METHOD FOR DEMODULATING A FREQUENCY-MODULATED SIGNAL AND DEMODULATOR PERFORMING THIS METHOD

METHODE DE DEMODULATION DE SIGNAUX MODULES EN FREQUENCE ET DEMODULATEUR UTILISANT CETTE METHODE

English Abstract

ABSTRACT OF THE DISCLOSURE
The method for demodulating a frequency-
modulated signal comprises considering the signal
as being the projection, on an axis Ox, of a
rotating vector rotating about a point O in a
coordinate Oxy in such a way that the frequency
variations of the signal correspond to the rotary
speed variations of this rotating vector. After
sampling the signal at a rhythm equal to 4 times
a frequency F' in the frequency band of the signal,
using an appropriate calculation, the position of
the rotating vector is determined by means of two
successive samples of the signal. The frequency
variation of the signal between two times spaced
by a cycle <IMG> is then deduced from the position of
the rotating vector at these times.

Claims

The embodiments of the invention in which an exclu-
sive property or privilege is claimed are defined as
follows:
Claim 1: A method for the demodulation of a frequency-
modulated signal, this signal being considered as the projection on an axis
Ox of a vector rotating about a point O in a coordinate Oxy and its
frequency variations being calculated from the variations of the rotatory
speed of the vector, comprising the steps of:
- sampling the signal at a fixed sampling frequency 4.F', F'
belonging to the frequency band of the signal,
- delaying each value x(t), of the signal sampled at time t, with
delays <IMG>
- calculating a value of the frequency variation at time t
according to the formula:
.DELTA.T(t)= <IMG> and
- producing the demodulated signal from said calculated value
.DELTA.F(t).
Claim 2: A method as in claim 1 including the further steps of
converting said frequency modulated signal to a digital signal and
converting the demodulated signal to an analog signal.
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Claim 3: A demodulator for a signal frequency-modulated about a
frequency F, the frequency band width B of the modulated signal being
centred on F with <IMG> below unity, comprising:
- a sampler for sampling the modulated signal according to a
sampling frequency q.F', F' being a frequency in the frequency band of
the signal and q a positive real number;
- an analog/digital converter having an input connected to the
output of the sampler and having an output supplying a value for each
sample of the modulated signal;
- a first, a second and a third delay device, each having a delay
equal to <IMG> and being connected in series, an input of the first one
being connected to the output of the analog/digital converter, an input of
the second one being connected to the output of the first one, an input of
the third one being connected to an output of the second one, and the
third one having an output;
- a first calculating device having four inputs respectively
connected to the output of the analog/digital converter and to the outputs
of the three delay devices to receive respectively values x(t1),
<IMG> , and having an output, supplying a
value:
N = <IMG>
- a second calculating device having two inputs respectively
connected to the outputs of the first and second delay device to receive
respectively values <IMG> and <IMG> , and having an output,
supplying a value:
D = <IMG>

- a third calculating device having a first and a second input
respectively connected to the outputs of the first and second calculating
device and having an output, supplying a value:
.DELTA.F = <IMG> of the frequency variation;
- a comparator having an input coupled to the output of the
second calculating device and having an output, for supplying a logical
signal when the absolute value of V is greater than a predetermined value
S (S positive real);
- coupling means having an input connected to the output of the
third calculating device, a control input connected to the output of the
comparator and an output, for supplying the value .DELTA.F, which constitues
the demodulated signal, only when the absolute value of D exceeds the
value S.
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Description

I ~ B7t68
BACKGROUND OF THE INVENTION
The present invention relates to
methods for demodulating a frequtncy-rnodulated signal,
the demodulators perfonlling the~e Illethods and in
particular SECAM television systems i.ncorporating
such demodulators.
In the SECAM system, co].our info-rmation
frequency modulates a subcarr:ier located in the
vicinity of the end of the highest frequenci.es and
within the lurninance spectrum. The latter extends
from approximately 0 to 6 MHz and the subca mer, whose
frequency sweep extends between 3.9 and 4.7 M}lz is
mixed with the principal spectrum. Various systems
have been proposed for demodulating this subcarrier
by means of conventional frequency discriminators
but these have the disadvantage of being sensitive
to amplitude variations in the signal to be processed.
BRIEF SUMMARY OF THE INVENTION
The significance of the present invention
is that it is able to perfo~n a digital demodulation of
a frequency-modulated signal, particularly a chromin-
ance signal of a SECAM video signalS whilst having the
advantage of not being sensitive to amplitude
variations of the signal at a frequency which is low
compared with that of the centre frequency.
Accord:ing to the invention there is
provided a method for the demodulation of a frequency-
modulated signal consisting of considering this signal

