*2 Systems
`
`010 Control Systems
`
`mix
`
`Principles of
`
`Communication Systems
`
`HERBERT TAUB
`
`Professor of Electrical Engineering
`The City College of the City University of New York
`
`\
`\
`DONALD L. scHILLme
`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
`Dfissmmonr
`JOHANNESBURG
`KUALA LUMPUR
`LONDON
`MEXICO
`MONTREAL
`NEW DELHI
`PANAMA.
`RIO DE JANEIRO
`SINGAPORE
`SYDNEY
`TORONTO
`
`ZTE, Exhibit 1017-0001
`
`ZTE, Exhibit 1017-0001
`
`

`

`
`
`PRINCIPLES OF COMMUNICATION SYSTEMS
`
`
`
`
`
`
`
`
`
`
`
`
`
`Copyright © 1971 by MeGrew-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, recoraing, or
`otherwise, Without the prior written permission of the
`publisher.
`
`Library of Congress Catalog Card Number 72-109255
`
`07-062923-4
`
`
`
`14151617181920 VBVB
`
`876543
`
`
`
`ZTE, Exhibit 1017-0002
`
`ZTE, Exhibit 1017-0002
`
`

`

`”LE5 OF COMMUNICATION SYSTEMS
`ds to the circumstance where X
`
`.ted to the random variable 9 by
`as a uniform probability density
`Y are not independent but that,
`rrelated.
`
`are dependent but uncorrelated.
`=Ui+ai+a§+ -
`- -.
`are independent and each has a.
`: S 1. Find and plot the proba-
`(a.
`
`— X2 sin mat is a random prooess.
`variables each with zero mean and
`
`indom prooess, with E(M(t)) = 0
`
`lary?
`do such thatfew) = l/er, —1r S
`:on + 9)) = Mo/2.
`Is Z(l) now
`
`13.1 density G(f) = 11/2 for — on g
`gh a low-pass filter which has a
`1d H (f) = 0 otherwise. Find the
`output of the filter.
`
`3d through a low-pass RC network
`
`ontput 110180 of the HBtWOI'k-
`
`,
`,
`_n1;%3the Theory Of Statistics,
`gin and Company, Boston, 1956.
`bios, and Stochastic Processes,”
`
`”
`
`3
`
`Amplitude-modulation Systems
`
`1.
`
`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 malto-
`planing. The individual message can eventually be separated by filtering.
`Frequency multiplexing involves the use of an auxiliary Waveform, usually
`smusoxdal, called a cow-tar.
`lThe operations performed on the Signal to
`achieve frequency multiplexmg 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
`
`AMPLITUDE-MODU LATION SYSTE
`
`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 frequency f; to a
`frequency f2. The process of frequency translation is one in which the
`original signal is replaced with a new signal whose spectral range extends
`from f; to f; and which new signal bears, in recoverable form, the same
`information as was borne by the original signal. We diseuss now a num-
`ber of useful purposes which may be served by frequency translation.
`
`FREQUENCY MULTIPLEXING
`
`Suppose that we have several different signals, all of which encompass the
`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. The single 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 one of the original signals to a difierent frdquency range. Suppose,
`say, that one signal is translated to the frequency range f; to f;, the second
`to the range fi’ to f;’, and so on.
`If these new frequency ranges do not
`overlap, then the signal may be separated at the receiving end by appro-
`priate bandpass filters, and the outputs of the filters processed to recover
`the original signals.
`
`PRACTICABILITY DF 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 In, an entirely impractical
`length. The required length may be reduced to the point of practicability
`by translating the audio tone to 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. The ratio of the highest audio
`
`frequency to the lowest is
`at one end of the range w-
`other end.
`Suppose, hOWE
`so that it occupied the ran
`Then the ratio of highest t.
`the processes of frequency
`band” signal into a “narrc
`veniently processed. The
`being used here to refer not
`to the fractional change in
`
`COMMON PROCESSING
`
`It may happen that we me
`similar in general character
`will then be necessary, as ‘
`quency range of our proces;
`range of the signal to be pr(
`elaborate, it may well be wi:
`in some fixed frequency ran;
`of each signal in turn to co
`
`3.2 A METHOD OF FR
`
`A signal may be translatet
`signal with an auxiliary sir
`us consider initially that thi
`
`vma) = Am cos mmt =
`
`in which Am is the constan
`The two-sided spectral ar
`Fig. 3.2-1a. The pattern 1
`located at f = f,,, and at
`multiplication of emu) with
`
`v56) = A, cos mat = A
`
`= A2” (ejwfll + e—J‘a’
`
`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-
`rl from one region in the fre-
`:e that a signal is bandlimited,
`ding from a frequency f1 to a
`ranslation is one in which the
`1 whose spectral range extends
`in recoverable form, the same
`gnal. We discuss now a num—
`d by frequency translation.
`
`als, all of which encompass the
`that all these signals be trans-
`inel in such a manner that, at
`y recoverable and distinguish-
`may be a single pair of wires
`antenna from another. Such
`
`may be achieved by translating
`at frequency range. Suppose,
`uency range f; to f;, the second
`3 new frequency ranges do not
`at the receiving end by appro—
`the filters processed to recover
`
`:hannel, 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 point of practicability
`‘requency.
`
`ust discussed, suppose that we
`1y from the antenna, and that
`a no problem. We would still
`Let us assume that the audio
`The ratio of the highest audio
`
`AM PLITU DE-MODU LATION SYSTEMS
`
`B3
`
`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‘ + 10‘) Hz.
`Then the 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 number of 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 apparatus is rather
`elaborate, it may well be wiser to leave the processing apparatus to operate
`in some fixed frequency range and instead to translate the frequency range
`of each signal in turn to correspond to this fixed frequency.
`\
`h
`
`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 consider initially that the signal is sinusoidal in waveform and given by
`
`vm(t) = Am cos wmt = Am cos Barfmt
`= % (em-t + 3—59.“) 2 £22 (312:5; + e—jixfml)
`
`(3.2—1a)
`(3.241,)
`
`in which Am is the constant amplitude and fm = com/213' is the frequency.
`The two—sided spectral amplitude pattern of this signal
`is shown in
`Fig. 3.2-1c. The pattern consists of two lines, each of amplitude elm/2,
`located at f = fm and at f = —f,... Consider next
`the result of the
`multiplication of 2),..(t) with an auxiliary sinusoidal signal
`
`Mt) = A. cos act = Ac cos 21rfct
`= ‘i (eat + W“) = 142—“ (err-l + were
`
`(32-21:)
`(32-21:)
`
`in which A, is the constant amplitude and fa is the frequency. Using the
`trigonometric identity cos 0: cos 5 = %cos (a + [3) + %cos (a — [9), we
`
`ZTE, Exhibit 1017-0005
`
`ZTE, Exhibit 1017-0005
`
`

