB: Frequeny disrimination Phase disrimination
More informationTexas Instruments Analog Design Contest
Texas Instruments Analog Design Contest Oregon State University Group 23 DL Paul Filithkin, Kevin Kemper, Mohsen Nasroullahi 1. Written desription of the projet Imagine a situation where a roboti limb
More informationSingle Sideband (SSB) AM
Single Sideband (SSB) AM Leture 7 Why SSB-AM? Spetral eiieny is o great importane. Conventional & DSB-SC oupy twie the message bandwidth. All the inormation is ontained in either hal the other is redundant.
More informationIncompatibility Of Trellis-Based NonCoherent SOQPSK Demodulators For Use In FEC Applications. Erik Perrins
AFFTC-PA-12071 Inompatibility Of Trellis-Based NonCoherent SOQPSK Demodulators For Use In FEC Appliations A F F T C Erik Perrins AIR FORCE FLIGHT TEST CENTER EDWARDS AFB, CA 12 MARCH 2012 Approved for
More informationSerial PN Acquisition Using Smart Antenna and Censored Mean Level CFAR Adaptive Thresholding for a DS/CDMA Mobile Communication
01 IEEE 14th International Conferene on High Performane Computing and Communiations Serial PN Aquisition Using Smart Antenna and Censored Mean Level CFAR Adaptive Thresholding for a DS/CDMA Mobile Communiation
More informationComparison of OFDM Radar and Chirp Sequence Radar
Comparison of OFDM Radar and Chirp Sequene Radar Johannes Fink, Friedrih K. Jondral Communiations Engineering Lab, Karlsruhe Institute of Tehnology Karlsruhe, GERMANY {Johannes.Fink, Friedrih.Jondral}@kit.edu
More informationTimber Structures: Rotational stiffness of carpentry joints
Timber Strutures: Rotational stiffness of arpentry joints T. Desamps - Assistant Professor Faulté Polytehnique de Mons, Rue du Jonquois, 53 7000 Mons, Belgium Thierry.Desamps@fpms.a.be J. Lambion - Researher
More informationEDGE AND LAPLACE BASED RESTORATION OF HAZY IMAGES
www.ijrar.om INTERNATIONAL JOURNAL OF RESEARCH IN COMPUTER APPLICATIONS AND ROBOTICS ISSN 2320-7345 EDGE AND LAPLACE BASED RESTORATION OF HAZY IMAGES 1 Priya Singh Patel, 2 Prof. Manisha Rathore Abstrat:
More informationAn Assisted GPS Acquisition Method using L2 Civil Signal in Weak Signal Environment
Journal of Global Positioning Systems (004) Vol. 3, No. -: 5-3 An Assisted GPS Aquisition ethod using L Civil Signal in Wea Signal Environment Deu Jae Cho Department of Eletronis, Chungnam National University,
More informationCHAPTER 9. Sinusoidal Steady-State Analysis
CHAPTER 9 Sinusoidal Steady-State Analysis 9.1 The Sinusoidal Source A sinusoidal voltage source (independent or dependent) produces a voltage that varies sinusoidally with time. A sinusoidal current source
More informationThe Design of a Spatial Diversity Model to Mitigate Narrowband and Broadband Interference in DSSS Ad Hoc Networks
The Design of a Spatial Diversity Model to Mitigate Narrowband and Broadband Interferene in DSSS Ad Ho Networks Sonia Furman, and Mario Gerla University of California, Los Angeles Abstrat Spatial diversity
More informationCoherent Detection Method with Compensation at Transmitter in Time Division Duplex System
Coherent Detetion Method with Compensation at Transmitter in Time Division Duplex System Young An Kim 1, Choong Seon Hong 1 1 Department o Eletronis and Inormation, Kyung Hee University, 1 Seoheon, Giheung,
More informationReasons for Choosing Encoding Techniques. Signal Encoding Techniques. Reasons for Choosing Encoding Techniques. Signal Encoding Criteria
Reaon for Chooing Enoding Tehnique Signal Enoding Tehnique Chapter 6 Digital data, digital ignal Equipment le omplex and expenive than digital-to-analog modulation equipment Analog data, digital ignal
More informationFlexible Folded FIR Filter Architecture
Flexible Folded FIR Filter Arhiteture I. Milentijevi, V. Ciri, O. Vojinovi Abstrat - Configurable folded bit-plane arhiteture for FIR filtering that allows programming of both number of taps and oeffiient
More informationNumerical modeling of DPSK pressure signals and their transmission characteristics in mud channels
66 Pet.Si.(9)6:66-7 DOI.7/s8-9-4-8 Numerial modeling of DPSK pressure signals and their transmission harateristis in mud hannels Shen Yue, Su Yinao, Li Gensheng 3, Li Lin and Tian Shoueng 3 College of
More informationOutline : Wireless Networks Lecture 6: Physical Layer Coding and Modulation 1. Basic Modulation Techniques. From Signals to Packets.
