Principles of Communications Lecture 8: Baseband Communication Systems. Chih-Wei Liu 劉志尉 National Chiao Tung University

Size: px
Start display at page:

Download "Principles of Communications Lecture 8: Baseband Communication Systems. Chih-Wei Liu 劉志尉 National Chiao Tung University"

Transcription

1 Principles of Communications Lecture 8: Baseband Communication Systems Chih-Wei Liu 劉志尉 National Chiao Tung University

2 Outlines Introduction Line codes Effects of filtering Pulse shaping toward zero ISI Zero-forcing equalization Eye diagrams Synchronization Commun.-Lec8 2

3 Introduction Digital vs. analog signals Analog sampling quantization digital Baseband vs. passband Channel distortion ISI (Channel) bandwidth limitation Commun.-Lec8 3

4 Line Codes Baseband data format used to represent digital data (for transmission purpose). Examples are given on the next page Operation: time or frequency shaping Purposes: usually to cope with the channel limitations (or provide extra function such as synchronization) Needed for certain applications Commun.-Lec8 4

5 Non-return-to-zero (NRZ) change NRZ mark (data1-> change in level; data0 -> no change) Unipolar return-to-zero (URZ) <1/2 width pulses> Polar RZ Bipolar RZ ( 0 -> 0 level; 1 -> alternate sign Split phase (Manchester) ( 1 -> level A to level A at 1/2 interval; 0 -> level A to level A at 1/2 interval) Commun.-Lec8 cwliu@twins.ee.nctu.edu.tw 5

6 Purposes of Line Codes Self synchronization Proper power spectrum Transmission bandwidth Transparency Error detection capability Good error probability performance Commun.-Lec8 6

7 Power Spectra (I) The transmitted signal is a pulse train: X() t = a p( t kt Δ). k= The amplitudes can be viewed as random variables with R = a a m = 0, ± 1, ± 2, m k k+ m The autocorrelation function of the waveform is R X ( τ ) = R r( τ m= k m mt ), K 1 in which r( τ) = p( t+ τ) p( t) dt. T Commun.-Lec8 cwliu@twins.ee.nctu.edu.tw 7

8 Power Spectra (II) The power spectral density is the Fourier transofrm of R ( τ ): S ( f) = FT[ R ( τ)] = FT[ R r( τ mt)] X X m m= = R FT[( r τ mt)] = R S ( f) e = m= m m r m= j2 mtf r( ) π m. m= S f R e j2π mtf 2 1 P( f) Note that Sr( f ) = FT[ r( τ )] = FT[ p( t) p( t)] =. T T X Commun.-Lec8 cwliu@twins.ee.nctu.edu.tw 8

9 Example 1: NRZ Assume the message m[n] is random (white noise) with equally 0 and 1 values. Step 1: Compute R m based on the above assumption and format Step 2: Compute r(t) based on the pulse shape. 1. NRZ, 50% "0" and 50% "1". R = A + ( A) = A, m= 0; m R = A + A( A) + ( A) A+ ( A) = 0, m 0. m pt () =Π( t/ T) P( f) = Tsinc( Tf) S f = A S f = A T Tf Therefore, NRZ ( ) r( ) sinc ( ). Commun.-Lec8 cwliu@twins.ee.nctu.edu.tw 9

10 Example 2: Unipolar RZ 2. Unipolar RZ, 50% 1-level and 50% 0-level A + (0) = A, m= Rm = A A+ A + A+ = A m pt () =Π(2 t/ T) P( f) = sinc( f) , 0 T T 2 2 T T 1 1 SURZ ( f) = sinc ( f) A + A T T 1 1 = sinc ( f ) 4 2 A + A e 4 4 m= m= j2π mtf m=, m 0 j2π mtf 2 n= m= n= T 2 T A n j2π mtf 1 n = sinc ( f) A ( f ). e ( f ) δ δ 4 4 T n= T Q = m= T n= T m= e Commun.-Lec8 cwliu@twins.ee.nctu.edu.tw 10

11 Commun.-Lec8 11

12 Inter-symbol Interference (ISI) Intersymbol interference refers to one specific type of distortion. It is typically due to insufficient bandwidth of the channel. Note: Narrow BW Long time-duration Example: Rectangular waveforms through a lowpass RC filter. The neighboring pulses smear out and interfere with each other. Commun.-Lec8 cwliu@twins.ee.nctu.edu.tw 12

13 BW= 1bit/sec Commun.-Lec8 13

14 BW= 0.5bit/sec Commun.-Lec8 14

15 ISI Reduction Pulse shaping: Assume the channel is ideal (flat) with the minimum BW (W). What shape of pulse warrants ISI-free transmission? Equalization: If the channel is non-ideal (not ideally flat LPF), an equalizer helps in reducing ISI. Commun.-Lec8 15

16 Pulse Shaping Consider 2W independent samples per second are transmitted through a channel with bandwidth W Hz. The output is as follows. n yt () = yn() t = ansinc 2 W t. n n 2W = = The samples at t = m/ 2 W are ISI-free, Q sinc( m n) = 0. Are there other pulse shapes warrant ISI-free? m p(t) -T 0 T 2T t a1 p( t T ) Sampling of p(t-2t) a2 p( t 2T ) a3 p( t 3T ) Commun.-Lec8 cwliu@twins.ee.nctu.edu.tw 16 t

17 Raised Cosine Family Raised Cosine: a example of ISI-free pulses raised cosine spectra at BW edges. 1 β T, f 2T T πt 1 β 1 β 1+ β PRC ( f) = 1+ cos 2 f f β 2T < 2T 2T 1+ β 0 f > 2T Roll-off factor β: β=0 rectangular pulse (sinc) β=1 cosine in freq; time pulse has narrow main lobe with very low sidelobes Commun.-Lec8 cwliu@twins.ee.nctu.edu.tw 17

18 Time pulse of the raised cosine: p RC cos( πβt/ T) t ( t) = sinc( ), β is called the roll-off factor. 2 1 (2 βt/ T) T cosine curves Commun.-Lec8 cwliu@twins.ee.nctu.edu.tw 18