`

`M
`
`PRINCIPLES OF COMMUNICATION SYSTEMS
`
`AMPLITUDE-MODULATION SYSTEM
`
`1
`
`Amplitude at
`spectral component
`
`A
`_2_
`
`L‘
`:1
`
`:
`;-r.
`-r.,.
`0
`rm
`i
`E
`Amplitude
`I
`l
`A._A
`w+_ __,c______*_ _______ _+_
`U!)
`
`I
`I
`'fffm '5 'f..+f,..
`°
`fc‘f...
`fr Hf”,
`f
`
`(a)
`
`f
`
`.
`
`(.1) Spectral pattern of A... cos amt.
`Fig. 3.2-1
`Product AMAa cos wmt cos wit.
`
`(b) Spectral pattern of the
`
`have for the product um(t)vc(t)
`
`A A
`040%“) = a 5 [cos (me + mm” + cos (we _ (radii
`
`\
`= Ari" (eflm’wm + rmfiunn
`\
`+ ei(‘°u"“m” + e—J'("’=—“m)‘)
`
`(3.2-3a)
`
`(3.2435)
`
`The new spectral amplitude pattern is shown in Fig. 3.2-15. Observe that
`the two original spectral lines have been translated, both in the positive-
`frequency direction by amount fa 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. + f... and the
`other of frequency fa —- fm. Note that while the product signal has
`four spectral components each of amplitude AmAc/tl, there are only two
`frequencies, and the amplitude of each sinusoidal component is AWL/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 f”. Before transiation 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 components in this two-sided Spectral
`pattern give rise to eight sinusoidal waveforms. While the original signal
`extends in range up to a. frequency m, the signal which results from multi-
`plication has sinusoidal components covering a range 23"“, from f: en fin
`to fa + fM-
`
`A
`
`mp
`
`Spectrum of signal
`before translation \
`
`l I ll
`
`f
`‘ c'fM fl;
`
`Ill |
`
`-fc+f”
`
`_____
`
`r
`
`—,
`
`Fig. 3.2-2 An original signal con
`translated through multiplicaticm
`symmetrically arranged “b0“ fr
`
`Finally, we consider in
`to be translated may not be r
`sinusoidal components at st.
`the case if the signal were of
`the signal is represented in t
`transform, that is, in terms
`
`(a)
`
`“Z
`flu
`
`I
`
`‘fc +13,
`uf°
`_f‘ “f"
`(,1) The spectral dens
`Fig. 3.2-3
`spectral density of m(t) cos 2wa.
`
`ZTE, Exhibit 1017-0006
`
`ZTE, Exhibit 1017-0006
`
`

