BSTJ 60: 10. December 1981: Study of a Time-Compression Technique for TV Transmission Using a Chirp Filter and Envelope Detection. (Eng, K.Y.; Haskell, B.G.)

9.9 MB·English

‘Study of a Time-Compression Technique for
TV Transmission Using a Chirp Filter and
Envelope Detection

By KY. ENG and BG. HASKELL
(atanascrot reoetved January 19, 1981)

We study atime compression far expansion technique for possible
aplication in communication signal procesting, ey Broadcast
‘quality Tv transmission through satellites. The method ees a linear
Chirp, @ linear dispersive filter realised by surface acoustic wae
(devices and an envelope detector. This tacknaque ts heuristic and ean
be viewed as a quasistationary model of the Pat wave involved.
Numerical results show that excessive distortion is created, and its
‘pplication to 3¥ tranamisnon is nat euitable untess some Kal of
‘quatization ix proved. One such form of equatization ia the chirp
transform processor which intolues considerably mare complet.
‘Simpler equalizatiana mey be possible ut.do not seem tobe straight:
forward.

INTRODUCTION

We study time-compression technique motivated hy the longs
standing interest in transmitting multiple broadcast-quality color 7
signals through o single sateliy raraponder, 1, usable we band
‘Width of 36 MH in» communieations savellite auch aa COMSTAR,
‘This can be done by the use of frequency division multiplexing (Fm)
However, the nonlinearity of the transponder exh eaube serious intel:
liiblo crosstalk and intermodlaion interference between the 1
‘tren unless the satelite power amplifier is backed off substantially.
Such a backoff, in vurn, leads to 2 reduction in the downlink earig-to-
roise ratio, As a rosul, there exita an optimum (oleoff between the
‘rons unl 9s, which limits the overall ayatem performance, and
‘achieving broadeastatualcy 7Y anemision becomes difficult.

11s posse to Gime compress each eean ine ofa color sgual by

aor
the nse of tinear chirp, Tine nan envelope
tltert. Twa or more time compressed an lines from differen, but
tgnchronized, Tv signal ean then be Live maltiplexed together i the
tine duvation of an onary TY scan Tive, This coneept of time
tcominension muliplering (Rea) is not new."* but recent advances in
fast analog-co-digtal converters, digitallo-analog converters and
charge-coupled devi have greatly facilitated the implementation of
time compression or expansion. However, because of their present
limitationt on bandwidth and speed, cime-compression factors for
achicrable 1 signals aro only 2 or 3. For largo time compressions,
prs redlzable by aurface acoustic wave (24W) technology are prom:
ihn candidates because of thet lange tmwe-bandvidth property. [a
‘nition ta high speed, the 2 application alan eoquires extremely high
‘inal fidelity. ‘There aze other applieations on the high-speed time
‘Expansion (or compression) of waveforms where the distortion require-
nent is less stringent than the 79 transmission ease. In the specific
‘ave of multiple tranamissions through asinglesrelite transponder,
there are many advantages in using TEM, eg, higher treneponder
tffiieney, ao intermediation, no crosstalk, possible compatibility
‘vith time division multiplex (ros) operations, ei. ‘The crucial ques-
tion is of course, how much distortion the eompreasion/expansion
process would intradace on the signals. This paper gives both analysis
nd numerical examples that Tustrate the method.

"The study revealed that considerable distortion is inroluced by
these operations, and its application to broadeast-quality'T transmis
sion would requie saw fer performance beyond tho present state of
tho urt, However ifthe distortion roquirement can be slated some
‘hot, then the present spprouc is advantageous hecause of ca sim
ply. On the other lund i igh signal fedlity is required, then some
Kind of equalization ia needled for the present technique. This has
‘olivate the sbady of an extention of the present methen! which is
‘Capable of producing high signal quality with saw flcer requirements
‘within the present slat of the arteven at compression factors of 10 or
nore, heat the expense of higher complexity, Thislatter development
th not diacaseed. here but is covered im Teof, 0. The remainder of th
paper covers the theoretical analyse an computer simulation. How
eer, the discussion of either ebjoct by ileal i not adequate forthe
omplowe understanding ofthe system. ‘The theoretical nnalysis sta
Tisheo that although the basic concepe was dorived. heuristically
‘through physiel ineerpretations cca be vowed as a quasi-stationary
fppronimaion to the fime-compression process. The computer sim
Intion, on the other hand, provides the quantitative results that lead
te the conclusion thet the resuling distortion is excessive for todas’
sao filter parameters

2874 THE BELL SYSTEM TECHINICAL JOURNAL, DECEMBER 1981
N THEORETICAL ANALYSIS

In chisseccon, we describe and anatie the proposed compression
method using rv as an example. We first deveriben heuristic argument
tow the technique iaupposed ta work, We then derive the imple
responce of genetal nr—the understanding of whichis important co
‘tho subsoquent analysis and siulation. A brief step-by-step analysis
‘of the compression process is shown, and its result revenls that the
Vechnique can be interpreted 8 a quasiatationary approximation of
tho chirp signal. The mathematical expresions describing the time
compressor are complicated; th, numeral result are obtained using
‘computer simulation ditcusied in Section TM, Various other proper=
ties are ala diacuaed,

