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ELECTRICAL
(NASA-CB-1 20492) ANALYSIS OF AN IMPULSE
NOISE SUPPRESSOR FOR FM DEMODULATORS
Final Report (Auburn Univ.) 39 p HC
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ANALYSIS OF AN IMPULSE
NOISE SUPPRESSOR FOR
FM DEMODULATORS
Prepared by
TELEMETRY SYSTEMS LABORATORY •
AUBURN UNIVERSITY
AUBURN, ALABAMA
RESEARCH PERSONNEL
Sidney N. Janies
FINAL REPORT
June 1, 197^
CONTRACT NAS8-20765
GEORGE C. MARSHALL SPACE FLIGHT CENTER
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
HUNTSVILLE , ALABAMA
FOREWORD
This technical report is the final report for contract NAS8-20765-
One other technical report was submitted during the last extention of
the contract which was entitled: "A Comparison of Special-Purpose and
General-Purpose Computers for Data Compression" by H. C. Cobb, IV and
S. N. James, November, 1973-
11
TABLE OF CONTENTS
LIST OF FIGURES iv
I, INTRODUCTION . 1-1
II. THEORETICAL CONSIDERATIONS IN FM CLICK NOISE 2-1
A. Basic System
B. System with Additive Noise
C. Threshold Effects
III. EXPERIMENTAL RESULTS USING AN FM CLICK SUPPRESSOR 3-1
A. Previous Test Results on an FM Click
Suppressor Circuit
B. Click Noise Generation Using the R-1037-A
Telemetry Receiver
C. Characteristics of the Click Suppressor
D. Click Suppression Using the R-1037-A
IV. CONCLUSIONS. ..... 4-1
REFERENCES R-l
in
LIST OF FIGURES
2-1. FM Demodulator ♦ 2-3
2-2 (a). Phasor Diagram Above Threshold. .... 2-6
2-2(b). Phasor Diagram Near Threshold 2-6
2-3. Output Noise Characteristics 2-8
"l". Block Diagram of Click-Detecting, Signal-Holding
Click Suppressor. ........ * 3-2
" 2 ". Schematic of Final Click Suppressor Circuit 3-3
"22". Test Signal Generator . . 3-4
"3". Oscilloscope Traces Before (Top) and After (Bottom)
Click Suppression. The Modulation Component has the
Same Amplitude in Both Traces. Modulation Frequency
is 30 kHz, Derivation is +_ 80 kHz, IF Bandwidth is
262 kHz, Input SNR is 5 dB • . 3-5
"4". Output Noise Power Before and After Click Suppression
(Unmodulated Carrier) 3-6
3-1. Experimental Click Generation • . . . 3-T
3-2. Output Signal for 12 db Input Signal -to-Noise Ratio,
Modulation Index of 3 3-9
3-3. Output Signal for 10 db Input Signal-to-Noise Ratio,
Modulation Index of 3, Multiple Oscilloscope Traces . . . 3-10
3-4. ' Output Signal for 6 db Input Signal-to-Noise Ratio,
Modulation Index of 3, Multiple Oscilloscope Traces . . . 3-11
3-5- Output Signal for 2 db Input Signal-to-Noise Ratio,
Modulation Index of 3, Multiple Oscilloscope Traces . . . 3-12
3-6. Number of Clicks as a Function of Input Signal-to-
Noise Ratio 3-13
iv
3-7. Before and After Click Suppression for Simulated
Signal 3-lU
3-8. Output Signal Before (Top Trace) and After Click
Suppresion, 10 KHz Signal and 12 db S^ , Modu-
lation Index of 3 i . . * 3-15
3-9. Output Signal Before (Top Trace) and After Click
Suppression, 10 KHz Signal and 10 db S^/jj., Modu-
lation Index of 3 . . . . 1 3-16
3-10. Output Noise Before (Top Trace) and After Click
Suppression Unmodulated Carrier, 10 db S^/jf 3-18
3-11. Output Noise Before (Top Trace) and After Click
Suppression, Unmodulated Carrier, 6 db . 3-19
3-12. Output Noise Before (Top Trace) and After Click
Suppression, Unmodulated Carrier, 2 db ....... 3-20
3-13- Output Noise Before and After Click Suppression
For an Unmodulated Carrier 3-21
V
I. Introduction
This technical report is concerned with the evaluation of an FM
click noise suppressor built by the ADCOM Corporation, Cambridge,
Massachusetts under contract NAS8-21209.
