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In Fig. 4, values of r and q obtained by the optimisation
method are plotted as a function of frequency. Graphs of this
kind should help in choosing the adequate vertex plate radius
and location for operating a given antenna at any desired frequency. It is seen that, while r undergoes strong changes in the
given frequency range, the corresponding changes in q are relatively weak. It should be noted that for frequencies lower than
about 3 GHz, the radius of the optimum vertex plate becomes
large in respect to the reflector focus length. This could deteriorate the desired radiation pattern of the antenna.
Experimental results 3 have shown the highest value of the
reflection coefficient at the feed of the antenna to be — 32 dB in
the frequency range 7-125-7-750 GHz with a vertex plate of
radius 13-325 cm; the corresponding theoretical results obtained by our method fall between —33 dB and —31-8 dB in
the same frequency range.
Acknowledgments: The authors would like to thank Andrew
Antenna Systems, Lochgelly, Fife, Scotland, for kindly providing them with their experimental results.
Department of Electrical Engineering
Technion—Israel Institute of Technology
Haifa, Israel
27 th October 1980
1 SILVER, s. (ED.): 'Microwave antenna theory and design' (McGrawHill, 1949)
POULTON, G. T., LIM, s. H., and MASTERMAN, P. H.: 'Calculation of
be related to a simple property of the speech being coded.
Analysis: In deriving the results presented in Reference 1 it was
assumed that at the receiver decoding commenced at the instant when the first symbol was received, irrespective of
whether the symbol was an injected symbol, or an actual data
symbol; and that the number of symbols injected in the time
interval TK associated with the Kth data symbol could be neglected in comparison with Si(t), the total number of symbols
injected up to time t.
In deriving the results of Reference 1 the total number of
received symbols was taken to be Rt, rather than the true value
which is R(t + 1), the additional 'one' being a consequence of
commencing decoding instantaneously on receipt of the first
symbol. Also, in deriving the expression for delay P in an injection system the number of injected symbols was taken to be
S,(t), rather than S,(f + TK), where TK is the time duration
between the instants at which the K\h and (K + l)th data
symbols are required by the decoder. When operating at a
transmission rate equal to the average rate at which data is
produced by the source, the effect of the simplifying approximations is negligible since the errors in delay estimates are
small in comparison with the actual delays involved. When
dealing with higher transmission rates, however, the necessary
minimum decoding delays are significantly reduced and it is
then necessary to remove the approximations in order to
obtain sufficiently accurate estimates of the delays.
Using the same arguments as were presented in Reference 1
it can be seen that, in the case of a symbol injection system, it is
necessary to introduce a delay /? at the decoder if distortion is
to be avoided, and that /? should be such that
input-voltage standing-wave ratio for a reflector antenna', Electron.
Lett., 1972,8, pp. 610-611
+ X Ti>(K-l)x
CORY, H., BHAN, K. K., and CLARRICOATS, P. J. B.: 'The reflection
coefficient at the feed of a radome covered reflector antenna'.
Research report, Faculty of Engineering, Queen Mary College,
University of London, August, 1978
+ S,(t + TK)r
i= 1
T( = t;
COLLIN, R., and ZUCKER, F. J. (EDS.): 'Antenna theory' (McGraw-
(K - I) = Rcum(t);
r = l/R
Hill, 1969), pt. 2
and S;(r + TK) is the number of symbols injected at the transmitter in the period up to the time instant t + TK. Rewriting
eqn. 1 gives
0013-5194/80/250945-03$!. 50/0
S,(t + TK) - Rt}
Indexing terms: Speech, Data transmission
Explicit expressions are derived for the limiting delay in time
encoded speech-type systems operating at data transmission
rates higher than the average rate at which information is
produced by the variable-rate source.
Introduction: In an earlier publication1 expressions were
derived for the delays involved in variable-information-rate
source to constant-transmission-rate schemes of data compression with attention being restricted to the case in which the
transmission rate was set equal to the average rate at which
information was produced by the source.
Recently2 it has been shown, in cases in which transmission
bandwidth constraints are not so severe, that, if the transmission rate is increased above the average rate at which the
source produces its data, then the time delays involved in the
buffering of time encoded speech can be significantly reduced.
The purpose of this letter is to show that if certain simplifying approximations that were made in deriving the results of
Reference 1 are removed then it is possible to derive explicit
expressions for the values of the delays involved in timeencoded speech-type systems and that when the rate of transmission exceeds a value determined by the maximum rate of
change of /?„„,(£), where Kcum(0 is the cumulative total number
of information symbols generated by the source, the delay can
4th December 1980
which means that the minimum necessary delay is
P > j {Rcum(t) + S,(t) + kK -
where XK is the number of symbols injected during the time
interval TK. Expr. 3 is a fully accurate statement of the minimum decoding delay P necessary in an injection system..