I~67~68
as being the projectivn on an axls Ox of a vectorrotatlng about a point O in a coordinate Oxy,
determining the variations in the rotation speed
of this rotating vector starting from a linear com~
bination ratio of samples of the value of the
projection on axis Ox of the rotating vector and
determining the var-Lations of the frequency of the
signal to be demodulated as a function of the variat-
ions of the rotary speed of the rotating vector.
The invention also relates to demodulators
for performing this method.
BRIEF DESCRIPTION OE' THE DRAWINGS
The invent;on is described in greater
detail hereinafter relative to non-limitative embodi-
ments and with reference to the attached ~awings,
wherein show:
Fig 1 a circuit diagram of a digital demodulator
according to the invention.
Fig 2 a circuit diagram of another digital demodulator
according to the invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMFNTS
The prior art precise synchronization
devices are not shown in the drawings in order to
make the latter clearer and simplify the description~
In Fig 1, an input terminal 1 receiving
a SECAM video signal is coupled to a sampler 3
across a band pass filter 2. The output of sampler
3 is coupled across an analog/digital converter 4
to the input of a Eirst delay network or device 5
and to a Eirst input of a calculating device 6. The
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output o~ the cleLay device 5 is connected to a
seconcl lnput of the calculating device 6. The output
of the calculati-ng devlce 6 -is connected to the
input of a second delay device 7 and to a first
input o:E a suhtracter 8, whereof a second input
is connected to the output of t:he second delay
device 7. The output of subtracter 8 is connected
to each oE the first inputs of a comparator circu:it
9, a su~tracter 10 and a selection circuit 11. The
two inputs o:f the comparator ci.rcuit 9 and subtracter
10 respectively receive the digital values 4 and
2 ~ A second input and a contro:l. input of the select-
ion circuit l.l are respectively coup:Led to the output
of subtracter 10 and to the output of the comparator
circuit 9. The output of the selection circuit 11
is connected to the input of a third delay device
12 and a first input of an adder 13, whereof a
second input is connected to the output of the third
delay devi.ce 12. The output of adder 13 is connected
to a first input of a memory 14 and to a first input
of a multiplier 15, whereof a second input is connected
to the output of memory 14. A second input of memory
14 is coupled to the output of the calculating
device 6 across a fourth delay device 20. The output
of multipl;.er 15 is connected to the input of a
smoothing device 21. The output of the smoothing
device 21 is coupled to a first input of a subtracter
24 across a sampler 22 and to a second input of sub-
tracter 24 across a fifth de]ay device 23. The sampler
22 also has a controlled input receiving a signal Hs.
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~ ~ ~7~ 68
The subtracters 8 and 10, the comparator
circuit 9 and circu;.t 11 constitute a determinatlon
device 17. In the same way, the third delay device
12 and adder 13 form a first supplementary deter-
mination device 18. Finally, memory 14 and multiplier15 constitute a second supplementary determinatlon
device 19.
The embodiment described relative to
Fig 1 makes it possible to demodulate the chrominance
signal of a SECAM video signal comprising a luminance
slgnal, mainly located i.n the low part of the principal
spectrum which extends Erom 0 to 6MHz and the chromin-
ance signal frequency-modulated about a subcarrier
i.n the vicinity of 4.3M~z and whose frequency sweep
extends between 3.9 and 4.7 MHz.
The operation of this digital demodulator
will be better understood by means of a simple
theoretical development, whose main stages will be
described hereinafter.
The demodulation of a chrominance
signal of a SECAM video signal amounts to the deter-
mination of the frequency of a sine wave varying
in a frequency band B of 0.8 MHz centered around
the frequency F equaL to 4.3MHz. It can be considered
that this sine wave is obtained by the projection
x(t) on an axis Ox of an orthogonal coordinate Oxy
of a rotating vector z(t) rotating about the origin
0 at the angular velocity 2~ (F + ~F)9 S F being