`

`
`
`5 OF COMMUNICATION SYSTEMS
`
`AMPLITUDE-MODULATION SYSTEMS
`
`85
`
`ll
`ment
`
`la)
`
`Amplitude of spectral
`components
`
`Spectrum of signal
`before translation
`
`—’—-1———
`f
`ItII
`I|
`
`W
`
`(a)
`
`||1
`
`l| f
`
`——l—
`fL. -f,,,
`
`I
`m
`fl+f
`
`,
`
`f
`
`5) Spectral pattern 0f the
`
`5 (we —- w...)t]
`
`(3.2-3a)
`
`(“F“m" + e'iWFN-J‘)
`
`(3.2-3b)
`
`in Fig. 3.2-15. Observe that
`msloted, both in the positive-
`;0 in the negative—frequency
`10W four spectral components
`of frequency fa + fin and the
`rhile the product signal has
`a A...A./4, there are only two
`isoidal component is AmAc/2.
`I. in Fig. 3.2-2. Here a signal
`of four sinusoidal signals, the
`y fM. Before translation by
`:rn displays eight components
`multiplication, we find this
`ositive— and the negative—fre—
`ients in this two-sided spectral
`ms. While the original signal
`ignal which results from multi—
`ing a range 2fM: from fr. — fM
`
`‘fc ‘fu
`
`‘fc
`
`‘Ia "HM
`
`0
`
`’i: ”(it
`
`fc
`
`(0) The spectral density |M(jw)l of a. nonperiodic signal ma).
`Flg. 3.2-3
`spectral density of m(t) cos 21M.
`
`I: +ij
`
`(b) The
`
`
`
`ZTE, Exhibit 1017-0007
`
`___l__III I_II_I__,
`M"-.-
`fr-fM I;
`f=+fM
`f
`fit!
`0
`first
`fies—fr:
`'I;
`"fc'I'fu
`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 about 1‘}.
`
`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 number of
`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 terms of its spectral density. Thus let the signal
`it
`
`|M (110)]
`
`o
`
`f
`u
`
`f
`
`(a)
`
`_f
`"
`
`
`
`ZTE, Exhibit 1017-0007
`
`

`

`W
`
`BE
`
`PRINCIPLES OF COMMUNICATION SYSTEMS
`
`AM PLITU DE-MO DU LATION SYSTEMS
`
`Its Fourier trans-
`m(&) be bandlimited to the frequency range 0 to far.
`is shown in Fig.
`form is M ( jw) = 5[m(l)]. The magnitude l]|[(jw)l
`3.2-3a. The transform M (jw)
`is symmetrical about f = 0 since we
`assume that -m(l) is a real signal. The spectral density of the signal which
`results when m0) is multiplied by cos mat 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) = 3‘[m(t)], then
`
`91mm 00S wall = }é[M(jw + J'wc) + MUw — jwcll
`
`(3-2-4)
`
`The spectral range occupied by the original signal is called the base-
`baml frequency range or simply the basebrmal. 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
`0r heteradyning.
`In the translated signal, the part of the signal which
`consists of spectral components above the auxiliary signal, in the range
`f.2 to f; + fM, is called the upper-sidcbcnd signal. The part of the signal
`which consists of spectral components below the auxiliary signal, in the
`range fc — fM to f6, is called the lower—sidewall signal. The two sideband
`signals are also referred to as the sum and the dzfierancg frequencies,
`respectively. The auxiliary signal of frequency\ fc is variously referred to
`as the local oscillator signal, the mixing signal, the heterodym'ng 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 somewhat different from what was intended.
`Given a signal occupying a baseband, say, from zero to fly, and an auxiliary
`signal 1",, it would often be entirely adequate to achieve a simple transla-
`tion, giving us a signal occupying the range fa to f9 + far, that is, the upper
`sideband. We note, however, that translation by multiplication results
`in a signal that occupies the range f, — fin to f, + fM. 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 process is, of itself, neither an advantage nor a
`disadvantage.
`It is, 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(t) has been translated out of its baseband through
`multiplication with cos wot. 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
`771.05) cos out by cos wpt is a sig
`band. Alternatively, we ma;
`
`[m(t) cos wet] cos wot = n
`
`_ :n
`
`Thus, the baseband signal in
`addition to the recovered has
`
`range extends from 2f, — fM
`latter signal need cause no d
`consequently the spectral ra‘
`baseband signal are widely E
`signal is easily removed by a
`This method of signal 1'
`important inconvenience whu
`rem. Suppose that the auxi
`from the auxiliary signal us
`angle is 6', then, as may be v:
`waveform will be proportion;
`file to maintain H = O, the 8
`should happen that 6 = r/2,
`for example, that 6 drifts be
`the signal strength will wax a
`ing entirely from time to tin
`Alternatively, suppose
`cisely at frequency in but i:
`“rerlfy (Prob. 3.3-2) that thr
`tional to m(l) cos 2w Aft, rest
`even be entirely unacceptab
`frequencies present in the b:
`:Listinct possibility in many
`L:nall percentage change in f.
`Larger than fM-
`In telephci
`ieemed acceptable.
`We note, therefore, th.‘
`{can requires that there be a
`i~ precisely synchronous wit
`: :-int of the first multiplicati‘
`.. fired initial phase discrepa:
`
`ZTE, Exhibit 1017-0008
`
`ZTE, Exhibit 1017-0008
`
`