19 Nyquist s Pulse Shaping Criterion A pulse shape p( t) with a Fourier transform P( f k= k 1 P( f + ) = T, f T 2T 1, n = 0 then its sampled values pnt ( ) =. 0, n 0. ) satisfying Commun.-Lec8 cwliu@twins.ee.nctu.edu.tw 19

20 Proof of Nyquist's Pulse Shaping Criterion j2π ft pt () = P( f) e df j2π fnt nt p nt = P f e df Sampling at, ( ) ( ) 2k+ 1 2 T j 2 π fnt pnt ( ) = P( f) e df k= 2k 1 2 T 1 2T k j2π f ( unt+ kn) = Pu ( + ) e du; u= f k= 1 2 T T 1 k j2π funt = 2 T Pu ( + ) e du 1 2 T T k= 1 2 T j 2 π funt 1, n = 0 = Te du = 1 2 T 0, n 0 k T Commun.-Lec8 cwliu@twins.ee.nctu.edu.tw 20

21 Pulse Transmission System xt () = ah( t kt). k= k T v() t = y() t h () t = [ x() t h ()] t h (). t R C R Consider the combined effect of three filters, we would like to have vt ( ) to be ISI-free. Commun.-Lec8 cwliu@twins.ee.nctu.edu.tw 21

22 Transmitter and Receiver Filters Let vt ( ) = A ap ( t kt t) k= k RC d where A represents a scale factor and t a possible delay. Ap ( t t ) = h () t h () t h (), t or in frequency domain, RC d T C R j2π ftd RC ( ) = T ( ) C ( ) R( ). AP f e H f H f H f If H ( f) is given, then H C T d ( f) H ( f) = 1 H ( f) The overall spectrum should satisfy the Nyquist criterion to avoid ISI. A filter design problem. Practically, H c (f) is unknown of time-varying R C Commun.-Lec8 cwliu@twins.ee.nctu.edu.tw 22

23 Let H ( f) = H ( f) = 1 H ( f) T R C 1/2 Commun.-Lec8 cwliu@twins.ee.nctu.edu.tw 23

24 Zero-Forcing Equalization Now, assume digital processing at the receiver. Purpose: Design an FIR filter that compensates for the channel distortion zero-isi. Show an example of zero-isi equalizer design. Commun.-Lec8 24

25 Let the combined impulse response after the channel be pc( t), Pass such a pulse through our finite-length equalizer, then n peq() t = αn pc( t nδ). n= N If the resulting pulse satisfies the zero-isi condition, ISI-free transmission is achieved. Assume that Δ= T, the condistion is n 1, m = 0 peq( mt) = αn pc[( m n) T] = m= 0, ± 1, K, ± N. n= N 0, m 0 Notice that we only enforce the zero-isi condition on the 2N + 1 samples. Why? We only have 2N + 1 coefficients (variables) and can only achieve this much. Solve the 2N + 1 equations and you obtain the zero-forcing equalizer. Commun.-Lec8 cwliu@twins.ee.nctu.edu.tw 25

26 0 M pc(0) pc( T) L pc( 2 NT) a N 0 pc( T) pc(0) pc(( 2N 1) T) a N+ 1 1 L + = M M M 0 pc(2 NT) pc(0) an M 0 Example: A 3-tap equalizer The equalizer cannot eliminate ISI beyond its span. Commun.-Lec8 cwliu@twins.ee.nctu.edu.tw 26

27 Eye Diagrams Eye diagram: Constructed by overlapping a number of segments of the base-band signals A qualitative measure of the system performance. (Lee et al., Digital Comm., 1994) Commun.-Lec8 cwliu@twins.ee.nctu.edu.tw 27

28 Increasing bandwidth may mitigate ICI, but will also allows more noise to enter. Another example of trade-offs in commu systems design Amplitude jitter: ICI causes the amplitude of each symbol fluctuate. eye eye Timing jitter: ICI causes the timing of each symbol fluctuate. The best place to sample the signal. Commun.-Lec8 28

29 Symbol, Bit, Word, and Frame Bits Symbol (a single pulse in transmission) --- carrier sync., symbol timing Bits Word --- word sync. Words Frame --- frame sync. (Benedetto et al., Digital Tansmission Theory, 1987) Commun.-Lec8 29

30 Synchronization Methods : (1) external sync signals; (2) self-synchronization: derivation from the modulated signals Example 1: squaring the received NRZ signals and PLL Sync signal Commun.-Lec8 cwliu@twins.ee.nctu.edu.tw 30

31 Example 2 4 Sync signal Commun.-Lec8 cwliu@twins.ee.nctu.edu.tw 31

32 Carrier Modulation Simple modulation applied to baseband digital signals Example: Let dt ( ) be the NZR waveform. Amplitude Shift-Keying (ASK): x ( t) = A[1 + d( t)]cos(2 π f t) ASK c c π Phase Shift-Keying (PSK): xpsk ( t) = Ac cos[2 π fct+ d( t)] 2 Frequency Shift-Keying (FSK): x ( t) = A cos[2π f t+ k d( α) dα] FSK c c f t Commun.-Lec8 cwliu@twins.ee.nctu.edu.tw 32

33 Commun.-Lec8 33

Square Root Raised Cosine Filter

Square Root Raised Cosine Filter Wireless Information Transmission System Lab. Square Root Raised Cosine Filter Institute of Communications Engineering National Sun Yat-sen University Introduction We consider the problem of signal design

More information

EE5713 : Advanced Digital Communications

EE5713 : Advanced Digital Communications EE5713 : Advanced Digital Communications Week 12, 13: Inter Symbol Interference (ISI) Nyquist Criteria for ISI Pulse Shaping and Raised-Cosine Filter Eye Pattern Equalization (On Board) 20-May-15 Muhammad

More information

Weiyao Lin. Shanghai Jiao Tong University. Chapter 5: Digital Transmission through Baseband slchannels Textbook: Ch