Although in the case of general transmission rates it does not
appear possible to obtain a simpler result than eqn. 3 above, it
is possible if the transmission rate R is such that
to simplify the result in an important way. In this case
S,(t + TK) = R(t + TK) + 1 - i W + TK)
and since
/ *
it follows from eqn. 4 that
S,(t + TK) = R(t + TK) -
and hence on substituting for S,(t + TK) in eqns. 2 or 3, the
minimum necessary delay P is found to be
Vol. 16 No. 25
P > {7-KU,
Conclusions: The physical significance of this result is that for
injection-type systems in which the transmission rate R is
greater than the maximum rate of change of Rcum(t), the minimum necessary delay is equal to the longest interval between
successive zero crossings of the speech signal. Measurements
indicate that for bandpass filtered speech the delay will be
approximately 3 ms.
Department of Electrical Engineering
Imperial College of Science & Technology
Exhibition Rd., London SW7
22nd October 1980
go = - j l
TURNER, L. F., FRANGOULIS, E. F., and ALCAIM, A.: 'Some considera-
tions relating to the performance of variable-information-ratesource to constant-transmission-rate schemes of data compression',
IEE J. Comput. & Dig. Tech., 1979, 2, (3), pp. 134-141
Fig. 1 shows the experimental arrangement used. The sensor
consists of a single-mode Hitachi HLP 1400 laser and an external reflector whose position is modulated by the incident field
to be measured. The intensity of the laser output is monitored
with a large area photodiode placed near to the rear facet of
the laser.
The sensor acts in the following manner. The external
reflector feeds light back into the laser cavity, the phase of
which is determined by the distance d. When light is fed back in
phase with the light in the laser cavity the effect is to raise the
facet reflectance; when the light is out of phase the facet
reflectance is lowered. The gain at lasing threshold g0, with a
single external reflector, is given by
l n
where Ro is the facet reflectance without feedback (032 in this
case) and R the facet reflectance with feedback. Consequently,
the threshold current level may be changed by altering the
MASON, D. c , and BALSTON, D. M.: 'Relationship between system
delay and transmission rate in time-encoded speech', Electron.
Lett., 1980, 16, pp. 128-130
0013-5194/80/250947-02$!. 50/0
(682/ 2|
distance from laser
Fig. 2 Laser output as a function of distance of reflector from the laser
facet; periodicity is {X/2)
Indexing terms: Acoustic sensors, Diode lasers
A new sensor capable of detecting sinusoidal displacements as
small as ~ 9 x 1 0 " 5 nm has been constructed. The sensor,
employing phase modulation of light fed back into the laser
cavity by an external reflector, has been successfully tested as
an acoustic sensor.
Recently there has been considerable interest in acoustic,1
magnetic 2 and acceleration 3 sensors using single-mode optical
fibres in interferometers. In these approaches the incident field
to be detected induces a phase modulation in the light passing
through a single-mode fibre which is then detected.1 Other
approaches using optical fibres rely on intensity modulation
transduction mechanisms. 4 Recently there has been interest in
the properties of external cavity diode lasers; 5 in this letter a
new sensor using a single-mode laser and an external reflector
is described.
phase of the light fed back into the laser cavity.6 Shown in Fig.
1 is the output characteristic of the HLP 1400 laser with no
feedback, with feedback in phase (to the left of the no feedback
line) and out of phase (to the right); the reflectivity of the
reflector was 4%. The reflector was within 10 ^m of the laser's
facet. By continuously moving the reflector while running the
laser above threshold (for no feedback) an intensity modulation takes place; this is shown in Fig. 2. From Fig. 1 it can be
seen that the maximum modulation depth is obtained when
the driving current is 72 mA (i.e. at threshold when the feedback is in phase with the laser's output). By placing the
reflector at point A shown in Fig. 2, it can be seen that small
movements of the reflector (i.e. changing the phase of the feedback) results in relatively large changes in the output intensity.
Consequently, the modulation of the external reflector's position (say by an acoustic wave) produces an intensity modulation which is detected.
spectrum analyser
current , mA
Fig. 1 Laser output characteristics as a function of driving current for
free running laser ( # ) and laser with 4% feedback (O)
Insert: experimental configuration
frequency, kHz
Fig. 3 Variation of the minimum detectable displacement and equivalent
phase shift with frequency for 4% (O) and 98% ( # ) reflectors
4th December 1980
Vol. 16 No. 25
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