the frequency sweep value and t representing time.0 The equation of x(t3 is given by:
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I ~7~6~
r
x(t) = cos L2~F +~ F)t + ~O~ = cos ~(t)
The vector (in quadrature), whose
projection on axis Ox corresponds to the projectlon
y(t) on axis Oy of vector-z(t) is obtained by
delayi.ng z(t) by a quarter cyc:Le of said sine wave,
4(F +~ F) . As the relative band of the
chromi.nance s:ignal ls small compared with .4.3MHz
(0.8MHz comparecl wlth 4.3MHz), an approximation of
this vecto-r ;n quad:rature i~s obtai.ned by delaying
z(t) by ~ ~= ~1F . This leacls to the following
value oE y(t):
y(t~ = x(t ~ 4lF~) = cos~ 2~ (F + ~F) (t ~ 4F)~ ~o]
= sin ~(t) ~ 2 E~ ]
Starting Erom x(t) and y(t) lt is
pos~sible to make an estimate O(t) of the angle ~(t)
of the vector z(t) with axis Ox: sin[~(t) ~ ~2
~(t) = ~rc tg x(t) with tg ~(t) = ~
At the end o:E a cycle of F J Z( t) has
rotated in the coordinate Oxy by
2~ ~ to within 2~ . Thus, the variation of the
angle ~ ~ between two times of interval F is linked
: with the frequency deviatlon ~ F by the following
cxprcs.s;on:
~ e(t') = O(t + F ) - O(t) ~ with t' = t + F
so th.~t: ~ ~(t') = 2~ ~F ~ .
In practice, it is sufficient to sample
the chrominance .signal at a rhythm equal to 4 times the
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J&'~:~68
~Erequency ~`, store a sarnple :Eor time 4F and makean estimate of the variati.on oE angle ~ ~(t') by
:Eormu:la ~ a:Eter ca:Lculat;.ng 0 (t) and e(t + 1) by
means of :Eormul.a ~ . The va:lue h e(tt) makes it
obtai.n an est;.mate ~F oE the value o ~ F by formula
The operation o:E the device of Fig 1
ls as .Eollows:
The S~.C~M video signal received by the
-Lnput terrnina:L 1 ls f:i:Ltered by :E:;:ter 2 :in order to
select onLy the chromLnance signal. Filter 2 is a
l~ancl ~ S lil.l:cr o[ 3.9 to ~.7M~IZ~ wh.l.ch corre~pond.
to the frequency spectrum of the chromi.nance signal>
This chromillance s;.gna:l is then sampled by the sampler
3 in accordance with a sampling frequency 4F and
converted into binary signals by the analog/digital
c~nver-ter 4.The delay device 5 delays the sample
supplied by converter 4 by a time ~ = 41F . At the
sampling time tl, the calculating device 6 receives
at its inputs the digital value of a sample x(tl~
suppli.ed by converter 4 and the cligital value of a
sample x(tl - 4~ ) supplied by the delay device 5.
Cal.cu:Lat;.ng ~dev;ce 6 mal<es it possible to calculate
the value ~ o:E formula ~ . Delay device 7
introducc.~ a delay of ~' = 1 . At a sampling
time t2 = tl + F subtracter 8 respectively receives
: ~t its inputs the v~lue _ 1~ F supplied by
calculating device 6 and the value -4~r-- supplied
~y the del~y devi.c~ 5 a-nd by means o formula ~
makesit possib.Le to calculate ~ ~ , said value
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r~
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be;ng equaL to ~2 on the ba.sis of formula ~ .
The values supp~ed by the calculating
device 6 are deEined to within -~ by reason of
their definition (formula ~ ). A correction is
necessary for certain cases of subtraction. For
this purpose, it is mereLy necessary to compare
~ H(t2) and ~ , whereby for a value oE ~ 0(t2)
below ~, ~(t2) is retained, whilst for a vaLue o
~ e(t2) above ~, ~(t2) is replaced by ~(t2) ~ S,
S being the sign of ~(t2).
The different stages of this correction
calculation are obtainecl in the examp:le clescribed
in Fig 1. Thus, subtracter 8~supplies ~ ,
F~ E3(t2) FS
subtracter 10 calculates 4~ ~ 4 , comparator
circuit 9 compares ~ to ~- and controls the
se]ection circuit 11 in order to provide the correct
value ~ , ~ being an estimate of the frequency
variation between times t2 and tl ~
The error made on 2 due to the
approximation made in the above theoretical develop-
ment l;F~l, is dependent on the time at which the
signal is sampled, L.e. the position of vector z~t)
in coordinate Oxy at the time of sampling, as well
as on the frequency to be demodulated.
Experience shows and theory confirms
that the systematic error is considerably reduced
by taking the arithmetic mean of two values of ~ F
obtained from two positions which are approximately
in quadrature. This is the function of the first
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t :~ 67168
supplementary device 18. Thus, adder 13 carries
out the addition Of Va1IIe 2 4F) 1i
time t2 ~ 1F by the seLeclion circuit 1~ and the