Weiyao Lin. Shanghai Jiao Tong University. Chapter 5: Digital Transmission through Baseband slchannels Textbook: Ch Principles of Communications Weiyao Lin Shanghai Jiao Tong University Chapter 5: Digital Transmission through Baseband slchannels Textbook: Ch 10.1-10.5 2009/2010 Meixia Tao @ SJTU 1 Topics to be Covered

More information

Digital Communications

Digital Communications Digital Communications Chapter 9 Digital Communications Through Band-Limited Channels Po-Ning Chen, Professor Institute of Communications Engineering National Chiao-Tung University, Taiwan Digital Communications:

More information

Signal Design for Band-Limited Channels

Signal Design for Band-Limited Channels Wireless Information Transmission System Lab. Signal Design for Band-Limited Channels Institute of Communications Engineering National Sun Yat-sen University Introduction We consider the problem of signal

More information

Summary: ISI. No ISI condition in time. II Nyquist theorem. Ideal low pass filter. Raised cosine filters. TX filters

Summary: ISI. No ISI condition in time. II Nyquist theorem. Ideal low pass filter. Raised cosine filters. TX filters UORIAL ON DIGIAL MODULAIONS Part 7: Intersymbol interference [last modified: 200--23] Roberto Garello, Politecnico di orino Free download at: www.tlc.polito.it/garello (personal use only) Part 7: Intersymbol

More information

Pulse Shaping and ISI (Proakis: chapter 10.1, 10.3) EEE3012 Spring 2018

Pulse Shaping and ISI (Proakis: chapter 10.1, 10.3) EEE3012 Spring 2018 Pulse Shaping and ISI (Proakis: chapter 10.1, 10.3) EEE3012 Spring 2018 Digital Communication System Introduction Bandlimited channels distort signals the result is smeared pulses intersymol interference

More information

Lecture 5b: Line Codes

Lecture 5b: Line Codes Lecture 5b: Line Codes Dr. Mohammed Hawa Electrical Engineering Department University of Jordan EE421: Communications I Digitization Sampling (discrete analog signal). Quantization (quantized discrete

More information

that efficiently utilizes the total available channel bandwidth W.

that efficiently utilizes the total available channel bandwidth W. Signal Design for Band-Limited Channels Wireless Information Transmission System Lab. Institute of Communications Engineering g National Sun Yat-sen University Introduction We consider the problem of signal

More information

Line Codes and Pulse Shaping Review. Intersymbol interference (ISI) Pulse shaping to reduce ISI Embracing ISI

Line Codes and Pulse Shaping Review. Intersymbol interference (ISI) Pulse shaping to reduce ISI Embracing ISI Line Codes and Pulse Shaping Review Line codes Pulse width and polarity Power spectral density Intersymbol interference (ISI) Pulse shaping to reduce ISI Embracing ISI Line Code Examples (review) on-off

More information

II - Baseband pulse transmission

II - Baseband pulse transmission II - Baseband pulse transmission 1 Introduction We discuss how to transmit digital data symbols, which have to be converted into material form before they are sent or stored. In the sequel, we associate

More information

Principles of Communications

Principles of Communications Principles of Communications Chapter V: Representation and Transmission of Baseband Digital Signal Yongchao Wang Email: ychwang@mail.xidian.edu.cn Xidian University State Key Lab. on ISN November 18, 2012

More information

Example: Bipolar NRZ (non-return-to-zero) signaling

Example: Bipolar NRZ (non-return-to-zero) signaling Baseand Data Transmission Data are sent without using a carrier signal Example: Bipolar NRZ (non-return-to-zero signaling is represented y is represented y T A -A T : it duration is represented y BT. Passand

More information

Digital Baseband Systems. Reference: Digital Communications John G. Proakis

Digital Baseband Systems. Reference: Digital Communications John G. Proakis Digital Baseband Systems Reference: Digital Communications John G. Proais Baseband Pulse Transmission Baseband digital signals - signals whose spectrum extend down to or near zero frequency. Model of the

More information

ELEN E4810: Digital Signal Processing Topic 11: Continuous Signals. 1. Sampling and Reconstruction 2. Quantization

ELEN E4810: Digital Signal Processing Topic 11: Continuous Signals. 1. Sampling and Reconstruction 2. Quantization ELEN E4810: Digital Signal Processing Topic 11: Continuous Signals 1. Sampling and Reconstruction 2. Quantization 1 1. Sampling & Reconstruction DSP must interact with an analog world: A to D D to A x(t)

More information

Es e j4φ +4N n. 16 KE s /N 0. σ 2ˆφ4 1 γ s. p(φ e )= exp 1 ( 2πσ φ b cos N 2 φ e 0

Es e j4φ +4N n. 16 KE s /N 0. σ 2ˆφ4 1 γ s. p(φ e )= exp 1 ( 2πσ φ b cos N 2 φ e 0 Problem 6.15 : he received signal-plus-noise vector at the output of the matched filter may be represented as (see (5-2-63) for example) : r n = E s e j(θn φ) + N n where θ n =0,π/2,π,3π/2 for QPSK, and

More information

2A1H Time-Frequency Analysis II

2A1H Time-Frequency Analysis II 2AH Time-Frequency Analysis II Bugs/queries to david.murray@eng.ox.ac.uk HT 209 For any corrections see the course page DW Murray at www.robots.ox.ac.uk/ dwm/courses/2tf. (a) A signal g(t) with period

More information

A Family of Nyquist Filters Based on Generalized Raised-Cosine Spectra

A Family of Nyquist Filters Based on Generalized Raised-Cosine Spectra Proc. Biennial Symp. Commun. (Kingston, Ont.), pp. 3-35, June 99 A Family of Nyquist Filters Based on Generalized Raised-Cosine Spectra Nader Sheikholeslami Peter Kabal Department of Electrical Engineering

More information

Consider a 2-D constellation, suppose that basis signals =cosine and sine. Each constellation symbol corresponds to a vector with two real components

Consider a 2-D constellation, suppose that basis signals =cosine and sine. Each constellation symbol corresponds to a vector with two real components TUTORIAL ON DIGITAL MODULATIONS Part 3: 4-PSK [2--26] Roberto Garello, Politecnico di Torino Free download (for personal use only) at: www.tlc.polito.it/garello Quadrature modulation Consider a 2-D constellation,