Chapter II presents a short theoretical justification for the
existence of FM click noise near threshold conditions. Several
references are listed where more detailed theoretic,al analysis of
click noise can be found. ^
Chapter III is a summary of experimental tests which were performed
on this click noise suppressor. These tests were performed to verify
previous test results (al^o included in Chapter III) and to determine
the range and "worse case" type of operation for the suppressor.
Chapter IV is a summary of the conclusions reached as a result of
these tests and suggestions for future work in this area.
1-1
II. Theoretical Considerations in FM Click Noise
Most modem communication theory texts include a fairly complete
*
discussion of noise effects in FM systems including threshold and click
12
characteristics. * This chapter is a summary of the derivations and
conclusions presented in reference 1 and does not include all the details
for a complete presentation.
A. Basic System
The block diagram of Fig. 2-1 shows a typical FM demodulator. The
demodulation takes place from some intermediate frequency, f ^ , to the
baseband signal v Q {t). If we assume the input signal to he of the
form
v i (t) = A eos[<i).jt + Q(t)] 2-1
then the output will be
v (t) = a 2-2
o dt
where a is a system constant and the message is proportional to the
derivative dQ(t)/dt. If the modulation is such that
t
Q(t) ~ K J* m(A)dX 2-3
—CO
then the output signal power is
S Q = a 2 K 2 m 2 (t). 2-4
2-1
B. System with Additive Noise
If an unmodulated carrier and hand-limited noise is added it may-
be expressed in quadrature component as
v i (t) = Acosw^(t ) + n c (t)cosoi i t - n s (t)sinw i t 2-5
or
^(t) = E(t)cos[w i t + 0 ( t ) J
where
2-6
R(t) = W[A +
n c (t )]
+ [n a (t)]‘
and
e(t) = tan” 1 ilili .
A+n c (t)
Assuming the noise is much less than the signal the output of the
demodulator may be written as
dn g (t )
dt
2-7
which leads to a . power density spectrum over the baseband frequency of
G n {f >=^n 2 _ 8
for i f l 1 § where n/2 is the input power density which is assumed to
be white Gaussian noise over the input band-width. The output noise
power is then found by integrating the power density spectrum over the
2-2
Discriminator
VO = a SbM
4 dt
FIGURE 2-1. FM DEMODULATOR
2-3
base-band frequencies from -f m to +f m :
= 8rr£ s!a f 3
3 m
2-9
An approximate signal-to-noise ratio can now be found from equation 2-1+
and 2-9 as
S 0 _ 3 K 2 m 2 (t) A 2 /2
N 0 k * 2 f m 2 nf m
If the message is assumed to be sinusoidal then
_a-2 62 £i
Mo 2 *i
where 8 = Af/ftn is the modulation index and is the input signal-
to-noise ratio.
A signal-to-noise ratio gain factor may be found then as
^o^Nq _ 3_ g2
Si/Hi 2
2-12
This is the type of results normally calculated to compare FM to other
types of modulation and shows the improved performance expected from the
wide band FM signal by trading band-width for signal-to-noise ratio gain.
2-1+
This result was calculated for small additive noise and does not predict
the threshold effects found when the noise level approaches the signal
level.
C. Threshold Effect
As the noise level in an FM signal increases equation 2-11 predicts
a linear related input and output signal -to-noise ratio. However at low
signal -to-noise ratios, about 10 db, another effect takes place and that
is the generation of noise impulse or clicks in addition to the expected
smooth Gaussian noise.
One way of demonstrating how these impulses occur is to examine the
phasor diagram of equation 2-5 or 2-6 as shown in Fig. 2-2(a) and (b).
If the noise variation is small compared to the carrier amplitude A
then the locus of R(t) is near A as shown in Fig. 2-2(a). This type
of variation produces phase changes which are small and thus the corre-
sponding frequency changes are small. However if the noise is large,
producing a locus such as shown in Fig. 2-2 (b), the phase change is 2 tt
radians and the corresponding time derivative must change from 0 to 2ir
and back to 0. This results in a noise pulse in the output. More
complicated phase variation which does not encircle the origin of the
phasor diagram will produce impulses which are triplets or higher order
impulses. Since their average value is zero and most of their harmonic
content is outside the baseband filter limits they are normally not
included as part of the contributing output noise.
2-5
This output noise due to spikes can be calculated as
w s = hiut 2 f ;
T s
2-13
where T g is the mean time between impulses and can be calculated as
Using these relations and combining both smooth Gaussian noise and
impulse noise leads to a signal-to-noise ratio of
£o _ [3K 2 m 2 (t)/^ir 2 f m ](S i /N i )
N 0 l+(/TB/f m )(S 1 /N i ) erf c ^f m /B)(S i /N i )
2-15
This result is only valid for unmodulated carriers. If the carrier is
modulated then the impulses are more frequent and the threshold effect
occurs sooner as the noise increases. A typical set of output noise
characteristics is shown in Fig, 2-3 where the modulation is assumed
to be sinusoidal.
