a Systems
`
`ck Control Systems
`
`StS
`
`Principles of
`Communication Systems
`
`HERBERT TAUB
`
`Professor of Electrical Engineering
`The City College of the City University of New York
`
`\
`\
`DONALD L. SCHILLING
`Associate Professor of Electrical Engineering
`The City College of the City University of New York
`
`McGraw-Hill Book Company
`SAN FRANCISCO
`NEW YORK
`ST. LOUIS
`DUSSELDORF
`JOHANNESBURG
`KUALA LUMPUR
`LONDON
`MEXICO
`MONTREAL
`NEW DELHI
`PANAMA
`RIO DE JANEIRO
`SINGAPORE
`SYDNEY
`TORONTO
`
`ZTE, Exhibit 1017-0001
`
`ZTE, Exhibit 1017-0001
`
`

`

`
`
`Library of Congress Catalog Card Number 72-109255
`
`07-062923-4
`
` PRINCIPLES OF COMMUNICATION SYSTEMS
` 14151617181920 VBVB
`
`Copyright © 1971 by McGraw-Hill, Inc. All rights
`reserved. Printed in the United States of America. No
`part of this publication may be reproduced, stored in a
`retrieval system, or transmitted, in any form or by any
`means, electronic, mechanical, photocopying, recording, or
`otherwise, without the prior written permission of the
`publisher.
`
`876543
`
`
`ZTE, Exhibit 1017-0002
`
`ZTE, Exhibit 1017-0002
`
`

`

`?LES OF COMMUNICATION SYSTEMS
`
`ds to the circumstance where X
`
`ited to the random variable @ by
`as a uniform probability density
`¥ are not independent but that,
`rrelated.
`
`are dependent but uncorrelated.
`=oitoitoy+-+-.
`are independent and each has a
`:1. Find and plot the proba-
`ta.
`— Xe sin wot is a random process.
`variables each with zero mean and
`
`indom process, with E(M(t)) = 0
`
`lary?
`We such that fa(8) = 1/27, —7 <
`wot + 9)) = Mo/2.
`Is Z(t) now
`
`‘al density G(f) = n/2for —0 <
`gh a low-pass filter which has a
`ad H(f) = O otherwise. Find the
`output of the filter.
`2d through a low-pass RC network
`
`output noise of the network.
`
`n to the Theory of Statistics,”
`:, 1963.
`3inn and Company, Boston,1956.
`bles, and Stochastic Processes,”
`
`3
`Amplitude-modulation Systems
`
`One of the basic problems of communication engineering is the design
`and analysis of systems which allow many individual messages to be
`transmitted simultaneously over a single communication channel. A
`method by which such multiple transmission, called multiplexing, may
`be achieved consists in translating each message to a different position
`in the frequency spectrum. Such multiplexing is called frequency multi-
`plecing. The individual message can eventually be separated by filtering.
`Frequency multiplexing involves the use of an auxiliary waveform, usually
`sinusoidal, called a carrier. The operations performed on thesignal to
`achieve frequency multiplexing results in the generation of a waveform
`which may be described as the carrier modified in that its amplitude,
`frequency, or phase, individually or in combination, varies with time.
`Such a modified carrier is called a modulated carrier.
`In some cases the
`modulation is related simply to the message; in other cases the relation-
`ship is quite complicated.
`In this chapter, we discuss the generation and
`characteristics of amplitude-modulated carrier waveforms.!
`
`ZTE, Exhibit 1017-0003
`
`ZTE, Exhibit 1017-0003
`
`