More information

Sample Problems for the 9th Quiz

Sample Problems for the 9th Quiz Sample Problems for the 9th Quiz. Draw the line coded signal waveform of the below line code for 0000. (a Unipolar nonreturn-to-zero (NRZ signaling (b Polar nonreturn-to-zero (NRZ signaling (c Unipolar

More information

EE 661: Modulation Theory Solutions to Homework 6

EE 661: Modulation Theory Solutions to Homework 6 EE 66: Modulation Theory Solutions to Homework 6. Solution to problem. a) Binary PAM: Since 2W = 4 KHz and β = 0.5, the minimum T is the solution to (+β)/(2t ) = W = 2 0 3 Hz. Thus, we have the maximum

More information

FBMC/OQAM transceivers for 5G mobile communication systems. François Rottenberg

FBMC/OQAM transceivers for 5G mobile communication systems. François Rottenberg FBMC/OQAM transceivers for 5G mobile communication systems François Rottenberg Modulation Wikipedia definition: Process of varying one or more properties of a periodic waveform, called the carrier signal,

More information

1. Band-pass modulations. 2. 2D signal set. 3. Basis signals p(t)cos(2πf 0 t) e p(t)sin(2πf 0 t) 4. Costellation = m signals, equidistant on a circle

1. Band-pass modulations. 2. 2D signal set. 3. Basis signals p(t)cos(2πf 0 t) e p(t)sin(2πf 0 t) 4. Costellation = m signals, equidistant on a circle TUTORIAL ON DIGITAL MODULATIONS Part 14: m-psk [last modified: 2010-11-25] Roerto Garello, Politecnico di Torino Free download at: www.tlc.polito.it/garello (personal use only) 1 m-psk modulations 1. Band-pass

More information

EE4061 Communication Systems

EE4061 Communication Systems EE4061 Communication Systems Week 11 Intersymbol Interference Nyquist Pulse Shaping 0 c 2015, Georgia Institute of Technology (lect10 1) Intersymbol Interference (ISI) Tx filter channel Rx filter a δ(t-nt)

More information

Digital Band-pass Modulation PROF. MICHAEL TSAI 2011/11/10

Digital Band-pass Modulation PROF. MICHAEL TSAI 2011/11/10 Digital Band-pass Modulation PROF. MICHAEL TSAI 211/11/1 Band-pass Signal Representation a t g t General form: 2πf c t + φ t g t = a t cos 2πf c t + φ t Envelope Phase Envelope is always non-negative,

More information

Revision of Lecture 4

Revision of Lecture 4 Revision of Lecture 4 We have discussed all basic components of MODEM Pulse shaping Tx/Rx filter pair Modulator/demodulator Bits map symbols Discussions assume ideal channel, and for dispersive channel

More information

ADAPTIVE EQUALIZATION AT MULTI-GHZ DATARATES

ADAPTIVE EQUALIZATION AT MULTI-GHZ DATARATES ADAPTIVE EQUALIZATION AT MULTI-GHZ DATARATES Department of Electrical Engineering Indian Institute of Technology, Madras 1st February 2007 Outline Introduction. Approaches to electronic mitigation - ADC

More information

LOPE3202: Communication Systems 10/18/2017 2

LOPE3202: Communication Systems 10/18/2017 2 By Lecturer Ahmed Wael Academic Year 2017-2018 LOPE3202: Communication Systems 10/18/2017 We need tools to build any communication system. Mathematics is our premium tool to do work with signals and systems.

More information

Principles of Communications

Principles of Communications Principles of Communications Weiyao Lin, PhD Shanghai Jiao Tong University Chapter 4: Analog-to-Digital Conversion Textbook: 7.1 7.4 2010/2011 Meixia Tao @ SJTU 1 Outline Analog signal Sampling Quantization

More information

Optimized Impulses for Multicarrier Offset-QAM

Optimized Impulses for Multicarrier Offset-QAM Optimized Impulses for ulticarrier Offset-QA Stephan Pfletschinger, Joachim Speidel Institut für Nachrichtenübertragung Universität Stuttgart, Pfaffenwaldring 47, D-7469 Stuttgart, Germany Abstract The

More information

FROM ANALOGUE TO DIGITAL

FROM ANALOGUE TO DIGITAL SIGNALS AND SYSTEMS: PAPER 3C1 HANDOUT 7. Dr David Corrigan 1. Electronic and Electrical Engineering Dept. corrigad@tcd.ie www.mee.tcd.ie/ corrigad FROM ANALOGUE TO DIGITAL To digitize signals it is necessary

More information

a) Find the compact (i.e. smallest) basis set required to ensure sufficient statistics.

a) Find the compact (i.e. smallest) basis set required to ensure sufficient statistics. Digital Modulation and Coding Tutorial-1 1. Consider the signal set shown below in Fig.1 a) Find the compact (i.e. smallest) basis set required to ensure sufficient statistics. b) What is the minimum Euclidean

More information

Analog Electronics 2 ICS905

Analog Electronics 2 ICS905 Analog Electronics 2 ICS905 G. Rodriguez-Guisantes Dépt. COMELEC http://perso.telecom-paristech.fr/ rodrigez/ens/cycle_master/ November 2016 2/ 67 Schedule Radio channel characteristics ; Analysis and

More information

Digital Communications

Digital Communications Digital Communications Chapter 5 Carrier and Symbol Synchronization Po-Ning Chen, Professor Institute of Communications Engineering National Chiao-Tung University, Taiwan Digital Communications Ver 218.7.26

More information

8 PAM BER/SER Monte Carlo Simulation

8 PAM BER/SER Monte Carlo Simulation xercise.1 8 PAM BR/SR Monte Carlo Simulation - Simulate a 8 level PAM communication system and calculate bit and symbol error ratios (BR/SR). - Plot the calculated and simulated SR and BR curves. - Plot

More information

DIGITAL COMMUNICATIONS. IAGlover and P M Grant. Prentice Hall 1997 PROBLEM SOLUTIONS CHAPTER 6