Several systems such as the higher order phase locked loop and the
FM demodulator with feedback have been proposed to extend the threshold
3
of FM systems.
2-7
III. Experimental Results Using an FM Click Suppressor
A. Previous Test Results on an FM Click Suppressor Circuit
The results presented in this section were taken from "Development
and Testing of an Impulse Noise Suppressor for FM Demodulators,"
February 5, 19^9* Contract NAS8-21209, ADCOM Corporation, Cambridge,
Massachusetts, "Figure 1" shows the basic block diagram of the click
suppressor and the circuit diagram is shown in "Figure 2." This circuit
was used to suppress clicks generated by the test signal generator
shown in "Figure 22." Note that the discriminator bandwidth was. 2 MHz
which is considerably larger than the IF bandwidth of 2 62 KHz. This
was to insure that wideband clicks would be passed by the Discriminator.
"Figure 3" shows typical results using the click suppressor when the
carrier was modulated. "Figure U" shows the reduction in output noise
using the click suppressor for an unmodulated carrier.
B. Click Noise Generation Using the R-1037 a Telemetry Receiver
Since the same test system described in section A was not available
a typical telemetiy receiver (R-1037-A Telemetry Receiver by Vitro Elec-
tronics, Silver Spring, Maryland) was used. Even though this system
will not generate the larger number of impulses near threshold it does
present a more realistic application of the click suppressor. Figure
3-1 shows the experimental test set up used to generate the click noise.
Notice that the IF bandwidth is 300 KHz but the demodulator bandwidth
is 150 KHz. This demodulator bandwidth will not allow the wider band-
width or higher order click to be passed.
3-1
ADVANCED COMMUNICATIONS • RESEARCH AND DEVELOPMENT
Ail Resistance Values are in Ohms
All Capacitance Values are in /iF
Fig. 2 Schematic of Final Click Suppressor Circuit
REPRODUCIBILITY OF THE
ORIGINAL PAGE IS POOR
ad /com
t- 56 04
Fig. 22 Test Signal Generator
3-U
40
ADVANCED COM Ai UNICATIONS • RESEARCH AND DEVELOPMENT-
/I I A
COM
B-S587
Fig. 3 Oscilloscope Traces Before (Top) and After (Bottom) Click
Suppression. The Modulation Component has the Same Am-
plitude in Both Traces. Modulation Frequency is 30 kHz,
Derivation is ± 80 kHz, IF Bandwidth is 262 kHz,
Input SNR is 5 dB.
3-5
6
• RESEARCH AND DEVELOPMENT
ADVANCED COMMUNICATIONS
PS133
Input SNRfdBJ
ADVANCED
Fig. 4 Output Noise Power Before
and After Click Suppression
(Unmodulated Carrier)
3-6
7
COMMUNICATIONS • RESEARCH AND DEVELOPMENT
Figures 3-2, 3-3, 3-4 and. 3-5 show typical noise characteristics
near and "below threshold for this receiver. Figure 3-6 shows a plot
of the number of dominate clicks as a function of input signal-to-noise
ratio. Since this data was taken from photographed scope traces some
of the smaller clicks may have been missed.
, C. Characteristics of the Click Suppressor
The click suppressor circuit shown in "Figure 2" was apparently
modified before these tests were requested but the circuit operates
as predicted. The major changes were the addition of two transistors,
one in the high-pass filter section, and the other in the pulse shaping
network and the absence of a delay element. Several different lengths
of delay line were used for this element but little difference could be
seen from just using a short circuit connection.
Figure 3-7 shows typical before and after click suppression results
using a sine wave signal and an additive narrow pulse for click noise.
The suppressor would not detect clicks longer than about 5 microseconds
or smaller than about 1 volt . The signal frequency limit was about 100
KHz.
D. Click Suppression Using the R-1037-A Telemetry Receiver
Using the test system of section B and C the click suppressor was
used to suppress click noise generated by a typical receiver. Figure
3-8 and 3-9 show typical before and after click suppression results.
The "before" signal contains some high frequency clicks but the suppression
introduces much more distortion in the signal by trying to suppress these
3-8
FIGURE 3
■HV-V'
-2. OUTPUT SIGNAL FOR 12 tfb INPUT SIGNAL-TO-NOISE RATIO,
MODULATION INDEX OF 3.