`

`3 OF COMMUNICATION SYSTEMS
`
`Its Fourier trans-
`) to fM.
`1M ( jam is shown in Fig.
`ical about f = 0 since we
`.1 density of the signal which
`shown in Fig. 3.2-3b. This
`.f the results shown in Figs.
`ly verify (Prob. 3.2-2) that
`
`ij — jwcll
`
`(3-2-4)
`
`final signal is called the base-
`On this basis, the original
`l signal. The operation of
`.oidal signal is called mixing
`ihe part of the signal which
`uxiliary signal, in the range
`gnal. The part of the signal
`v the auxiliary signal, in the
`1d signal. The two sideband
`.d the dificrence frequencies,
`ncy f, is variously referred to
`al, the heterodyning signal, or
`plication. The student will
`s contexts in which the differ-
`
`‘ranslation by multiplication
`rent from what was intended.
`)m zero to flu, and an auxiliary
`-e to achieve a simple transla-
`"',. to fa + fill, that is, the upper
`tion by multiplication results
`' t0 fa + fM- This feature of
`may, depending on the appli-
`cence, or even an advantage.
`lf, neither an advantage nor a
`hat there is no other operation
`I.
`
`I SIGNAL
`
`1 out of its baseband through
`
`signal to be recovered? The
`islation, which is accomplished
`
`AMPLITUDE-MODULATION SYSTEMS
`
`37
`
`simply by multiplying the translated signal with cos wet. 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
`711(6) cos cat by cos coat is a signal whose spectral range is back at base-
`band. Alternatively, we may simply note that
`
`[m(t) cos wet] cos mat = m(t) cos2 cost = m(t)(}fi + }§ cos 2cm)
`(3.3-1a)
`
`= 9292 + “Tm cos 2th
`
`(3.3-1b)
`
`Thus, the baseband signal m(t) reappears. We note, of course, that in
`addition to the recovered baseband signal there is a signal whose spectral
`range extends from 2f, — fM to 2fc + far. As a matter of practice, this
`latter signal need cause no difliculty. For most commonly f, >> f1”, and
`consequently the spectral range of this doublevfrequency signal and the
`baseband signal are widely separated. Therefore the double—frequency
`signal is easily removed by a low—pass filter.
`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 diilers in phase
`from the auxiliary signal used in the initial translation.
`If this phase
`angle is 0, then, as may be verified (Prob. 3.3—1), the recovered baseband
`waveform will be proportional to m(t) cos 9. Therefore, unless it is possi-
`ble to maintain 0 = 0, the signal strength at recovery will suffer.
`If it
`should happen that 9 = vr/2, the signal will be lost entirely. Or consider,
`for example, that 6 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 fc but is instead at fn + Af.
`In this case we may
`verify (Prob. 3.3~2) that the recovered baseband signal will be propor-
`tional to 7910!) cos 2‘» Aft, resulting in a signal which will wax and wane or
`even be entirely unacceptable if of is comparable to, or larger than, the
`frequencies present in the baseband signal. This latter contingency is a.
`distinct possibility in many an instance, since usually 3% >> far so that a
`small percentage change in fc will cause a Af which may be comparable or
`larger than f".
`In telephone or radio systems, an offset Af 5 30 Hz is
`deemed acceptable.
`We note, 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
`point of the first multiplication.
`In such a synchronous or coherent system
`a med initial phase discrepancy is of no consequence since a simple phase
`
`—-_'———""""""'
`
`ZTE, Exhibit 1017-0009
`
`ZTE, Exhibit 1017-0009
`
`