2.1 A phystes interpretation

[A Block diagram is ahown in Fig. 1. The inp signal v(t) consis of
successive sean lines, cach with duration of 7) seconds, and the
Voluge is binied to be positive It i maltipied symehronouy by &
Detiolie chirp signal ee) with w center frequency fx and a chirp sunge
of Bf, The instantancous frequency of o(@) weep linearly from
(4 —Af/2) to (fo Af/2) over wach sean ine duration 7. The lowest
frequency of he chirp sigal is assumed to be much grealer thas the
hhghest frequency in the FY signal. The input (0) to the LDF ston
an amplitade-ruadulaved chirp waveform, For simplicity, lets restrict
four aduencon tou single sean Hine nay (0, 7). tn ths ntorval (0)
chinps from (fy = 87,72) to (fo + Bf/2) with the Tv signal the

AAA..

TRANSMISSION TME COMPRESSION 2075
cavelope modulation, As for the up, we assume that it has a band
sriddh Bf centered at f, wad A> Af

“Auwin, forthe purpose of n simple llurration, let us assume that
Af = Af; and, over its peatband, the Lov has e constant guin and
near group delay characeriatie decreasing from Sr ta vera, where Ar
fs the delay dapersion of the :pr. At the time instant ¢ = 0 x() bes
fn inctantancons frequency (fo ~Afy/2) and an envelope magnitude
Proportional lo v(l). This “envelope piece” ia delayed by’ Ar as it
fansite throvgh the 10r. Simiary, at Ty the instamancous
frequency of (2) the highest chirp frequency which gives @ =70
delay for the passage through the 15. Th between these to end
points, the unvelope of s(f) ie delayed lineasly from Ar vo rer
Baquivalonty, the envelope of z(l) over che interval (0, 7) is time
compressed fo (dr, 7 in the ior output, An envolope detector is
then ueed to retrieve the tme-compresial Tv signal Similar compres:
tion occurs for ill the other tean Hines, and as a result tho envelope
Aderecor output consis ofa sequence of compresced TY bursts. TT we
denote the duration ofeach burl by 7, the vaso (7/1) i ale the
time-compmession ratio (rex)

Tis emy tn how that, in gonera, for a given st of Z
So

n,8f, and

a
nae, 0

ren- (1-884) ®

1 is clear from the sbove description that time expansion is also
weible by che ute of an increasing celay characteristic in the LOE,
nd in such ease the ter will core 4 Unexpansion ter

122 Impulse response ofa goneral LDF

‘We conser the gurl ease of an iaslied Ln ne shown in Fig. 20,
‘Te banded ofthe luer i Feentered at fa The group delay vavios
Tineatly over the passband s shown in the Alagram. ‘The transfer
fanction of the fier, sing analyticsigal notation, bs

of a /—fom B ef,

m=

4 ‘i

2976 THE BELL SYSIEM TECHNICAL JOURNAL, DECEMBER 861
YY
YE

eo

Fe 2 Chacactctice and imps seaperia of a8 20, (9) ‘Tiler Sein.
cor Thigate mops

where

ra

ag w
1 is che group delay’ sf aml ju i 4 constant. ‘The inverse Fourier
feanaforen of Hf) give the impae sesponse A(t), he deviation for
‘lee given in Appendix A. Neglecting same mal envelope and phase
perturbations good approximation (sulficienl or our present consid
‘ration) fer A) ss

ma =

0 elsowhere, °

‘hero the multiplying constant has purvosely been dropped, ad gas
constant, A sketch of le) is show in Fig 2 It iy't near cep
seavelnem slarting at 1c — &r/3 and ending at va + 41/2, with the
Inatancancous Frequency varying ftom fy - Sf/2to y+ A//2 ata chirp
rate af a

23 Anaysis of time comeression
Tn this analy, we agin reteit our iacusson co a single scam ine

‘TRANSWISSION TME COMPRESSION 2377
for simplicity. We denote thia input acan line by A(t) in Une incerval
(017. Referring to Pig 1, the linear chirp signal bs given by

soo (6-22

here ia the chirp rare defined by
a

Pesan] 0s

B o
and go is # constant, The parametors find Af. are the chip center
fequency and deviation, respectively, There are also two implicit
eruptions: (jase A: and (i) o> che gba frequency inthe ©
geal

"The LDF input ie the produc of che input Al) and ct,

A). fovah ones

xonatnas|(so82)eebvvel steno
ecto the i ie oar
alegeay ater tre teas
em cab er sr a
Sera wats tb te wage

Tn hae ans gi eh
Rye ria remem eat

ie tela haractert o er

2378 THE BELL SYSTEM TECHNICAL JOURNAL, DECEMBER 1981
-*

ar
‘Also note in Fig. thatthe delay at f+ r/2s zero a some constr
{olay through the device has been rupped for simplicity. Using the
reuull of Section 22, the impute responce of the LDF ia

