pcm noise and companding

7/21/2019 PCM Noise and Companding

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Chapter 3:

PCM Noise and Companding Quantization Noise

Signal to Noise Ratio PCM Telephone System

Nonuniform Quantization

Companding

Huseyin Bilgekul

Eeng360 Communication Systems IDepartment of Electrical and Electronic Engineering

Eastern Mediterranean ni!ersity


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#$e process of %uanti&ation can 'e interpreted as an additi!e noise

process(

) #$e signal to quantization noise ratio*S+,-./S+ is gi!en as

Quantization NoiseQuantization Noise

Signal

X

.uanti&ed Signal

XQ

.uanti&ation +oise

nQ

2!erage o4er5 * -

2!erage o4er5 Q

Q

XSNR

n=


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Effects of Noise on PCMEffects of Noise on PCM#4o main effects produce t$e noise or distortion in t$e CM output

7.uanti&ing noise t$at is caused 'y t$e M8step %uanti&er at t$e CM transmitter(7Bit errors in t$e reco!ered CM signal9 caused 'y c$annel noise and improper filtering(

) If t$e input analog signal is 'and limited and sampled fast enoug$ so t$at t$e aliasing noise on t$ereco!ered signal is negligi'le9 t$e ratio of t$e reco!ered analog peak signal po4er to t$e total a!eragenoise po4er is

) #$e ratio of t$e a!erage signal po4er to t$e a!erage noise po4eris

7Mis t$e num'er of %uanti&ed le!els used in t$e CM system(7Peis t$e pro'a'ility of 'it error in t$e reco!ered 'inary CM signal at t$e recei!er D2C 'efore it is con!erted

'ack into an analog signal(


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Effects of Quantizing NoiseEffects of Quantizing Noise

) IfPeis negligi'le9 t$ere are no 'it errors resulting from c$annel noise and no ISI9 t$e eak S+,resulting fromonly %uanti&ing error is

) #$e 2!erage S+,due to %uanti&ing errors is

) 2'o!e e%uations can 'e e;presses in deci'elsas9


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DESIGN O ! PCM SIGN!" O# $E"EP%ONE S&S$EMSDESIGN O ! PCM SIGN!" O# $E"EP%ONE S&S$EMS

) 2ssume t$at an analog audio !oice8fre%uency*@A- telep$one signal occupies a 'and from 300to 39:00H&( #$e signal is to 'e con!erted to a CM signal for transmission o!er a digitaltelep$one system( #$e minimum sampling fre%uency is ";3(: / 6( ksample/sec(

) #o 'e a'le to use of a lo48cost lo48pass antialiasing filter9 t$e @A signal is o!ersampled 4it$a sampling fre%uency of ksamplessec() #$is is t$e standard adopted 'y t$e nites States telep$one industry() 2ssume t$at eac$ sample !alues is represented 'y 'its t$en t$e 'it rate of t$e 'inary CM

signal is

) #$is 6:8k'its signal is called a DS80 signal *digital signal9 type &ero-(

) #$e minimum a'solute 'and4idt$ of t$e 'inary CM signal is

8

#$isBis for a sin;; type pulse sampling

CM" "

snfRB =


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DESIGN O ! PCM SIGN!" O# $E"EP%ONE S&S$EMSDESIGN O ! PCM SIGN!" O# $E"EP%ONE S&S$EMS

)


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Nonuniform QuantizationNonuniform Quantization

Many signals suc$ as speec$ $a!e a nonuniform distri'ution(

7#$e amplitude is more likely to 'e close to &ero t$an to 'e at $ig$er le!els(

Nonuniform quantizers$a!e une%ually spaced le!els

7#$e spacing can 'e c$osen to optimi&e t$e S+, for a particular type of signal(

" : 6

"

:

6

8"

8:

86

Input sample

X

Output sample

XQ

8"8:868

Example: Nonuniform 3 bit quantizer

d


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CompandingCompanding

) +onuniform %uanti&ers are difficult to make and e;pensi!e(

) 2n alternati!e is to first pass t$e speec$ signal t$roug$ anonlinearity 'efore %uanti&ing 4it$ a uniform %uanti&er(

) #$e nonlinearity causes t$e signal amplitude to 'e

Compressed(

7#$e input to t$e %uanti&er 4ill $a!e a more uniform

distri'ution(

) 2t t$e recei!er9 t$e signal isExpanded'y an in!erse to t$e

nonlinearity() #$e process of compressing and e;panding is called

Companding(


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'"a( Companding'"a( Companding

) #elep$ones in t$e (S(9 Canada and

Fapan use 8la4 companding

7


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Non )niform *uantizingNon )niform *uantizing) @oice signals are more likely to $a!e amplitudes near &ero t$an at e;treme peaks(

) Aor suc$ signals 4it$ non8uniform amplitude distri'ution %uanti&ing noise 4ill 'e$ig$er for amplitude !alues near &ero(

) 2 tec$ni%ue to increase amplitudes near &ero is called Companding(

Effect of non linear %uanti&ing can 'e

can 'e o'tained 'y first passing t$eanalog signal t$roug$ a compressor

and t$en t$roug$ a uniform %uanti&er(

xQ(

.

)

y

Uniform Quantizer

C*(-

x

Compressor

x


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2200 2300 2400 2500 2600 2700 2800 2900 3000-1

-0.5

0

0.5

1

2200 2300 2400 2500 2600 2700 2800 2900 3000-1

-0.5

0

0.5

1

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-1

-0.5

0

0.5

1

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-1

-0.5

0

0.5

1

E+amp,e:E+amp,e: ',a( Companding',a( Companding

xJnK/speec$ song

yJnK/C*xJnK-

Companded Signal

Segment of

xJnK

Segment of yJnK

Companded Signal

Close @ie4 of t$e Signal

, d! , d , d, C di


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!',a( and!',a( and ,a( Companding,a( Companding) #$ese t4o are standard companding met$ods() u8La4 is used in +ort$ 2merica and Fapan) 28La4 is used else4$ere to compress digital telep$one signals

N# f C dSN# f C d


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SN# of CompanderSN# of Compander)#$e output S+, is a function of input signal le!el for uniform %uanti&ing(

)But it is relati!ely insensiti!e for input le!el for a compander

SN# P f f C dSN# P f f C d


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SN# Performance of CompanderSN# Performance of Compander

)#$e output S+, is a function of input signal le!el for uniform %uanti&ing()But it is relati!ely insensiti!e for input le!el for a compander(

) = :(>>- "0Log*V/xrms- for niform .uanti&er@ is t$e peak signal le!el andxrmsis t$e rms !alue

) = :(>>- "0logJLn*1 N-K for N8la4 companding

) = :(>>- "0 logJ1 Ln 2K for 28la4 companding


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-./0 12'4ps PCM Computer modem-./0 12'4ps PCM Computer modem

) #$e @(0 C Modem transmits data at ?6k's from a C

!ia an analog signal on a dial8up telep$one line() 2 lawcompander is used in %uanti&ation 4it$ a !alue

for of "??(

) #$e modem clock is sync$roni&ed to t$e 8ksample sec

clock of t$e telep$one company() > 'its of t$e 'it CM are used to get a data rate of?6k's * Are%uencies 'elo4 300H& are omitted to get ridof t$e po4er line noise in $armonics of 60H&-(

) S+, of t$e line s$ould 'e at least ?"dB to operate on?6k'ps(

) If S+, is 'elo4 ?"dB t$e modem 4ill fall'ack to lo4erspeeds * 33(3 k'ps9 "(k'ps or ":k'ps-(

pcm noise and companding

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