DIGITAL COMMUNICATIONS. IAGlover and P M Grant. Prentice Hall 1997 PROBLEM SOLUTIONS CHAPTER 6 DIGITAL COMMUNICATIONS IAGlover and P M Grant Prentice Hall 997 PROBLEM SOLUTIONS CHAPTER 6 6. P e erf V σ erf. 5 +. 5 0.705 [ erf (. 009)] [ 0. 999 979 ]. 0 0 5 The optimum DC level is zero. For equiprobable

More information

Projects in Wireless Communication Lecture 1

Projects in Wireless Communication Lecture 1 Projects in Wireless Communication Lecture 1 Fredrik Tufvesson/Fredrik Rusek Department of Electrical and Information Technology Lund University, Sweden Lund, Sept 2018 Outline Introduction to the course

More information

Lecture 27 Frequency Response 2

Lecture 27 Frequency Response 2 Lecture 27 Frequency Response 2 Fundamentals of Digital Signal Processing Spring, 2012 Wei-Ta Chu 2012/6/12 1 Application of Ideal Filters Suppose we can generate a square wave with a fundamental period

More information

IB Paper 6: Signal and Data Analysis

IB Paper 6: Signal and Data Analysis IB Paper 6: Signal and Data Analysis Handout 5: Sampling Theory S Godsill Signal Processing and Communications Group, Engineering Department, Cambridge, UK Lent 2015 1 / 85 Sampling and Aliasing All of

More information

Direct-Sequence Spread-Spectrum

Direct-Sequence Spread-Spectrum Chapter 3 Direct-Sequence Spread-Spectrum In this chapter we consider direct-sequence spread-spectrum systems. Unlike frequency-hopping, a direct-sequence signal occupies the entire bandwidth continuously.

More information

Lecture 2. Fading Channel

Lecture 2. Fading Channel 1 Lecture 2. Fading Channel Characteristics of Fading Channels Modeling of Fading Channels Discrete-time Input/Output Model 2 Radio Propagation in Free Space Speed: c = 299,792,458 m/s Isotropic Received

More information

Communication Theory Summary of Important Definitions and Results

Communication Theory Summary of Important Definitions and Results Signal and system theory Convolution of signals x(t) h(t) = y(t): Fourier Transform: Communication Theory Summary of Important Definitions and Results X(ω) = X(ω) = y(t) = X(ω) = j x(t) e jωt dt, 0 Properties

More information

2A1H Time-Frequency Analysis II Bugs/queries to HT 2011 For hints and answers visit dwm/courses/2tf

2A1H Time-Frequency Analysis II Bugs/queries to HT 2011 For hints and answers visit   dwm/courses/2tf Time-Frequency Analysis II (HT 20) 2AH 2AH Time-Frequency Analysis II Bugs/queries to david.murray@eng.ox.ac.uk HT 20 For hints and answers visit www.robots.ox.ac.uk/ dwm/courses/2tf David Murray. A periodic

More information

Timbral, Scale, Pitch modifications

Timbral, Scale, Pitch modifications Introduction Timbral, Scale, Pitch modifications M2 Mathématiques / Vision / Apprentissage Audio signal analysis, indexing and transformation Page 1 / 40 Page 2 / 40 Modification of playback speed Modifications

More information

ECS332: Midterm Examination (Set I) Seat

ECS332: Midterm Examination (Set I) Seat Sirindhorn International Institute of Technology Thammasat University at Rangsit School of Information, Computer and Communication Technology ECS33: Midterm Examination (Set I) COURSE : ECS33 (Principles

More information

7 The Waveform Channel

7 The Waveform Channel 7 The Waveform Channel The waveform transmitted by the digital demodulator will be corrupted by the channel before it reaches the digital demodulator in the receiver. One important part of the channel

More information

GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING Final Examination - Fall 2015 EE 4601: Communication Systems

GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING Final Examination - Fall 2015 EE 4601: Communication Systems GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING Final Examination - Fall 2015 EE 4601: Communication Systems Aids Allowed: 2 8 1/2 X11 crib sheets, calculator DATE: Tuesday

More information

Data Detection for Controlled ISI. h(nt) = 1 for n=0,1 and zero otherwise.

Data Detection for Controlled ISI. h(nt) = 1 for n=0,1 and zero otherwise. Data Detection for Controlled ISI *Symbol by symbol suboptimum detection For the duobinary signal pulse h(nt) = 1 for n=0,1 and zero otherwise. The samples at the output of the receiving filter(demodulator)

More information

This examination consists of 11 pages. Please check that you have a complete copy. Time: 2.5 hrs INSTRUCTIONS

This examination consists of 11 pages. Please check that you have a complete copy. Time: 2.5 hrs INSTRUCTIONS THE UNIVERSITY OF BRITISH COLUMBIA Department of Electrical and Computer Engineering EECE 564 Detection and Estimation of Signals in Noise Final Examination 6 December 2006 This examination consists of

More information

NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY DEPARTMENT OF ELECTRONICS AND TELECOMMUNICATIONS

NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY DEPARTMENT OF ELECTRONICS AND TELECOMMUNICATIONS page 1 of 5 (+ appendix) NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY DEPARTMENT OF ELECTRONICS AND TELECOMMUNICATIONS Contact during examination: Name: Magne H. Johnsen Tel.: 73 59 26 78/930 25 534

More information

ECS 332: Principles of Communications 2012/1. HW 4 Due: Sep 7

ECS 332: Principles of Communications 2012/1. HW 4 Due: Sep 7 ECS 332: Principles of Communications 2012/1 HW 4 Due: Sep 7 Lecturer: Prapun Suksompong, Ph.D. Instructions (a) ONE part of a question will be graded (5 pt). Of course, you do not know which part will

More information

Homework 4. May An LTI system has an input, x(t) and output y(t) related through the equation y(t) = t e (t t ) x(t 2)dt

Homework 4. May An LTI system has an input, x(t) and output y(t) related through the equation y(t) = t e (t t ) x(t 2)dt Homework 4 May 2017 1. An LTI system has an input, x(t) and output y(t) related through the equation y(t) = t e (t t ) x(t 2)dt Determine the impulse response of the system. Rewriting as y(t) = t e (t