`

`82
`
`PRINCIPLES OF COMMUNICATION SYSTEMS
`
`3.1 FREQUENCY TRANSLATION
`It is often advantageous and convenient, in processing a signal in a com-
`munications system, to translate the signal from one region in the fre-
`quency domain to another region. Suppose that a signal is bandlimited,
`or nearly so, to the frequency range extending from a frequencyf; to a
`frequency fo. The process of frequency translation is one in which the
`original signal is replaced with a new signal whose spectral range extends
`from jf; to fz and which new signal bears, in recoverable form, the same
`information as was borne by theoriginal signal. We discuss now a num-
`ber of useful purposes which may be served by frequency translation.
`
`FREQUENCY MULTIPLEXING
`Suppose that we haveseveral different signals, all of which encompassthe
`same spectral range. Let it be required that all these signals be trans-
`mitted along a single communications channel in such a manner that, at
`the receiving end, the signals be separately recoverable and distinguish-
`able from each other.
`Thesingle channel may be a single pair of wires
`or the free space that separates one radio antenna from another. Such
`multiple transmissions,i.e., multiplexing, may be achieved by translating
`each oneof theoriginal signals to a different fréquency range. Suppose,
`say, that one signalis translated to the frequency range f; to f;, the second
`to the range f;’ to fy’, and so on.
`If these new frequency ranges do not
`overlap, then the signal may be separated at the receiving end by appro-
`priate bandpassfilters, and the outputsof the filters processed to recover
`the original signals.
`
`PRACTICABILITY OF ANTENNAS
`
`When free space is the communications channel, antennas radiate and
`receive the signal.
`It turns out that antennas operate effectively only
`when their dimensions are of the order of magnitude of the wavelength
`of the signal being transmitted. A signal of frequency 1 kHz (an audio
`tone) corresponds to a wavelength of 300,000 m, an entirely impractical
`length. The required length may be reduced to the point of practicability
`by translating the audio toneto a higher frequency.
`
`NARROWBANDING
`
`Returning to the matter of the antenna, just discussed, suppose that we
`wanted to transmit an audio signal directly from the antenna, and that
`the inordinate length of the antenna were no problem. We would still
`be left with a problem of another type. Let us assume that the audio
`range extends from, say, 50 to 10¢ Hz.
`Theratio of the highest audio
`
`AMPLITUDE-MODULATION SYSTE
`
`frequency to the lowest is
`at one end of the range w:
`other end.
`Suppose, howe
`so that it occupied the ra)
`Then the ratio of highest ts
`the processes of frequency
`band” signal into a “narrc
`veniently processed. The
`being used hereto refer not
`to the fractional change in
`
`COMMON PROCESSING
`
`It may happen that we m:
`similar in general characte
`will then be necessary, as 1
`quency range of our proces;
`range of the signal to be pr
`elaborate, it may well be wis
`in somefixed frequency ran;
`of each signal in turn to co
`
`3.2 A METHOD OF FR
`
`A signal may be translate
`signal with an auxiliary sir
`us considerinitially that th:
`
`Um(t) = Am COS wat =
`Ba (ofint $e
`
`in which A,, is the constan
`The two-sided spectral ar
`Fig. 3.2-la. The pattern .
`located at f =f, and at
`multiplication of v(t) with
`
`v.(é) = A. cosw,t = A
`= “ (erect + ew
`
`in which A, is the constant
`trigonometric identity cos ,
`
`ZTE, Exhibit 1017-0004
`
`ZTE, Exhibit 1017-0004
`
`

`

`°LES OF COMMUNICATION SYSTEMS
`
`1 processing a signal in a com-
`ul from one region in the fre-
`ie that a signal is bandlimited,
`ding from a frequency f, to a
`ranslation is one in which the
`| whose spectral range extends
`in recoverable form, the same
`mal. We discuss now a num-
`d by frequency translation.
`
`als, all of which encompass the
`‘hat all these signals be trans-
`ainel in such a mannerthat, at
`y recoverable and distinguish-
`may be a single pair of wires
`antenna from another. Such
`aay be achieved by translating
`at frequency range. Suppose,
`uency range f,to fy, the second
`3 new frequency ranges do not
`at the receiving end by appro-
`the filters processed to recover
`
`shannel, antennas radiate and
`ennas operate effectively only
`magnitude of the wavelength
`of frequency 1 kHz (an audio
`000 m, an entirely impractical
`ed to the pointof practicability
`requency.
`
`ust discussed, suppose that we
`ly from the antenna, and that
`>no problem. We would still
`Let us assume that the audio
`The ratio of the highest audio
`
`AMPLITUDE-MODULATION SYSTEMS
`
`83
`
`frequency to the lowest is 200. Therefore, an antenna suitable for use
`at one end of the range would be entirely too short or too long for the
`other end. Suppose, however, that the audio spectrum were translated
`so that it occupied the range, say, from (10° + 50) to (10° + 104) Hz.
`Thenthe ratio of highest to lowest frequency would be only 1.01. Thus
`the processes of frequency translation may be used to change a ‘‘wide-
`band”signal into a “narrowband” signal which may well be more con-
`veniently processed. The terms “wideband” and “narrowband” are
`being used here to refer not to an absolute range of frequencies but rather
`to the fractional change in frequency from one band edge to the other.
`
`COMMON PROCESSING
`
`It may happen that we may have to process, in turn, a numberof signals
`similar in general character but occupying different spectral ranges.
`It
`will then be necessary, as we go from signal to signal, to adjust the fre-
`quency range of our processing apparatus to correspond to the frequency
`range of the signal to be processed.
`If the processing apparatusis rather
`elaborate, it may well be wiser to leave the processing apparatus to operate
`in somefixed frequency range and instead to translate the frequency range
`of each signal in turn to correspond to this fixed frequency.
`\
`\
`
`3.2 A METHOD OF FREQUENCY TRANSLATION
`A signal may be translated to a new spectral range by multiplying the
`signal with an auxiliary sinusoidal signal. To illustrate the process, let
`us considerinitially that the signalis sinusoidal in waveform and given by
`Um(t) = Am COS mt = Am COS 2rfnt
`(3.2-1a)
`= = (eftmt 4 griitmt) = - (ef*Int 4. 6-i2t/n!)
`(3.2-1b)
`in which A,, is the constant amplitude and fn = wn/2m is the frequency.
`The two-sided spectral amplitude pattern of this signal
`is shown in
`Fig. 3.2-la. The pattern consists of two lines, each of amplitude A,,/2,
`located at f =f, and at f = —f,. Consider next
`the result of the
`multiplication of v»(#) with an auxiliary sinusoidal signal
`(8.2-2a)
`v(t) = A, cos wé = A, cos Irfjt
`(3.2-2)
`= Ot (int + ertid) = BE (git 4. git
`in which A,is the constant amplitude and f, is the frequency. Using the
`trigonometric identity cos a cos 6 = lgcos (a + 6) + lgcos (a — 8), we
`
`ZTE, Exhibit 1017-0005
`
`ZTE, Exhibit 1017-0005
`
`

