Formatting and Baseband. Formatting & Baseband. Page 1. Formatting and Baseband Modulation. CSE4214 Digital Communications

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1 CSE4214 Digital Communication CSE4214 Digital Communication Chapter 2 Formatting Formatting and Baeband Modulation Formatting & Baeband Formatting and Baeband 3 4 Page 1 1

The reulting digital ymbol are then repreented by baeband waveform (Pule Modulation or Line Coding).

2 What i Formatting? Information can take either of the three form: 1. Textual information 2. Analog ignal 3. Digital data Before the ignal are tranmitted over a digital communication channel, an information bearing ignal mut be converted to digital ymbol (Formatting). The reulting digital ymbol are then repreented by baeband waveform (Pule Modulation or Line Coding). Block Diagram Block diagram repreenting formatting and tranmiion of baeband ignal. 5 6 Textual Data (1) Textual Data (2) American Standard Code for Information Interchange (ASCII) for encoding alphanumeric Extended Binary Coded Decimal Interchange Information (EBCDIC) for encoding alphanumeric Page 2 2

3 Meage and Symbol Meage and Symbol: Example n Textual meage comprie a equence of alphanumeric character. n Example: Hello, how are you. n Textual meage i converted into a equence of bit, i.e. bit tream or baeband ignal. n Symbol are formed by a group of k bit from a finite ymbol et of M=2 k uch ymbol. n A ytem uing a ymbol et ize of M i referred to a an M-ary ytem CSE4214 Digital Communication Formatting Analog Information Periodic Sampling n Typically, dicrete-time ignal are formed by periodically ampling a continuou-time ignal : x(n)=x a (nt ) The ampling interval T i the ampling period, and f =1/ T i the ampling frequency in ample per econd. n The ampling proce: x a (t) f =1/T x (t) Convert impule into ample x(n) S a (t) 12 Page 3 3

4 x a (t) Illutration of Ideal Sampling 0 T 2T 3T 4T 5T 6T 7T 8T 9T 10T 11T = a( t) δ ( t nt ) n= 0 T 2T 3T 4T 5T 6T 7T 8T 9T 10T 11T x ( t) = x ( t) ( t) = x ( t) δ ( t nt ) = x ( nt ) δ ( t nt ) a a a a n= n= 0 T 2T 3T 4T 5T 6T 7T 8T 9T 10T 11T Fourier Tranform of a CT Sampled Signal n Fourier tranform pair: X ( ω) = ( ) = 1 x( t) e jωt jωt x t X ( ω) e dω 2π n Fourier tranform of ampled ignal : n= dt 1 2π X ( ω) = X a( ω nω ), ω = T T π X ( ω) = X a( ω nω ), ω = T T n= n The Fourier tranform of the continuou-time ampled ignal X (ω) i a periodic function of ω coniting of a uperpoition of hifted replica of X a (ω), caled by 1/T. For ω > X a (ω) 2ω B The overlap < of the Fourier tranform of each of the term of the ampled ω ω B ignal i 0 ω called aliaing B X (ω) X (ω) n=-2 n=-2 n=-1 n=-1 1/T n=1 n=2 n=0 n=1 n=2 ω ω ω ω ω ω 0 ω B ω B ω 16 Page 4 4

Sampling Theorem : Example n A bandlimited continuou-time ignal, with highet frequency(bandwidth) B Hz, can be uniquely recovered from it ample provided that the ampling rate F 2B ample per econd.

5 Sampling Theorem : Example n A bandlimited continuou-time ignal, with highet frequency(bandwidth) B Hz, can be uniquely recovered from it ample provided that the ampling rate F 2B ample per econd. n The frequency F = 2B i called the Nyquit ampling frequency. n If the ignal i ampled at le than the Nyquit rate, then the aliaing occur Natural Sampling Illutration of Natural Sampling n Replace impule train in ideal ampling with a pule train p(t) (alo know a the gating waveform). n The pule train where n The pule train can be implemented by an on/off witch Page 5 5

6 Analog-to-Digital Converion n Component : anti-aliaing filter, ample and hold, analog-to-digital converter (quantization). Anti- Aliaing Filter Sample and Hold Block Diagram of an ADC Analog to Digital Anti-aliaing Filter n The role of anti-aliaing filter i to cut off the frequency component that i higher than the half of ampling frequency. n Ideally, the anti-aliaing filter hould have a lowpa frequency repone, 1, Ha( jω) = 0, Ω < Ω Ω Ω / 2 / 2 Such a brickwall filter can t be realized uing practical analog circuit, hence, mut be approximated. T T Anti-aliaing Filter Effect on Signal Band Anti-Aliaing Filter Deign X a ( jω) ( jω) 1 1/A 0 H a Ω p Ω T 2 Spectrum of aliaed component of input Ω 0 = ΩT Ω p Ω T Ω 23 n Requirement : 1. Approximate linear phae in paband n n 2. Paband edge > highet frequency in ignal 3. Stopband edge < half of ampling frequency Four type of analog filter 1. Butterworth filter : good paband, low roll-off 2. Chebyhev filter : good roll-off and linear phae 3. Elliptic filter : fat roll-off, non-linear phae 4. Beel filter : cloe to linear phae, wide tranitionband Deign can be done in Matlab 24 Page 6 6