More information

3.2 Complex Sinusoids and Frequency Response of LTI Systems

3.2 Complex Sinusoids and Frequency Response of LTI Systems 3. Introduction. A signal can be represented as a weighted superposition of complex sinusoids. x(t) or x[n]. LTI system: LTI System Output = A weighted superposition of the system response to each complex

More information

Solutions to Problems in Chapter 4

Solutions to Problems in Chapter 4 Solutions to Problems in Chapter 4 Problems with Solutions Problem 4. Fourier Series of the Output Voltage of an Ideal Full-Wave Diode Bridge Rectifier he nonlinear circuit in Figure 4. is a full-wave

More information

Carrier frequency estimation. ELEC-E5410 Signal processing for communications

Carrier frequency estimation. ELEC-E5410 Signal processing for communications Carrier frequency estimation ELEC-E54 Signal processing for communications Contents. Basic system assumptions. Data-aided DA: Maximum-lielihood ML estimation of carrier frequency 3. Data-aided: Practical

More information

Module 4. Signal Representation and Baseband Processing. Version 2 ECE IIT, Kharagpur

Module 4. Signal Representation and Baseband Processing. Version 2 ECE IIT, Kharagpur Module Signal Representation and Baseband Processing Version ECE II, Kharagpur Lesson 8 Response of Linear System to Random Processes Version ECE II, Kharagpur After reading this lesson, you will learn

More information

Chapter 5 Frequency Domain Analysis of Systems

Chapter 5 Frequency Domain Analysis of Systems Chapter 5 Frequency Domain Analysis of Systems CT, LTI Systems Consider the following CT LTI system: xt () ht () yt () Assumption: the impulse response h(t) is absolutely integrable, i.e., ht ( ) dt< (this

More information

EE4601 Communication Systems

EE4601 Communication Systems EE4601 Communication Systems Week 13 Linear Zero Forcing Equalization 0 c 2012, Georgia Institute of Technology (lect13 1) Equalization The cascade of the transmit filter g(t), channel c(t), receiver filter

More information

ENSC327 Communications Systems 2: Fourier Representations. Jie Liang School of Engineering Science Simon Fraser University

ENSC327 Communications Systems 2: Fourier Representations. Jie Liang School of Engineering Science Simon Fraser University ENSC327 Communications Systems 2: Fourier Representations Jie Liang School of Engineering Science Simon Fraser University 1 Outline Chap 2.1 2.5: Signal Classifications Fourier Transform Dirac Delta Function

More information

Chapter 12 Variable Phase Interpolation

Chapter 12 Variable Phase Interpolation Chapter 12 Variable Phase Interpolation Contents Slide 1 Reason for Variable Phase Interpolation Slide 2 Another Need for Interpolation Slide 3 Ideal Impulse Sampling Slide 4 The Sampling Theorem Slide

More information

2.1 Basic Concepts Basic operations on signals Classication of signals

2.1 Basic Concepts Basic operations on signals Classication of signals Haberle³me Sistemlerine Giri³ (ELE 361) 9 Eylül 2017 TOBB Ekonomi ve Teknoloji Üniversitesi, Güz 2017-18 Dr. A. Melda Yüksel Turgut & Tolga Girici Lecture Notes Chapter 2 Signals and Linear Systems 2.1

More information

L6: Short-time Fourier analysis and synthesis

L6: Short-time Fourier analysis and synthesis L6: Short-time Fourier analysis and synthesis Overview Analysis: Fourier-transform view Analysis: filtering view Synthesis: filter bank summation (FBS) method Synthesis: overlap-add (OLA) method STFT magnitude

More information

VID3: Sampling and Quantization

VID3: Sampling and Quantization Video Transmission VID3: Sampling and Quantization By Prof. Gregory D. Durgin copyright 2009 all rights reserved Claude E. Shannon (1916-2001) Mathematician and Electrical Engineer Worked for Bell Labs

More information

Chapter 5 Frequency Domain Analysis of Systems

Chapter 5 Frequency Domain Analysis of Systems Chapter 5 Frequency Domain Analysis of Systems CT, LTI Systems Consider the following CT LTI system: xt () ht () yt () Assumption: the impulse response h(t) is absolutely integrable, i.e., ht ( ) dt< (this

More information

EE4512 Analog and Digital Communications Chapter 4. Chapter 4 Receiver Design

EE4512 Analog and Digital Communications Chapter 4. Chapter 4 Receiver Design Chapter 4 Receiver Design Chapter 4 Receiver Design Probability of Bit Error Pages 124-149 149 Probability of Bit Error The low pass filtered and sampled PAM signal results in an expression for the probability

More information

LECTURE 16 AND 17. Digital signaling on frequency selective fading channels. Notes Prepared by: Abhishek Sood

LECTURE 16 AND 17. Digital signaling on frequency selective fading channels. Notes Prepared by: Abhishek Sood ECE559:WIRELESS COMMUNICATION TECHNOLOGIES LECTURE 16 AND 17 Digital signaling on frequency selective fading channels 1 OUTLINE Notes Prepared by: Abhishek Sood In section 2 we discuss the receiver design

More information

Carrier Transmission. The transmitted signal is y(t) = k a kh(t kt ). What is the bandwidth? More generally, what is its Fourier transform?