`

`a4
`
`PRINCIPLES OF COMMUNICATION SYSTEMS
`
`AMPLITUDE-MODULATION SYSTEM
`
`Amplitude of
`spectral component
`
`:
`|
`An
`
`
` os
`
`|
`
`ss
`
`a -—-4-------- | |sape |
`
`Amplitude
`AnA,
`
`-f-f,
`
`-f
`
`-f+f,
`
`0
`
`h-f,
`
`f Gh,
`
`(a) Spectral pattern of Am cos wmt.
`Fig. 3.2-1
`product AmAe COS Wmt COS wel.
`
`(b) Spectral pattern of the
`
`have for the product v,.(#)v.(t)
`re
`
`Um(t)oc(t) = 5 * [eos (we + wm)é + cos (w. — wm)
`
`_ ieee (election4 grituctont
`|
`
`\
`f ei@e-omdt + g-Hwe-owt)
`
`(3.2-3a)
`
`(32-30)
`
`The new spectral amplitude pattern is shown in Fig. 3.2-1b. Observe that
`the two original spectral lines have been éranslated, both in the positive-
`frequency direction by amount f. and also in the negative-frequency
`direction by the same amount. There are now four spectral components
`resulting in two sinusoidal waveforms, one of frequency f. + fm and the
`other of frequency f. — fm. Note that while the product signal has
`four spectral components each of amplitude A,,A,/4, there are only two
`frequencies, and the amplitude of each sinusoidal component is 4n,A./2.
`A generalization of Fig. 3.2-1 is shown in Fig. 3.2-2. Here a signal
`is chosen which consists of a superposition of four sinusoidal signals, the
`highest in frequency having the frequency fu. Before translation by
`multiplication, the two-sided spectral pattern displays eight components
`centered around zero frequency. After multiplication, we find this
`spectral pattern translated both in the positive- and the negative-fre-
`quency directions. The 16 spectral componentsin this two-sided spectral
`pattern give rise to eight sinusoidal waveforms. While the original signal
`extends in range up to a frequency fy,the signal which results from multi-
`plication has sinusoidal components covering a range 2fm, from f. — fu
`to fo + fu.
`
`a
`7
`
`(b)
`
`F
`
`Amp
`
`Spectrum of signal
`before translation
`
`~~
`se
`
`hySeine=
`
`Fig. 3.2-2. An original signal con
`translated through multiplication
`symmetrically arranged about /..
`
`Finally, we consider in
`
`to be frenaiated may not be r
`sinusoidal components at sk
`the case if the signal were of
`the signal is represented in t
`transform, that is, in terms
`
`ce)
`
`ee
`
`~h
`“hth
`“haha
`(a) ‘The epeoteal dene
`Fis. 124°
`spectral density of m(t) cos 2zf.t.
`
`ZTE, Exhibit 1017-0006
`
`ZTE, Exhibit 1017-0006
`
`