~ ,. F ( -t
value 2 supplied by the delay device 12 delayed
by 1F
The vaLue 2~ F obtained at the output
of the Ei-rst supplementary determination device 18
can be Eurther ;mproved, wh;lst still considering
that the err~r made o-n ~ F is onLy dependent on the
value ~(t) ancl the Erequency to be demodulated. This
i~s the r(lnctioll o~: the secotld supplementary device
19. The values of ~(t) obtained, to within a
multipllcat;ve factor at the output of delay device
20 with delay ~", and the value 2~ F obtained at the
OlltpUt of adder 13 control the value of a correction
factor 1 + ~n appLiec] to the multiplier 15, in order
to generate a value `~ F equal to (1 ~ n) ~ F at
its output. The delay ~' is equal to the signal
processing time up to the output of adder 13. The
correction Eactor 1 ~ ~n introduced into memory 14
is theoretically determined. The smoothing device
21 is adapted to the selected calculation mode.
In order that the calculation result is
not sens;tive to variations of frequency F, a final
operation is carried out on the digital values obtalned
at the output of the smoothing device 21.
Like aLI television signals, the SECAM
televislon signal is constituted by a luminance signal,
a chrom;nance s;g-nal, a ~;eld synchronization signal0 and a line synchronization signal. In addition to these
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signals, the line synchronization signa:l is accom-
panied by a colour synchronization signal, called
a reference burst. This burst is formed by a train
of sine wave signals at the precise frequency of
the chrominance subcarrier.
Sampler 22 is controlled by signal HS
for selecting the value ~ fO of the samples corres-
ponding to this reference burst. For this purpose,
the control s;gnal HS is Eormed by a sequence of
square wave pulses characterizing the presence of
the reference burst. The values 3~ obtained at
the output Or ~he ~smooth~n~ device 21 ~re ~upplled
to the second input of subtracter 24 after being
delayed by delay dev;ce 23 for a time equal to the
processing time by sampler 22. The value present at
the first input of subtracter 24 is the value 3~fO.
The output of subtracter 24 supplies the final value
of the frequency sweep 4 ~ f = 3~ f - 3 ~ fO at each
cycle 41F to the terminal 16.
Fig 2 shows another digital demodulator,
whose operating principle involves a theoretical
development differing from that descr~s hereinbefore.
In Fig 2, an input terminal 1 is coupled
to the input of an analog/digital converter 4 across
a filter 2 in series with a sampler 3. The output of
converter 4 is coupled to each of the first inputs
of a first calculating device 33 and a second cal-
culating device 34 and to the input of a first delay
device 30. The output of delay device 30 is connected
to the ;nput of a second delay device 31 and to each
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7~6~
of the second inputs of calculating devices 33 and
34. The output of delay device 31 is coupled to each
of the third inputs o:E calculating devices 33 and
34 and to each of the fourth inputs of devices 33
S and 34 across a third delay device 32. The output
of the calculating device 33 ~md a first output of
the calculating device 3~ are respectively connected
to a first input and a second input of a third
calculating device 35. The output oE device 35 is
connected to the input of a smoothing device 50
ac.ross coupling means 36 having a control input
coupled to a second output of calculating devi.ce 34
across a threshold comparator 39. In the same way as
in Fig 1, the output of smoothing device 50 is
coupled to a flrst input of a subtracter 53 across
a sampler 51 and to a second input of subtracter 53
across a fourth delay device 52. The output of
subtracter 53 is connected to an output terminal 16.
As in the case of the demodulator
described in Fig 1, the main theoretical results
making it posslble to realise the demodulator of
Fig 2 are described.
As hereinbefore, a vector x(t) represent-
ing a sine wave, whose frequency is to be estimated
is considered in a coordinate Oxy.
Four values of x(t) are obtained at
regular time intervals equal to 41F' e.g.x(tl),
1 4F )~ x(t~ F)~ x(tl - 3-) t b i
random time. The expression of these four samples
x(tl- 4F)' i varying from 0 to 39 i.s as follows:
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, ~
.