Carrier Transmission. The transmitted signal is y(t) = k a kh(t kt ). What is the bandwidth? More generally, what is its Fourier transform? The transmitted signal is y(t) = k a kh(t kt ). What is the bandwidth? More generally, what is its Fourier transform? The baseband signal is y(t) = k a kh(t kt ). The power spectral density of the transmission

More information

SIGNAL SPACE CONCEPTS

SIGNAL SPACE CONCEPTS SIGNAL SPACE CONCEPTS TLT-5406/0 In this section we familiarize ourselves with the representation of discrete-time and continuous-time communication signals using the concepts of vector spaces. These concepts

More information

2016 Spring: The Final Exam of Digital Communications

2016 Spring: The Final Exam of Digital Communications 2016 Spring: The Final Exam of Digital Communications The total number of points is 131. 1. Image of Transmitter Transmitter L 1 θ v 1 As shown in the figure above, a car is receiving a signal from a remote

More information

EE303: Communication Systems

EE303: Communication Systems EE303: Communication Systems Professor A. Manikas Chair of Communications and Array Processing Imperial College London Introductory Concepts Prof. A. Manikas (Imperial College) EE303: Introductory Concepts

More information

SEISMIC WAVE PROPAGATION. Lecture 2: Fourier Analysis

SEISMIC WAVE PROPAGATION. Lecture 2: Fourier Analysis SEISMIC WAVE PROPAGATION Lecture 2: Fourier Analysis Fourier Series & Fourier Transforms Fourier Series Review of trigonometric identities Analysing the square wave Fourier Transform Transforms of some

More information

Communication Systems Lecture 21, 22. Dong In Kim School of Information & Comm. Eng. Sungkyunkwan University

Communication Systems Lecture 21, 22. Dong In Kim School of Information & Comm. Eng. Sungkyunkwan University Communication Systems Lecture 1, Dong In Kim School of Information & Comm. Eng. Sungkyunkwan University 1 Outline Linear Systems with WSS Inputs Noise White noise, Gaussian noise, White Gaussian noise

More information

This examination consists of 10 pages. Please check that you have a complete copy. Time: 2.5 hrs INSTRUCTIONS

This examination consists of 10 pages. Please check that you have a complete copy. Time: 2.5 hrs INSTRUCTIONS THE UNIVERSITY OF BRITISH COLUMBIA Department of Electrical and Computer Engineering EECE 564 Detection and Estimation of Signals in Noise Final Examination 08 December 2009 This examination consists of

More information

Physical Layer and Coding

Physical Layer and Coding Physical Layer and Coding Muriel Médard Professor EECS Overview A variety of physical media: copper, free space, optical fiber Unified way of addressing signals at the input and the output of these media:

More information

Power Spectral Density of Digital Modulation Schemes

Power Spectral Density of Digital Modulation Schemes Digital Communication, Continuation Course Power Spectral Density of Digital Modulation Schemes Mikael Olofsson Emil Björnson Department of Electrical Engineering ISY) Linköping University, SE-581 83 Linköping,

More information

ELECTRONICS & COMMUNICATIONS DIGITAL COMMUNICATIONS

ELECTRONICS & COMMUNICATIONS DIGITAL COMMUNICATIONS EC 32 (CR) Total No. of Questions :09] [Total No. of Pages : 02 III/IV B.Tech. DEGREE EXAMINATIONS, APRIL/MAY- 207 Second Semester ELECTRONICS & COMMUNICATIONS DIGITAL COMMUNICATIONS Time: Three Hours

More information

Multirate Digital Signal Processing

Multirate Digital Signal Processing Multirate Digital Signal Processing Basic Sampling Rate Alteration Devices Up-sampler - Used to increase the sampling rate by an integer factor Down-sampler - Used to decrease the sampling rate by an integer

More information

Radar Systems Engineering Lecture 3 Review of Signals, Systems and Digital Signal Processing

Radar Systems Engineering Lecture 3 Review of Signals, Systems and Digital Signal Processing Radar Systems Engineering Lecture Review of Signals, Systems and Digital Signal Processing Dr. Robert M. O Donnell Guest Lecturer Radar Systems Course Review Signals, Systems & DSP // Block Diagram of

More information

encoding without prediction) (Server) Quantization: Initial Data 0, 1, 2, Quantized Data 0, 1, 2, 3, 4, 8, 16, 32, 64, 128, 256

encoding without prediction) (Server) Quantization: Initial Data 0, 1, 2, Quantized Data 0, 1, 2, 3, 4, 8, 16, 32, 64, 128, 256 General Models for Compression / Decompression -they apply to symbols data, text, and to image but not video 1. Simplest model (Lossless ( encoding without prediction) (server) Signal Encode Transmit (client)

More information

References Ideal Nyquist Channel and Raised Cosine Spectrum Chapter 4.5, 4.11, S. Haykin, Communication Systems, Wiley.

References Ideal Nyquist Channel and Raised Cosine Spectrum Chapter 4.5, 4.11, S. Haykin, Communication Systems, Wiley. Baseand Data Transmission III Reerences Ideal yquist Channel and Raised Cosine Spectrum Chapter 4.5, 4., S. Haykin, Communication Systems, iley. Equalization Chapter 9., F. G. Stremler, Communication Systems,

More information

MATHEMATICAL TOOLS FOR DIGITAL TRANSMISSION ANALYSIS

MATHEMATICAL TOOLS FOR DIGITAL TRANSMISSION ANALYSIS ch03.qxd 1/9/03 09:14 AM Page 35 CHAPTER 3 MATHEMATICAL TOOLS FOR DIGITAL TRANSMISSION ANALYSIS 3.1 INTRODUCTION The study of digital wireless transmission is in large measure the study of (a) the conversion

More information

2.161 Signal Processing: Continuous and Discrete Fall 2008

2.161 Signal Processing: Continuous and Discrete Fall 2008 MIT OpenCourseWare http://ocw.mit.edu 2.161 Signal Processing: Continuous and Discrete Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Massachusetts

More information

2. SPECTRAL ANALYSIS APPLIED TO STOCHASTIC PROCESSES

2. SPECTRAL ANALYSIS APPLIED TO STOCHASTIC PROCESSES 2. SPECTRAL ANALYSIS APPLIED TO STOCHASTIC PROCESSES 2.0 THEOREM OF WIENER- KHINTCHINE An important technique in the study of deterministic signals consists in using harmonic functions to gain the spectral

More information

RADIO SYSTEMS ETIN15. Lecture no: Equalization. Ove Edfors, Department of Electrical and Information Technology

RADIO SYSTEMS ETIN15. Lecture no: Equalization. Ove Edfors, Department of Electrical and Information Technology RADIO SYSTEMS ETIN15 Lecture no: 8 Equalization Ove Edfors, Department of Electrical and Information Technology Ove.Edfors@eit.lth.se Contents Inter-symbol interference Linear equalizers Decision-feedback