`

`
`
`5 OF COMMUNICATION SYSTEMS
`
`AMPLITUDE-MODULATION SYSTEMS
`
`85
`
`if
`nent
`
`(a)
`
`Amplitude of spectral
`components
`
`Spectrum of signal
`before translation
`
`“hot Ets
`
`“hy
`
`9
`
`fy
`
`fo-tn fete
`
`Sf
`
`Fig. 3.2-2 An original signal consisting of four sinusoids of differing frequencies is
`translated through multiplication and becomes a signal containing eight frequencies
`symmetrically arranged aboutf..
`
`Finally, we consider in Fig. 3.2-3 the situation in which the signal
`to be translated may not be represented as a superposition of a numberof
`sinusoidal components at sharply defined frequencies. Such would be
`the case if the signal were of finite energy and nonperiodic.
`In this case
`the signal is represented in the frequency domain in terms of its Fourier
`transform, that is, in apatnd of its spectral density. Thus let the signal
`\
`|M (jw)|
`
`(a)
`
`~fy
`
`0
`
`fy
`
`f
`
`|F [m(£) Cos we #]|
`
`=f, =f,
`
`-h
`
`a +hy
`
`0
`
`f whe
`
`f
`
`f the
`
`(a) The spectral density |M(jw)| of a nonperiodic signal m(t).
`Fig. 3.23
`spectral density of m(t) cos 2xfct.
`
`(6) The
`
`af
`
`1 d
`
`y| f
`
`—
`
`it,
`
`e
`
`m
`f+f,
`
`(6)
`
`fF
`
`ih|1
`1I
`
`5) Spectral pattern of the
`
`3 (we — wWm)t]
`
`(3.2-3a)
`
`(W_-tm)t LgFW) t)
`
`(8.2-3b)
`
`in Fig. 3.2-1b. Observe that
`mslated, both in the positive-
`io in the negative-frequency
`1ow four spectral components
`of frequency fe + fm and the
`rhile the product signal has
`2 A»A./4, there are only two
`isoidal component is A,A./2.
`in Fig. 3.2-2. Here a signal
`of four sinusoidal signals, the
`y fu. Before translation by
`mm displays eight components
`multiplication, we find this
`ositive- and the negative-fre-
`rents in this two-sided spectral
`‘ms. While theoriginal signal
`ignal which results from multi-
`ing a range 2fm, from fe — fu
`
`
`
`ZTE, Exhibit 1017-0007
`
`ZTE, Exhibit 1017-0007
`
`