7 Frequency Repone of 4 Type of Filter Sample and Hold n Sample and hold i the mot popular ampling method. n Involve two operation: n Sample and hold Sample and Hold Circuit Analog-to-Digital Converter n Sample the analog ignal at uniform interval and hold the ampled value after each ampling operation for ufficient time for accurate converion by the A/D converter. Input Clock Hold Sample + - Output n n Convert an analog ignal into a binary coded digital ignal. Type of A/D converter 1. Integrating converter 2. Succeive approximation converter 3. Flah converter 4. Folding A/D converter 5. Pipelined A/D converter Page 7 7

8 CSE4214 Digital Communication Quantization A/D Converion n Uniform quantizer n Peak ignal power to average quantization noie power i: S N n q 2 3L SNR increae a a function of the number of quantization level quared. 30 Example of Sampling Original analog waveform Natural-ampled data Quantized ample Sample and Hold 31 Pule Code Modulation (PCM) n In pule modulation, ome parameter of a pule train i varied in accordance with the ample value of a meage ignal. n Pule-amplitude modulation (PAM) n Amplitude of regularly paced pule are varied. n Pule-width modulation (PWM) n Width of the individual pule are varied. n Pule-poition modulation (PPM) n Poition of a pule relative to it original of occurrence i varied. n Pule modulation technique are till analog modulation. For digital communication of an analog ource, quantization of ampled value i needed. 32 Page 8 8

9 PCM PCM - Example n A PCM ignal i obtained from the quantized PAM ignal by encoding each quantized ample to a digital codeword n In binary PCM each quantized ample i digitally encoded into an R-bit binary codeword. n Binary digit of a PCM ignal can be tranmitted uing many efficient modulation cheme PCM Waveform Example Uniform Quantization (1) PCM equence Pule repreentation For mot voice communication, very low peech volume predominate. Large amplitude are very rare while low amplitude are more often Pule waveform Page 9 9

Uniform Quantization (2) Nonuniform Quantization (1) Uing a uniform quantizer for peech ignal provide coare quantization at low amplitude Nonuniform quantizer are ued for peech

Nonuniform quantization i achieved by the proce of companding followed by uniform quantization.

10 Uniform Quantization (2) Nonuniform Quantization (1) Uing a uniform quantizer for peech ignal provide coare quantization at low amplitude Nonuniform quantizer are ued for peech ignal, which provide coare quantization at high amplitude and fine quantization at low amplitude. Nonuniform quantization i achieved by the proce of companding followed by uniform quantization Nonuniform Quantization (2) Two commonly ued compander are: µ law compander A law compander A( x / xmax) x 1 [ ] ymax gn( x) 0 < loge 1+ µ ( x / xmax) 1+ log A x = gn( ) = log [ 1+ µ ] 1+ log [ ( / )] 1 max A y ymax x y e A x xmax x e e ymax gn( x) < 1 1+ loge A A xmax CSE4214 Digital Communication Baeband Tranmiion 39 Page

PCM Waveform Type PCM Coding (1) n Nonreturn-to-zero (NRZ) n NRZ i mot commonly ued PCM waveform n NRZ-L (L for level) n NRZ-M (M for

Multilevel binary 41 1 = 1 voltage level, 0=another voltage level 1 (mark)=change in level, 0 (pace) = no change in level A

Coding (2) Bit per PCM Word and Bit per Symbol n PCM word ize n How many bit hall we aign to each analog ample?

11 PCM Waveform Type PCM Coding (1) n Nonreturn-to-zero (NRZ) n NRZ i mot commonly ued PCM waveform n NRZ-L (L for level) n NRZ-M (M for mark) n NRZ-S (S for pace) n Return-to-zero (RZ) n Unipolar-RZ, bipolar-rz, RZ-AMI(alternate mark inverion) n Phae encoded n Multilevel binary 41 1 = 1 voltage level, 0=another voltage level 1 (mark)=change in level, 0 (pace) = no change in level A complement of NRZ-M 1=half-bit-wide pule, 0=no pule 1 and 0 by oppoite-level pule 1=equal amplitude alternating pule 0=no pule 42 PCM Coding (2) Bit per PCM Word and Bit per Symbol n PCM word ize n How many bit hall we aign to each analog ample? 43 e pv pp e max = q 2 = V pp 2L V pp 2L pv pp 2 l = L 1 2 p $ 1 ' l log 2 & ) % 2 p ( e: quantization error, V pp peak-to-peak voltage q: quantization level 44 Page 11 11

12 M-ary Pule-Modulation n Multilevel ignaling - a group of k-bit i tranmitted by M=2 k level pule. Activity 1 The information in an analog waveform, with maximum frequency f m =3kHz, i to be tranmitted over an M-ary PAM ytem, where the number of pule level i M=16. The quantization error i pecified not to exceed (+/-)1% of the peak-to-peak analog ignal. (a) What i the minimum number of bit/ample, or PCM word ize that hould be ued in digitizing the analog waveform? (b) What i the minimum required ampling rate, and what i the reulting bit tranmiion rate? (c) What i the PAM pule or ymbol tranmit rate? (d) If the tranmiion bandwidth equal 12 khz, determine the bandwidth efficiency for thi ytem Page

ECE 6640 Digital Communications

ECE 6640 Digital Communication Dr. Bradley J. Bazuin Aitant Profeor Department of Electrical and Computer Engineering College of Engineering and Applied Science Chapter. Formatting and Baeband Modulation.