x(tl- 4F) ~ cosL~ (t.
= cos ~(t~ F~
with ~ = 2~ (F ~ F).
On the bas;.s o:E formula ~ , it i5 possible
to calculate ~ F on the basis o:E the fo.llowing
formula ~ :
2F ~ x(t~ F)- x(tl)- x(tl ~ ~F) ~ x(tl- 4lF
F = ~ arc sinl ~ - - 2 - ~ 1~ ~~ ~~ ~~ ~~~~
~ ~ 2x(tl ~ ~F~ ~ 2x(tl 4F )
= ~ arc s:in (D)
providecl that:
( 1 4F) 2x(tl ~ 4F) ~ ~ lNDI ~ 1
In practice, it is merely necessary to
sample the chromirlcmce signal at a rhythm equal to
4 times the frequency F, store the samples and cal-
culate ~F by form-lla ~ .
The operation of the device of Fig 2
;s ~s .~ol:lows:
In the same way as for Fig 1, the SECAM
vi.deo signa]. rece-.ived on input terminal 1 is processed
so as to obtain at the output of converter 4 digital
samples x(t) of the chrominance signal in accordance
with a frequency 41F Each of these samples is then
introduced into the clelay devices 30, 31, 32 to obtain
both sample x(tl) and samp.le x(tl ~ 41F) at a random
time tl. On the basis of these values, the calculating
devices 33 and 34 re~spect:i.vely calcu].~te the v~lues
N and D of formu:la ~ . In the same way, at each
sampling time, the cal.culating device 35 supplies
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~F on the basis of EormuLa ~ . Comparator 39 makes
it possibLe to compare~D¦ with S (S positive real),
the value S representing the threshold value below
whlch the approximation of arc sin (ND) is poor
5 ( ¦D~ small). When~D3 exceeds S and under this con-
clition only, comparator 39 control s the coupling
means 36 for couplirlg the output of device 35 to
the input of filter 21 and for permitting the passage
of the digital samples ~ F.
Elements S0, 51, 52 and 53 respectively
have the same definitions as elements 21, 22, 23 and
24 oE Fig 1 and malce Lt possible to generate the
digital values of the frequency sw~'ep at output
terminals 16 in order to be able to reconstitute
the demodulated signal.
The invention is not limited to the
embodlment descrlbed and represented, numerous
variants being possible thereto without passing
beyond the scope of the invention.
In particular in Fig l, the functions
performed by the delay device 5 and calculating device
6, delay device 7 and devices 17, 18 and 19 can be
performed by means of charge transfer devices and
the analog/digital converter 4 is then rendered
superfluous.
In the same way in Fig 2 delay devices
30, 31 and 32, calculating devices 33, 34 and 35,
comparator 39 and coupling means 36 can be replaced
by charge transfer devices~ the analog/digital con-
verter 4 again being rendered superfluous.-12-
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1 3 ~7~6~
-In the ernbocl;,ments desc-ribed rel.ative
to Figs 1, and 2, the~ chrom:inance signal is sarnp:led
at a rhythrll equa:l. to 4 t.;.me.s the frequency F equal
to 4.~MT-l7.. Ilowever, th;s va:l.ue F is tlOt restri.ctlve,
any Ete(ll1erlcy val.lle F' ;n the frequency 'band of the
Chl Om j T1anCC~ Si~,na:l bein~ suitable.
Mo-r-eove-r, -in the embodiment descr;bed
rel,ative to l?;,~ 2, t'he va.lue of the sampling rhythm
ccm be macle e~lucl:L to ~I ti,mes the Erequency F' (q
pos1tive rea:l.), formu:l..a ~ then being replaced by
the .Eo'l.lowi.n~ ~enera'l.:Formula:
~ F - ~ arc s;.n ~ F' (1 - ~). This
genera:l. rornluLa -is appl;cable for a random number o:E
samp:les, N ~nd D being Linear com'binations of success-
ive samp.Les.
It i.s a.ls() po;nted out that ;n Figs 1and 2, the respective posltions of filter 2, sampl,e
3 and ana'lo~ itcll converter 4 can be reversed.
F'inally, it is important to note that
the invent;.on i.s appllcable to any frequency-
modu.'l.ate~d s.i~n.-ll,, provi.ded that the frequency band
of the s:ignal. ;s smal,'l compared with the centre
frequency ~
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