`

`Slee
`
`86
`
`PRINCIPLES OF COMMUNICATION SYSTEMS
`
`AMPLITUDE-MODULATION SYSTEMS
`
`Its Fourier trans-
`m(t) be bandlimited to the frequency range 0 to fw.
`is shown in Fig.
`form is M(jw) = S[m(t)]. The magnitude |J/(jw)|
`3.2-3a. The transform M(jw) is symmetrical about f = 0 since we
`assume that m(f) is areal signal. The spectral density of the signal which
`results when m(t) is multiplied by cos w,é is shown in Fig. 3.2-3b. This
`spectral pattern is deduced as an extension of the results shown in Figs.
`3.2-1 and 3,2-2, Alternatively, we may easily verify (Prob. 3.2-2) that
`if M(jw) = F[n(é)], then
`
`Flm(t) cos wel] = 14[M(jo + joc) + M(jo — jue)]
`
`(3.2-4)
`
`Thespectral range occupied by theoriginal signal is called the base-
`band frequency range or simply the baseband. On this basis, the original
`signal itself is referred to as the baseband signal. The operation of
`multiplying a signal with an auxiliary sinusoidal signal is called mixing
`or heterodyning.
`In the translated signal, the part of the signal which
`consists of spectral components above the auxiliary signal, in the range
`f.tofe + fr, is called the upper-sideband signal. The part of the signal
`which consists of spectral components below the auxiliary signal, in the
`range f, — fu to f., is called the lower-sideband signal. The two sideband
`signals are also referred to as the swm and the difference frequencies,
`respectively. The auxiliary signal of frequency(f, is variously referred to
`as the local oscillator signal, the mixing signal, the heterodyning signal, or
`as the carrier signal, depending on the application. The student will
`note, as the discussion proceeds, the various contexts in which the differ-
`ent terms are appropriate.
`We may note that the process of translation by multiplication
`actually gives us something somewhatdifferent from what was intended.
`Given a signal occupying a baseband,say, from zero to fy, and an auxiliary
`signal f,, it would often be entirely adequate to achieve a simple transla-
`tion, giving us a signal occupying the range f, to f. + fu, that is, the upper
`sideband. We note, however, that translation by multiplication results
`in a signal that occupies the range f. — fw to f. + fu. This feature of
`the process of translation by multiplication may, depending on the appli-
`cation, be a nuisance, a matter of indifference, or even an advantage.
`Hence, this feature of the processis, of itself, neither an advantage nor a
`disadvantage.
`Itis, however, to be noted that there is no other operation
`so simple which will accomplish translation.
`
`3.3 RECOVERY OF THE BASEBAND SIGNAL
`
`Suppose a signal m(é) has been translated out of its baseband through
`multiplication with cos wt. How is the signal to be recovered? The
`recovery may be achieved by a reverse translation, which is accomplished
`
`simply by multiplying the tr
`the case may be seen by drawi
`noting that
`the difference-f
`mt) Cos wot by cos wet is a sif
`band. Alternatively, we ma:
`[m(t) cos wt] cos waé = n
`
`_ 4
`
`Thus, the baseband signal m
`addition to the recovered bas
`range extends from 2f, — fx
`latter signal need cause no d
`consequently the spectral ra:
`baseband signal are widely ¢
`signal is easily removed by a
`This method of signal r
`important inconvenience whi
`tem. Suppose that the auxi
`from the auxiliary signal us
`angle is 6, then, as may be vi
`waveform will be proportions
`ble to maintain 6 = 0, the s
`should happen that 6 = 7/2,
`ror example, that @ drifts ba
`the signal strength will wax a
`ing entirely from time to tin
`Alternatively, suppose
`cisely at frequency jf. but is
`verify (Prob. 3.3-2) that thi
`tional to m(t) cos 2m Aft, resi
`even be entirely unacceptab
`Trequencies present in the bz
`iistinet possibility in many
`small percentage changein f,
`zarger than fx.
`In telephor
`Leemed acceptable.
`Wenote, therefore, th:
`ion requires that there be a
`= precisely synchronous wit
`point of the first multiplicati
`« jixed initial phase discrepa:
`
`ZTE, Exhibit 1017-0008
`
`ZTE, Exhibit 1017-0008
`
`

`

`3 OF COMMUNICATION SYSTEMS
`
`Its Fourier trans-
`) to fx.
`is shown in Fig.
`\AI(jw)|
`ical about f = 0 since we
`l density of the signal which
`shown in Fig. 3.2-3b. This
`ff the results shown in Figs.
`ly verify (Prob. 3.2-2) that
`
`Ja — Joe)|
`
`(3.2-4)
`
`‘inal signal is called the base-
`Onthis basis, the original
`1 signal. The operation of
`oidal signal is called mixing
`che part of the signal which
`uxiliary signal, in the range
`znal. The part of thesignal
`vy the auxiliary signal, in the
`id signal. The two sideband
`d the difference frequencies,
`ney f, is variously referred to
`al, the heterodyning signal, or
`plication. The student will
`; contexts in which the differ-
`
`ranslation by multiplication
`rent from what was intended.
`om zero to fxr, and an auxiliary
`e to achieve a simple transla-
`*, to fe + fu, that is, the upper
`tion by multiplication results
`- to fe-+ fa. This feature of
`may, depending onthe appli-
`cence, or even an advantage.
`lf, neither an advantage nor a
`hat there is no other operation
`L.
`
`) SIGNAL
`
`1 out of its baseband through
`signal to be recovered? The
`islation, which is accomplished
`
`AMPLITUDE-MODULATION SYSTEMS
`
`87
`
`simply by multiplying the translated signal with cos wt. That such is
`the case may be seen by drawing spectral plots as in Fig. 3.2-2 or 3.2-3 and
`noting that
`the difference-frequency signal obtained by multiplying
`m(t) cos w¢ by cos wt is a signal whose spectral range is back at base-
`band. Alternatively, we may simply note that
`[m(E) Cos wel] COS wot = m(t) cos? wt = m(t) (14 + 44 cos 2wt)
`(3.3-1a)
`
`(3.3-1b)
`~ = + a) cos ug
`Thus, the baseband signal m(t) reappears. We note, of course, that in
`addition to the recovered baseband signalthere is a signal whose spectral
`range extends from 2f. — fir to 2f. + fu. As a matter of practice, this
`latter signal need cause nodifficulty. For most commonly f, >> far, and
`consequently the spectral range of this double-frequency signal and the
`baseband signal are widely separated. Therefore the double-frequency
`signal is easily removed by a low-passfilter.
`This method of signal recovery, for all its simplicity, is beset by an
`important inconvenience when applied in a physical communication sys-
`tem. Suppose that the auxiliary signal used for recovery differs in phase
`from the auxiliary signal used in the initial translation.
`If this phase
`angle is @, then, as may,be verified (Prob. 3.3-1), the recovered baseband
`waveform will be proportional to m(#) cos 8. Therefore, unless it is possi-
`ble to maintain @ = 0, the signal strength at recovery will suffer.
`If it
`should happen that @ = 7/2, the signalwill be lost entirely. Or consider,
`for example, that @ drifts back and forth with time. Then in this case
`the signal strength will wax and wane, in addition, possibly, to disappear-
`ing entirely from time to time.
`Alternatively, suppose that the recovery auxiliary signal is not pre-
`cisely at frequency f. but is instead at f. + Af.
`In this case we may
`verify (Prob, 3.3-2) that the recovered baseband signal will be propor-
`tional to m(t) cos 2x Aft, resulting in a signal which will wax and wane or
`even be entirely unacceptable if Af is comparable to, or larger than, the
`frequencies present in the basebandsignal. This latter contingency is a
`distinct possibility in many an instance, since usually f, > far so that a
`small percentage change in f, will cause a Af which may be comparable or
`larger than fy.
`In telephone or radio systems, an offset Af < 30 Hzis
`deemed acceptable.
`Wenote, therefore, that signal recovery using a second multiplica-
`tion requires that there be available at the recovery point a signal which
`is precisely synchronous with the corresponding auxiliary signal at the
`pointof the first multiplication.
`In such a synchronousor coherent system
`a fized initial phase discrepancy is of no consequence since a simple phase
`
`aairee
`
`ZTE, Exhibit 1017-0009
`
`ZTE, Exhibit 1017-0009
`
`