3-9
FIGURE 3-
’ 'Jv
3. OUTPUT SIGNAL FOR 10 db INPUT SI®AL-T0-N0ISE RATIO
MODULATION INDEX OF 3, MULTIPLE OSCILLOSCOPE TRACES
3-10
FIGURE 3-b.
OUTPUT SIGNAL FOR 6 db INPUT SIGNAL-TO-NOISE RATIO,
MODULATION INDEX OF 3, MULTIPLE OSCILLOSCOPE TRACES.
3-11
FIGURE 3-
V V ' .
*» *
» . i
• JL \
* A A .
t » * \
V • ' '■‘r'AT
5. OUTPUT SIGNAL FOR 2 db INPUT SIGNAL-TO-NOISE RATIO,
MODULATION INDEX OF 3, MULTIPLE OSCILLOSCOPE TRACES.
3-12
FIGURE 3-6. NUMBER OF CLICKS AS A FUNCTION
OF INPUT SIGNAL-TO-NOISE RATIO
3-13
FIGURE 3-7. BEFORE AMD AFTER CLICK SUPPRESSION
FOR SIMULATED SIGNAL.
3-1 U
FIGURE 3-8. OUTPUT SIGNAL BEFORE (TOP TRACE) AND AFTER CLICK
SUPPRESSION, 10 KHz SIGNAL AND 12 db S ± / v , MODU-
LATION INDEX OF 3.
FIGURE 3-9. OUTPUT SIGNAL BEFORE (TOP TRACE) AND AFTER CLICK
SUPPRESSION, 10 KHz SIGNAL AND 10 db S i / , MODU-
LATION INDEX OF 3. W i
3-16
clicks. As the frequency and width of the clicks increases the signal
distortion becomes very large as indicated in Figure 3-9.
Figure 3-10, 3-11 and 3-12 show output noise before and after
click suppression for an unmodulated carrier. Even though the clicks
are being suppressed, considerable distortion is introduced by the
suppressor. Figure 3-13 is a comparison of the RMS noise voltage before
and after click suppression. Here again the results show little im-
provement in using the click suppressor.
3-17
FIGURE 3-10. OUTPUT NOISE BEFORE (TOP TRACE) AND AFTER CLICK
SUPPRESSION UNMODULATED CARRIER, 10 db S. .
l/N.
3-18
FIGURE 3-11. OUTPUT NOISE BEFORE (TOP TRACE) AND AFTER CLICK
SUPPRESSION, UNMODULATED CARRIER, 6 tfb .
3-19
FIGURE 3-12. OUTPUT NOISE BEFORE (TOP TRACE) AND AFTER CLICK
SUPPRESSION, UNMODULATED CARRIER, 2 db S i/W- .
3-20
IV. Conclusions
The initial tests on the IW click-noise suppressor show that the
circuit does perform click suppression but over a limited range. Using
the circuit in a practical application introduces considerable error
as indicated by Figures 3-8 and 3-9* The results could probably be
improved by following the suppressor with a low pass filter to smooth
out the signal. Since the suppressor was designed for operation in a
circuit other than the R-1037-A telemetry receiver it probably could
be improved for such a specific application.
More information on the statistical characteristics of click noise
is needed if an optimum suppression technique is to be designed. In-
formation on frequency range, amplitude distribution, duration, etc.
as a function of the particular system being designed would be desirable.
During the performance of the experimental tests of this report many
parameters were observed to affect the characteristics of the click
noise.
One possible approach to better understanding the characteristics
of click noise would be to study their generation using deterministic
signals or simulated noise signals. This would help determine the
exact time signal conditions for generating different types of clicks
and how these clicks occur in different types of discriminators.
h-1
When more information on the characteristics of click noise is
known, suppressor systems could he designed taking into account the
discriminator as one possible choice of circuit modification as well
as adding a click suppressor. Discriminators like the phase-locked-
loop and demodulators with feedback should also be considered as part
of an optimum suppressor design.
h-2
REFERENCES
1) Taut), H. and D. L. Schilling, Principles of Communi cation Systems ,
Chapter 10, McGraw-Hill Book Co., New York, 1971.
2) Rice, S. 0., "Time-series Analysis," Chapter 25, John Wiley Inc.,
New York, 1963.
3) Schilling, D. D. and J. Billig, "Threshold Extension Capability of
the PLL and The FMFB, Proc. IEEE, May, 1 96b.
U) Ringdshl, I. and D. L. Schilling, "On the Distribution of the Spikes
Seen at the Output of an FM Discriminator Below Threshold," Proc.
IEEE, December, 196U.