`

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`83
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`PRINCIPLES OF COMMUNICATION SYSTEMS
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`Received DSB — SC
`signal
`s, Lt) = A cos mm! :05 my:
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`-
`Squaring
`CIfCLII
`
`
`
`Filter
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`centered
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`a! 21;,
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`Synchronizing
`.
`s: nal
`g
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`Flg. 3.3-] 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 some signal 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
`scheme is indicated in Fig. 3.3—1. To illustrate the operation of the syn—
`chronizer, we assume that the baseband signal is a sinusoid cos amt. The
`received signal is so!) = A cos wmt cos wet, with A a constant amplitude.
`This signal 3,-(2!) does not have a spectral component at the angular fre-
`quency we. The output of the squaring circuit is \“
`.93 (t) = fl2 cos2 wmt cos2 wet
`
`(3.3—2a)
`
`= A205 + yz cos mama + % cos 2mg)
`2
`= A? [1 + % cos 2(a), + mm” + % cos 2(w6 —— wmfi
`+ cos 2%: + cos 2wctl
`
`(33—21;)
`
`{3.3-2c)
`
`The filter selects the spectral component (Ag/4) cos 20ml, 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 by using, 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 amt.
`We turn our attention now to a modification of the method of fre—
`quency translation, which has the great merit of allowing recovery of the
`baseband signal by an extremely simple means. This technique is called
`amplitude modulation.
`
`3.4 AMPLITUDE MODULATION
`
`A frequency-translated signal from which the baseband signal is 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
`
`AM PLITUDE-MODULATION SYSTEMS
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`Ae cos u:c t
`
`ll
`
`In“)
`
`F
`
`Ac[l+m(lJ]coa‘-wcz
`I
`
`(0:) A sin
`Fig. 3.4-1
`(c) The sinusoidal c
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`ZTE, Exhibit 1017-0010
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`ZTE, Exhibit 1017-0010
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`

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`198
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`PRINCIPLES OF COMMUNICATION SYSTEMS
`
`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 no attenuation. The signal
`at the receiving terminal of the channel would then be the unattcnuated
`transmitted signal. We would then, in addition, have at the receiving
`end all the noise introduced at all points of the channel. This noise is also
`received without attenuation, no matter how far away from the receiving
`end the noise was introduced.
`If now, with this finite array of 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 noise figure
`(see Sec. 14.10).
`
`6.2 QUANTIZATION OF SIGNALS
`The limitation of the system we have been describing for communicating
`over long channels is that once noise has been introduced any place along
`the ohannel,_we are “stuck" with it. We now describe how the situation is
`modified by subjecting a signal to the operation of quantization.
`In
`quantizing a signal 7120:), we create a new signal 77140!) which is an approxi-
`mation to m(t). However, the quantized signal mg(t) has the great merit
`that it is, in large measure, separable from additive noise.
`The operation of quantization is illustrated in Fig. 6.2-1. A base-
`band signal m(t) is shown in Fig. 6.2-1a. This signal, which is called 11,-, is
`applied to the quantizer input. The output of the quantizer is called
`c... The quantizer has the essential feature that its input-output charac—
`teristic has the staircase form shown in Fig. 62-11). As a consequence, the
`output 00, shown in Fig. 6.2mlc, is the quantized waveform 12290:).
`It is
`observed that while the input a; = m(t) varies smoothly over its range, the
`quantized signal a, = 171,“) holds at one or another of a number of fixed
`levels .
`.
`. m_2, m_1, mg, ml, ”22,
`.
`.
`.
`, etc. Thus, the signal mq(t)
`either does not change or it changes abruptly by a quantum jump 3 called
`the step size.
`The waveform m’(t) shown dotted in Fig. 6.2—lc represents the out-
`put waveform, assuming that the quantizer is linearly related to the input.
`If the factor of proportionality is unity, a, = 2a, and m.’(t) = m(t). We
`see then that the level held by the waveform mg“) is the level to which
`m—’(t) is closest. The transition between one level and the next occurs at
`
`
`
`Illustrating the operatic.
`Fig. 6.2-1
`baseband signal mm.
`(b) The in}
`The quantizer output (solid line)
`shows the waveform of the output
`
`the instant when m.’(t) crosses
`levels.
`
`We see, therefore, that the
`the original signal. The quality
`by reducing the size of the steps,
`able levels. Eventually, with s1
`eye will not be able to distinguis
`To give the reader an idea of the
`in a practical system, we note tl
`quality of commercial color TV, v
`TV performance.
`Now let us consider that
`repeater somewhat attenuated a
`
`
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`ZTE, Exhibit 1017-0011
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`ZTE, Exhibit 1017-0011
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`