`

`
`
`38
`
`PRINCIPLES OF COMMUNICATION SYSTEMS
`
`Received DSB -—SC
`signal
`$,(t) =A COS wp,
`'
`
`™
`
`1 COS
`
`Wet
`eo
`
`
`Fitter
`Sag
`Synchronizing
`
`i
`signal
`wide
`
`
`
`Squaring
`centered
`bi
`:
`
`
`
`¥
`circuit
`
`2
`at 27,
`
`
`
`Fig. 3.3-1 A simple squaring synchronizer.
`
`shifter will correct the matter. Similarly it is not essential that the
`recovery auxiliary signal be sinusoidal (see Prob. 3.3-3). What is essen-
`tial is that, in any time interval, the number of cycles executed by the
`two auxiliary-signal sources be the same. Of course, in a physical system,
`where somesignal distortion is tolerable, some lack of synchronism may
`be allowed.
`When the use of a common auxiliary signal is not feasible, it is
`necessary to resort to rather complicated means to provide a synchronous
`auxiliary signal at the location of the receiver. One commonly employed
`schemeis indicated in Fig. 3.8-1.
`Toillustrate the operation of the syn-
`chronizer, we assume that the basebandsignal is a sinusoid cos wmf. The
`received signal is s;(f) = A COS wmt cos wet, with A a constant amplitude.
`This signal s;(¢) does not have a spectral component at the angular fre-
`quency w,. The output of the squaring circuit is \
`82 () = A? cos? wmt cos? wet
`= A(4 +14 cos Qunt)(14 + 14 cos 2u.2)
`= - [1 + 14 cos 2(we + omt + 14 cos 2(we — Wm)t
`+ cos 2wnt + cos 2ut]
`
`(8.3-2a)
`(3.3-2b)
`
`(8.3-2c)
`
`The filter selects the spectral component (A?/4) cos 2w,.t, which is then
`applied to a circuit which divides the frequency by a factor of 2.
`(See
`Prob. 3.3-4.) This frequency division may be accomplished byusing,for
`example, a bistable multivibrator. The output of the divider is used to
`demodulate (multiply) the incoming signal and thereby recover the base-
`band signal cos wnt.
`Weturn our attention now to a modification of the method of fre-
`quency translation, which has the great merit of allowing recovery of the
`basebandsignal by an extremely simple means. This techniqueis called
`amplitude modulation.
`
`3.4 AMPLITUDE MODULATION
`A frequency-translated signal from which the basebandsignalis easily
`recoverable is generated by adding, to the product of baseband and car-
`rier, the carrier signal itself. Such a signal is shown in Fig. 3.4-1. Figure
`
`AMPLITUDE-MODULATION SYSTEMS
`
`Ag COS We tfH
`m(t);
`
`Ac{1+m(t)]} cos we t
`4
`
`(a) A si
`Fig. 34-1
`(c) The sinusoidal ¢
`
`ZTE, Exhibit 1017-0010
`
`ZTE, Exhibit 1017-0010
`
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`