More information

Continuous Time Signal Analysis: the Fourier Transform. Lathi Chapter 4

Continuous Time Signal Analysis: the Fourier Transform. Lathi Chapter 4 Continuous Time Signal Analysis: the Fourier Transform Lathi Chapter 4 Topics Aperiodic signal representation by the Fourier integral (CTFT) Continuous-time Fourier transform Transforms of some useful

More information

Signals and Systems: Part 2

Signals and Systems: Part 2 Signals and Systems: Part 2 The Fourier transform in 2πf Some important Fourier transforms Some important Fourier transform theorems Convolution and Modulation Ideal filters Fourier transform definitions

More information

Summary II: Modulation and Demodulation

Summary II: Modulation and Demodulation Summary II: Modulation and Demodulation Instructor : Jun Chen Department of Electrical and Computer Engineering, McMaster University Room: ITB A1, ext. 0163 Email: junchen@mail.ece.mcmaster.ca Website:

More information

Mobile Communications (KECE425) Lecture Note Prof. Young-Chai Ko

Mobile Communications (KECE425) Lecture Note Prof. Young-Chai Ko Mobile Communications (KECE425) Lecture Note 20 5-19-2014 Prof Young-Chai Ko Summary Complexity issues of diversity systems ADC and Nyquist sampling theorem Transmit diversity Channel is known at the transmitter

More information

Channel capacity. Outline : 1. Source entropy 2. Discrete memoryless channel 3. Mutual information 4. Channel capacity 5.

Channel capacity. Outline : 1. Source entropy 2. Discrete memoryless channel 3. Mutual information 4. Channel capacity 5. Channel capacity Outline : 1. Source entropy 2. Discrete memoryless channel 3. Mutual information 4. Channel capacity 5. Exercices Exercise session 11 : Channel capacity 1 1. Source entropy Given X a memoryless

More information

EE123 Digital Signal Processing

EE123 Digital Signal Processing EE123 Digital Signal Processing Lecture 19 Practical ADC/DAC Ideal Anti-Aliasing ADC A/D x c (t) Analog Anti-Aliasing Filter HLP(jΩ) sampler t = nt x[n] =x c (nt ) Quantizer 1 X c (j ) and s < 2 1 T X

More information

Lecture 7: Wireless Channels and Diversity Advanced Digital Communications (EQ2410) 1

Lecture 7: Wireless Channels and Diversity Advanced Digital Communications (EQ2410) 1 Wireless : Wireless Advanced Digital Communications (EQ2410) 1 Thursday, Feb. 11, 2016 10:00-12:00, B24 1 Textbook: U. Madhow, Fundamentals of Digital Communications, 2008 1 / 15 Wireless Lecture 1-6 Equalization

More information

4.1 Introduction. 2πδ ω (4.2) Applications of Fourier Representations to Mixed Signal Classes = (4.1)

4.1 Introduction. 2πδ ω (4.2) Applications of Fourier Representations to Mixed Signal Classes = (4.1) 4.1 Introduction Two cases of mixed signals to be studied in this chapter: 1. Periodic and nonperiodic signals 2. Continuous- and discrete-time signals Other descriptions: Refer to pp. 341-342, textbook.

More information

Fundamentals of PLLs (III)

Fundamentals of PLLs (III) Phase-Locked Loops Fundamentals of PLLs (III) Ching-Yuan Yang National Chung-Hsing University Department of Electrical Engineering Phase transfer function in linear model i (s) Kd e (s) Open-loop transfer

More information

Chapter 10. Timing Recovery. March 12, 2008

Chapter 10. Timing Recovery. March 12, 2008 Chapter 10 Timing Recovery March 12, 2008 b[n] coder bit/ symbol transmit filter, pt(t) Modulator Channel, c(t) noise interference form other users LNA/ AGC Demodulator receive/matched filter, p R(t) sampler

More information

Homework 8 Solutions

Homework 8 Solutions EECS Signals & Systems University of California, Berkeley: Fall 7 Ramchandran November, 7 Homework 8 Solutions Problem OWN 8.47 (Effects from loss of synchronization.) In this problem we assume that c

More information

Analog Digital Sampling & Discrete Time Discrete Values & Noise Digital-to-Analog Conversion Analog-to-Digital Conversion

Analog Digital Sampling & Discrete Time Discrete Values & Noise Digital-to-Analog Conversion Analog-to-Digital Conversion Analog Digital Sampling & Discrete Time Discrete Values & Noise Digital-to-Analog Conversion Analog-to-Digital Conversion 6.082 Fall 2006 Analog Digital, Slide Plan: Mixed Signal Architecture volts bits

More information

R. Garello. Tutorial on digital modulations - Part 9b m-pam [ ] 2

R. Garello. Tutorial on digital modulations - Part 9b m-pam [ ] 2 TUTORIAL ON DIGITAL MODULATIONS Part 9: m-pam [2010-1-26] 26] Roerto Garello, Politecnico di Torino Free download at: www.tlc.polito.it/garello (personal use only) 1 m-pam constellations: characteristics

More information

A First Course in Digital Communications

A First Course in Digital Communications A First Course in Digital Communications Ha H. Nguyen and E. Shwedyk February 9 A First Course in Digital Communications 1/46 Introduction There are benefits to be gained when M-ary (M = 4 signaling methods

More information

GATE EE Topic wise Questions SIGNALS & SYSTEMS

GATE EE Topic wise Questions SIGNALS & SYSTEMS www.gatehelp.com GATE EE Topic wise Questions YEAR 010 ONE MARK Question. 1 For the system /( s + 1), the approximate time taken for a step response to reach 98% of the final value is (A) 1 s (B) s (C)

More information

Modulation & Coding for the Gaussian Channel

Modulation & Coding for the Gaussian Channel Modulation & Coding for the Gaussian Channel Trivandrum School on Communication, Coding & Networking January 27 30, 2017 Lakshmi Prasad Natarajan Dept. of Electrical Engineering Indian Institute of Technology

More information