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`PULSE-coca MODULATION
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`i
`
`m
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`
`
`(a) The
`Illustrating the operation of quantization. The step size is S.
`Fig. 6.2-1
`baseband signal 111(8).
`(1)) The input-output characteristic of the quantizer.
`(c)
`The quantizer output (solid line) response to m(t). The dashed waveform m’(t)
`shows the waveform of the output signal for a linear characteristic.
`
`the instant when m’(t) crosses a point midway between two adjacent
`levels.
`
`We see, 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 number of allow-
`able levels. Eventually, with small enough steps, the human ear 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.
`Now let us consider that our quantized signal has arrived at a
`repeater somewhat attenuated and corrupted by noise. This time our
`
`l i
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`PLES 0F co
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`N
`MMU 'CATlON SYSTEMS
`ti: least, use an infinite number
`.in of each repeater to be infini-
`iount to overcome the attenua—
`peaters.
`In the end we would
`Ld no attenuation. The signal
`ould then be the unattenuated
`ddition, have at the receiving
`the channel. This noise is also
`nv far away from the receiving
`h this finite array of repeaters,
`mere is nothing to be done but
`tnnel quieter.
`1ore dismal than has just been
`mplifier) introduces some noise
`are are cascaded, each repeater
`rds with respect to noise figure
`
`describingforcommunicating
`
`sen introduced any place along
`Iw describe how the situation is
`‘peration of quantization.
`In
`gnal mm) which is an approxi-
`ignal mq(t) has the great merit
`additive noise.
`trated in Fig. 6.2-1. A base—
`'his signal, which is called vs, is
`m1: of the quantizer is called
`that its input-output charac-
`i.2-lb. As a consequence, the
`ntized waveform m,,(t).
`It is
`es smoothly over its range, the
`' another of a number of fixed
`etc. Thus,
`the signal mq(t)
`y by a quantum jump S called
`
`Fig. 6.2—lc represents the out“
`is linearly related to the input.
`= as, and m'(t) = m(t). We
`'m mg“) is the level to which
`a level and the next occurs at
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`ZTE, Exhibit 1017-0012
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`ZTE, Exhibit 1017-0012
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`

`

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`ZIJD
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`PRINCIPLES OF COMMUNICATION SYSTEMS
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`repeater consists of a quantiaer and an amplifier. There is noise super-
`imposed on the quantized levels of mam. But suppose that we have
`placed the repeater at a point on the communications channel where the
`instantaneous noise 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 instances the noise results in an error in quanti—
`zation level. A noisy quantized signal is shown in Fig. 62—20..
`IThe
`allowable quantizer output levels are indicated by the dashed lines sepa-
`rated by amount S. The output of the quantizer is shown in 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 3/2,
`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 8/2, there is always a
`finite probability that, from time to time, the noise magnitude will exceed
`8/2. 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
`mg“). This effectively decreases the relative hoise power and hence
`decreases the probability P9 of an error in level. P., can also be reduced
`by increasing the step size 8. However,
`increasing S results in an
`increased discrepancy between the true signal arr/(t) and the quantized
`signal mm). This difference m-‘(t) — mq(t) can be regarded as noise and
`
`5
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`3
`
`Error
`
`in level
`
`Large noise excursion
`
`
`
`(a)
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`(b)
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`.-
`5
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`PULSE-CODE MODU LATIDN
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`is called quantization noise. He
`replica of the transmitted signal
`due to errors caused by additiv
`noises are discussed further in C
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`6.3 QUANTIZATION ERRD
`
`It has been pointed out that the
`from which it was derived differ
`
`This difference or error may be \
`process and is called quantizati
`square quantization error 56, wh‘
`and quantized signal voltages.
`Let us divide the total p:
`m(t