`
`
`198
`
`PRINCIPLES OF COMMUNICATION syYsSTEMS
`In the limit we might, conceptually at least, use an infinite number
`of repeaters. We could even adjust the gain of each repeater to be infini-
`tesimally greater than unity by just the amount to overcome the attenua-
`tion in the infinitesimal section between repeaters.
`In the end we would
`thereby have constructed a cable which had noattenuation. The signal
`at the receiving terminal of the channel would then be the unattenuated
`transmitted signal, We would then, in addition, have at the receiving
`endall the noise introduced atall points of the channel. This noise is also
`received without attenuation, no matter howfar awayfrom the receiving
`end the noise was introduced,
`If now, with this finite arrayof repeaters,
`the signal-to-noise ratio is not adequate, there is nothing to be done but
`to raise the signal level or to make the channel quieter,
`The situation is actually somewhat more dismal than has just been
`intimated,since each repeater (transistor amplifier) introduces some noise
`on its own accord. Hence, as more repeaters are cascaded, each repeater
`must be designed to more exacting standards with respect to notse figure
`(see Sec. 14.10).
`
`6.2 QUANTIZATION OF SIGNALS
`Thelimitation of the system we have beendescribing for communicating
`overlong channels is that once noise has been introduced any place along
`the channel,we are “stuck” with it. We nowdeScribe howthe situationis
`modified by subjecting a signal to the operation of quantization,
`In
`quantizing a signal m(t), we create a new signal m,(¢) which is an approxi-
`mation to m(t). However, the quantized signal m,(t) has the great merit
`that it is, in large measure, separable from additive noise.
`The operation of quantizationis illustrated in Fig. 6.2-1. A base-
`bandsignal m(t) is shown in Fig. 6.2-la. This signal, whichis called vz, is
`applied to the quantizer input. The output of the quantizer is called
`Yo. The quantizer has the essential feature thatits input-output charac-
`teristic has the staircase form shownin Fig. 6.2-1b, Asa consequence, the
`output %, shown in Fig, §.2-le, is the quantized waveform mt).
`Itis
`observed that while the input v; = m(£) varies smoothlyoverits range, the
`quantized signal », = m,(t) holds at one or another of a numberoffixed
`levels... m_2, m_1, mo, my Mz... , ete. Thus, the signal m,(t)
`either does not changeorit changes abruptly by a quantum jump § called
`the step size.
`The waveform m/(t) shown dotted in Fig. 6.2-le represents the out-
`put waveform, assuming that the quantizeris linearly related to the input.
`Tf the factor of proportionality is unity, », = »;, and m'(t) = m(). We
`see then that the level held by the waveform ma(t) is the level to which
`m'(t) is closest. The transition between one level and the next occurs at
`
`PULSE-CODE MODU LATION
`
`Fig. 6.2-1 Mlustrating the operatio:
`baseband signal i(é),
`(6) The inj
`The quantizer output (solid line)
`showsthe waveform of the output
`
`the instant when m’(t) crosses
`levels.
`Wesee, therefore, that the
`the original signal, The quality
`by reducingthesize of the steps,
`able levels, Eventually, with s1
`eye will not be able to distinguis
`To give the reader an idea. of the
`in @ practical system, we note tl
`quality of commercial color TV, y
`TV performance.
`Nowlet us consider that
`repeater somewhat attenuated a
`
`
`
`ZTE, Exhibit 1017-0011
`
`ZTE, Exhibit 1017-0011
`
`