Outline 18-759 : Wireless Networks Leure 6: Physial Layer Coding and Modulation 1 Peter Steenkiste Departments of Computer Siene and Elerial and Computer Engineering Spring Semester 2016 http://www.s.mu.edu/~prs/wirelesss16/
More informationMULTI-FREQUENCY EDDY CURRENT TESTING OF FERROMAGNETIC WELDS
U-FQUCY DDY CU SG OF FOGC WDS ODUCO C. W. Gilstad,. F. Dersh and. Deale David aylor esearh Center etals and Welding Division nnapolis D, 2142-567 Single frequeny phase analysis eddy urrent tehniques have
More informationEffect of orientation and size of silicon single crystal to Electro-Ultrasonic Spectroscopy
Effet of orientation and size of silion single rystal to Eletro-Ultrasoni Spetrosopy Mingu KANG 1, Byeong-Eog JUN 1, Young H. KIM 1 1 Korea Siene Aademy of KAIST, Korea Phone: +8 51 606 19, Fax: +8 51
More informationVoltage Sag Classification with Consideration of Phase Shift
First IEEE International Conferene on Energy Internet Voltage Sag Classifiation with Consideration of Phase Shift Pengfei Wei, onghai Xu State Key Laoratory of Alternate Eletrial Power System with Renewale
More informationMicro-Piezoelectric Head Technology of Color Inkjet Printer
DPP2: International Conferene on Digital Prodution Printing and Industrial Appliations Miro-Piezoeletri Head Tehnology of Color Inkjet Printer Takao Mimura & Shinri Sakai SEIKO EPSON Corporation Shiojiri-shi,
More informationNoise Robust AM-FM Demodulation using Least- Squares Truncated Power Series Approximation
oise Robust AM-FM Demodulation using Least- Squares Trunated ower Series Approximation Wooi-Boon Goh Shool of Computer Engineering, anyang Tehnologial University, Singapore 639798 aswbgoh@ntu.edu.sg ABSTRACT
More informationSecond Edition Simon Haykin, Michael Moher
Introdution to Analog And Digital Communiations Seond Edition Simon Haykin, Mihael Moher Chapter 6 Baseband Delta Transmission 6. Baseband Transmission o Digital Data 6.2 The Intersymbol Intererene Problem
More informationDispersion and Dispersion Slope Compensation of an Optical Delay Line Filter (DLF) based on Mach-Zehnder Interferometers
Dispersion and Dispersion Slope Compensation of an Optial Delay Line Filter (DLF) based on Mah-Zehnder Interferometers P.Pavithra 1, K.Karthika 2 1,2 Department of Eletronis and Communiation Engineering,
More informationInterference mitigation by distributed beam forming optimization
English Interferene mitigation by distributed beam forming optimization Matthias Kashub, Christian M. Blankenhorn, Christian M. Mueller and Thomas Werthmann Abstrat Inter-ell interferene is a major issue
More informationA Robust Image Restoration by Using Dark channel Removal Method
Volume 6, Issue 3, Marh 2017, ISSN: 2278 1323 A Robust Image Restoration by Using Dark hannel Removal Method Ankit Jain 1 (MTeh. sholar), Prof. Mahima Jain 2 Department Of Computer Siene And Engineering,
More informationOrthogonal Frequency Division Multiplexing modulation and inter-carrier interference cancellation
Louisiana State University LSU Digital Commons LSU aster's Theses Graduate Shool 23 Orthogonal Frequeny Division ultiplexing modulation and inter-arrier interferene anellation Yao Xiao Louisiana State
More informationReprint from IASTED International Conference on Signal and Image Processing (SIP 99). Nassau, Bahamas, October, 1999.
Reprint from IASTED International Conferene on Signal and Image Proessing (SIP 99). Nassau, Bahamas, Otober, 1999. 1 Filter Networks Mats Andersson Johan Wiklund Hans Knutsson Computer Vision Laboratory,
More informationStudy of the Variance in the Histogram Test of ADCs
Study of the Variane in the Histogram Test of ADCs F. Corrêa Alegria and A. Cruz Serra Teleommuniations Institute and Department of Eletrial and Computer Engineering Instituto Superior Ténio, Tehnial University
More informationAn Improved Doppler Frequency Offset Estimation Algorithm of OFDM System under High-speed Movement Environment
JOURAL OF COMPUTERS, VOL. 8, O. 2, DECEMBER 23 39 An Improved Doppler Frequeny Offset Estimation Algorithm of OFDM System under High-speed Movement Environment Yunlv Hong Department of Eletroni Engineering,
More informationMultiplication/Modulation Property For Continuous-Time.
Multipliation/Modulation Property For Continuous-Time. X( X(j) y(=(.( Y(j)=[C(j) X(j)]/2π )] ( )* ( [ 2 ) ( ). (. π j X j C t t T F X ( C(j) + = = = θ θ θ θ θ π d Xj j C jw Y ) ( ) ( 2 ) ( Multipliation/Modulation
More information