. C

cowan[re-$r' oi}, ones an
co
a sewher, C9)
ware 6—A//2 add constant. The oul han

o> J sta nde

-[

afent tn st-a4-hepre-af +

conte 8+ ahah fre w4ere |b ae

ost n+ or, an
where the limits of intagration are defined by
Tiamat an, a)
7.4 mint Th, as)
rand fe are defined in Fig. nd
MO am Sete a

| conslant phase term has been dropped in (oy. 12, and we will
Delces all unimportant constant mulipliers and phase shite in sub-
sequent diseusions. The intogrl of the ascond eosin term in og, (11)
fan be dacarded heen of the high frequency eotpenent 2 inthe
Intogrand. Therefore, x) becomes

[Aeron [ow Fla Oe Ft le

we

THARSMISSION TIME COMPRESSION 2379
Let un examine the above integral exprocsion carefully. Using unnlytic-
signal notation, we rewrite as

sin= [A n= 86
.
+005]
oof]
ev pot [are aes

sane
tes ecm none col en 0 0

saa [se mama

Ele}. oseemean an

Th the above, note that Als) is slow-moving function while the
exponential term contains a highly osuillcory chirp given by the
Gerivative of the bracketed argument with respect lo, i,

ile) tat AR AG al, DSrs Te. um

‘This can also be oblained hy simply taking the diference of the
instantaneous fequencie of x(t) and Ald ~ =) In eq (14). The conve
‘tion intogea involve is ustrated in Fg, 4 where we show (7) and
tbs the corresponding is) ata fixed ¢= fe ean be aeen that A)
Biviven by an integral over (7, 7,) of linear chirp wavefore al
{hip rato of (?— w) nd wich wo envelope modolation AC). Further
sore, the chi frequency f insie (Fi, 72) may vanish at some + a8
‘hown in Fig. 4 In uch case, the value of yf) is dominated by the
integral eq, (15) over the sail iterval sarrouading tha, where f
goes lo wero, This i, of cour, the well-lmoven quos-stationary ap-
proximation. The approximation ia good 3 the chirp rave (— a)
fn the interval (Ty, 73) ace large, and Ato) vanietion is slow by com
parison, Using thie approximation, at ¢~ ¢ inside che valid interval
(Tr act,

Ast = kat, as)

2800. THE BFLL SYSTEM TECHNICAL JOURNAL, DECEMBER +981
ig ¢—tomvesn ta

where Ais constant, and rs obtained by solving eg. (1) with fat
tozeroand t= 6, ic
mB t

B
‘This quasi stationary approximation i indeed equivalent to the plny-
ical interpretation destined in Secon 21. Ava check, let up derive
the Tea from the appreximation sbnve. We knw that Air) is nongero
only if0= 7 = 7. The corresponding ¢, ean be solved for using 64
(20), an the end points of & oonetiute che interval 7, Le,
W(t h- A TMa) AREA B

or(i-8) ov

rone(1-£)" ae ea

(20)

7

Therefore,

sshich agrees with og. (2) with the subatizurions of « and B according

TRANSMISSION TME COMPRESSION 2961
to the definition eas (1) and (7), rospectively, See Section 24 for 8
continued diacusson of A(0

"Ta finish our nnalyss of the éime compression, we netum to yin
9, (18) and expand the cosine tm:

Ltt) = y4Pe08 2rO{t) — y(chcin 20 (0, 3
where

wna aneea[ireacnemnso-a% |e @

and

wera nnaaenaecteenee oa} 9
tay nan tng ad tn
caren ha

att) = Lyn + tio 2)

24 Some fundemntal properties

‘We have just derived mathematical expressions for dhe tme-com-
pression process, ‘Thew expressions are too complicalsd for eaxy
Incerpretation, However, we have demonstrated thal the technique
‘work if'a quist-stationary approximalion ix made for che chirp
‘waveform. In other words the inscantansuus frajuency of the chip
‘wave could bo ust a If were a tationary carrier frequency in @
leady stato analysis

Making such an seeumplion, ic ic sean from oa, (2) that infinite
compression, TCR = w,realea i.47 = Af. und Ar ~ Tr (oe= fi). But
frown age. (05), (24), and (25), i ie obvinas thatthe OF output afer
synchronon detoetion (for @ = f) will ataally become the Fourier
‘fanaform of the input envelope A(), This ean alse be reagnized a
the well-known chirp transform of real-time transform’ commonly
toed in chirp radar and saW processors ‘Therefore he quané-ationary
rode invalid for this case

‘A case thers the quns-siationary approximation clessly holds is
hero fim» = and a” 0, ie the erp range i very large ad the
Aelay slope ofthe LO i clove to zero, The rat is of course, avery
Sight comprission, Le, the TCH br alihtly lnrger than L. Therefore,
trthout doing any specie ealelation, we soe thatthe quas-sationary
Thoamption i valid, at best, for small Texs, and it lonks dose.
Somewiere between ck = 1 and , Sinee our practical applications

2982 THE RELL SYSTEM TECHNICAL JOURNAL, DECEMBER 1981