`

`
`
`PLES OF COMMUNICATION SYSTEMS
`
`it least, use an infinite number
`in of each repeater to be infini-
`tount to overcomethe attenua-
`peaters.
`In the end we would
`id no attenuation. The signal
`ould then be the unattenuated
`ddition, have at the receiving
`the channel. This noiseis also
`rw far away from the receiving
`h this finite array of repeaters,
`aere is nothing to be done but
`innel quieter.
`iore dismal than has just been
`mplifier) introduces some noise
`2rs are cascaded, each repeater
`cds with respect to noise Jigure
`
`describing for communicating
`en introduced any place along
`»w describe how thesituation is
`peration of quantization.
`In
`snal m,(t) which is an approxi-
`ignal m,(t) has the great merit
`additive noise.
`trated in Fig. 6.2-1. A base-
`‘his signal, whichis called v;, Is
`yut of the quantizer is called
`that its input-output charac-
`32-16. Asa consequence, the
`atized waveform m,(t).
`It is
`es smoothly overits range, the
`* another of a numberoffixed
`ete. Thus,
`the signal m,(é)
`y by a quantum jumpS ealled
`
`Fig. 6.2-le represents the out-
`is linearly related to the input.
`=v, and m'(t) = m(t). We
`‘m m(t) is the level to which
`2 level and the next occurs at
`
`PULSE-CODE MODULATION
`
`199
`
`(a) The
`Illustrating the operation of quantization. The step size is S.
`Fig. 6.2-1
`baseband signal m(t).
`(b) The input-output characteristic of the quantizer.
`(e)
`The quantizer output (solid line) response to mt). The dashed waveform m'(2)
`shows the waveform of the output signal for a linear characteristic.
`
`the instant when m’(é) crosses a point midway between two adjacent
`levels.
`Wesee, therefore, that the quantized signal is an approximation to
`the original signal. The quality of the approximation may be improved
`by reducing the size of the steps, thereby increasing the numberof allow-
`able levels. Eventually, with small enough steps, the humanear or the
`eye will not be able to distinguish the original from the quantized signal.
`To give the reader an idea of the number of quantization levels required
`in a practical system, we note that 512 levels can be used to obtain the
`quality of commercial color TV, while 64 levels gives only fairly good color
`TV performance.
`Nowlet us consider that our quantized signal has arrived at a
`repeater somewhat attenuated and corrupted by noise. This time our
`
`ZTE, Exhibit 1017-0012
`
`ZTE, Exhibit 1017-0012
`
`

`

`
`
`)
`
`200
`
`PRINCIPLES OF COMMUNICATION SYSTEMS
`
`repeater consists of a quantizer and an amplifier. There is noise super-
`imposed on the quantized levels of m,(t). But suppose that we have
`placed the repeater at a point on the communications channel where the
`instantaneousnoise voltage is almost always less than half the separation
`between quantized levels. Then the output of the quantizer will consist
`of a succession of levels duplicating the original quantized signal and with
`the noise removed.
`In rare instancesthe noise results in an error in quanti-
`zation level. A noisy quantized signal is shown in Fig. 6.2-2a. The
`allowable quantizer output levels are indicated by the dashed lines sepa-
`rated by amount S. The output of the quantizer is shownin Fig. 6.2-2b.
`The quantizer output is the level to which the input is closest. There-
`fore, as long as the noise has an instantaneous amplitude less than S/2,
`the noise will not appear at the output. One instance in which the noise
`does exceed S/2 is indicated in the figure, and, correspondingly, an error
`in level does occur. The statistical nature of noise is such that even if
`the average noise magnitude is much less than S/2, there is always a
`finite probability that, from time to time, the noise magnitude will exceed
`S/2. Note that it is never possible to suppress completely level errors
`such as the one indicated in Fig. 6.2-2.
`We have shown that through the method of signal quantization,
`the effect of additive noise can be significantly reduced. By decreasing
`the spacing of the repeaters, we decrease the ‘attenuation suffered by
`m,(t). This effectively decreases the relative hoise power and hence
`decreases the probability P, of an error in level. P, can also be reduced
`by increasing the step size S. However,
`increasing S results in an
`increased discrepancy between the true signal m’(¢) and the quantized
`signal m,(¢). This difference m’(¢) — m,(t) can be regarded as noise and
`
`PULSE-CODE MODULATION
`
`is called quantization noise. He
`replica of the transmitted signal
`due to errors caused by additiv
`noises are discussed further in C
`
`6.3 QUANTIZATION ERRO
`
`It has been pointed out that the
`from which it was derived differ
`This difference or error may be +
`process and is called quantizatt
`square quantization error ¢?, wh
`and quantized signal voltages.
`Let us divide the total pe
`m(é) into M equal voltage inter
`center of each voltage interval
`.
`, Ma as shown in Fig. 6
`instantaneous value of the m:
`in this figure, m(¢) happens to
`output will be m:, the voltage c
`e = m(t) — mz.
`Let f(m) dm be the proba
`m— dm/2 to m+ dm/2. Th
`=
`mt+S8/2
`e= —* F(m)(m — m
`+f
`Now, ordinarily the probabilii
`signal m(¢) will certainly not
`the number M of quantization
`small in comparison with the
`In this case, it is certainly rea
`f(m)
`is constant within each
`term of Eq. (6.3-1) we set f(m
`f(m)