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Produced by the NASA Center for Aerospace Information (CASI)
JPL PUBLICATION 7993
Spectral Characteristics
of
C.onvol utionally
Coded
Digital Signals
Dariush Divsalar
Marvin K. Simon
(NASA

CR162295) SPECTRAL CHARACTERISTICS
OF CONVOLt1TIONALLY CODED DIGITAL SIGNALS
(Jet Propulsion Lab.)
85 p AC A^5
/MF A^1
CSCL 17B
G3/32
N79 32412
vnclas
35794
T,
Y'
A, „ *
'%f4
0^,
August 1, 1979
National Aeronautics and
Space Administration
Jet Propulsion Laboratory
California Institute of Technology
Pasadena,.
California
l
I^
JPL PUBLICATION 79•93
.:.
Spectral
Characteristics
of Convolutionally
Cooed Digital Signals
Dariush Divsalar
Marvin K. Simon
r
3
August 1, 1979
µ
National Aeronautics and
Space Administration
Jet Propulsion Laboratory
California Institute of Technology
Pasadena, California
{
TABLE OF CONTENTS
I.
Introduction
.
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..
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2
II, '
Convolutional Encoder Model
• . • • . • • • . . . . . .. • • . • •
• • • .
3
III.
Spectrum of a Cyclostationary Pulse Stream
• • • • • • • • . . • • • • • •
5
IV.
';Encoder Output Spectrum for Independent Binary Symbol Input
• • • •
8
A
The Case of a Purely Random Data Input (a = 0, p* a. 1/2)
13
I
4Y
B.
The Case of an Unbalanced NRZ Input (a
0,
P*
1/2)
. .. . . .
18
V. !
Encoder Output Spectrum for First Order Markov Input . . . . .. .
33
VI.
.Encoder Output Spectrum in the Presence of Alternate
Sy
mbol Inversion
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...
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44
VII.
Experimental Results .
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56
VIII.
Observations and Conclusions
.... ..
56
g
Ref
erences
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.....
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61
Appendix A: The Computation of Power Spectral Density for
Synchronous Data Pulse Streams
...
.... . ....
.... ..
.
62
Appendix B: Costas Loop Track'ag Performance fora
"
Convolutionally Encoded Suppressed Carrier Input Modulation
....
77
^
9
r
,:
s
w
l
ti • n
^,
J
LIST OF FIGURES
11
Figures
1.
A General Constraint Length K, Rate b/n Convolutional
Code
,
.........................................
4
2.
An Illustration of the Code Constraints of Equation (27) .
.
.
.
.
.
12
3.
Spectrum for Best Rate 1/3; Constraint Length 3
Convolutional Code; Dotted Curve is Spectrum of NRZ
.
.
16
4.
Spectrum for Best Rate 1/4; Constraint Length 3
Convolutional Code; Dotted Curve is Spectrum of NRZ
.
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17
5.
Spectrum for Best Rate 1/3, Constraint Length 3
Convolutional Code
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19
6a.
Spectrum for Best Rate 1/2, Constraint Length 3
Convolutional Code;
p* = Oa 1 .
.
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. .
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. .
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. .
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22
6b.
Spectrum for Best Rate 1/2, Constraint Length 3
Convolutional Code; p* = 0.3
.
. . .
.
.
. .
. .
. .
. .
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.
23
6c.
Spectrum for Best Rate 1/2, Constraint Length 3
Convolutional Code; p* = 0.5
. . . . .
. . . . .
. . . .
.
.
.
.
.
.
.
.
24
7a.
Spectrum for Best Rate 1/2, Constraint Length 7
Convolutional Code; p* = 0.1
. . .
. . . . .
,
,
,
,
,
,
,
,
,
26
7b.
Spectrum for Best Rate 1/2, Constraint Length 7
Convolutional Code; p* = 0.2
.. .
. .
. . . . .
. .
.
.
.
.
.
.
27
7c.
Spectrum for Best Rate 1/2, Constraint Length 7
Convolutional Code; p* = 0.3
. . . .
.
.
. .
. .
. . . . . .
.
.
.
.
.
.
28
8a.
Spectrum for Best Rate 1/2, Constraint Length 7
Convolutional Code; Sampler Reversed; p* = 0.1
. . , ,
,
,
,
,
,
,
30
8b.
Spectrum
for
Best Rate 1/2, Constraint Length 7
Convolutional Code; Sampler Reversed; p* = 0.2 .
. . ,
.
,
.
,
,
31
8c.
Spectrum for Best Rate 1/2, Constraint Length 7
Convolutional Code; Sampler Reversed; p* = 0.3
, , , ,
,
,
,
,
.
.
32
9a.
Power Spectrum of First Order Markov Source; p
t
= 0.1 ,
,
,
,
,
,
,
.
,
39
9b.
Power Spectrum of First Order Markov Source; pt = 0, 3 ,
.
,
,
,
,
40
9c.
Power Spectrum of First Order Markov Source; pt = 0.5 ,
,
,
,
.
,
41
9d. ,
Power Spectrum of First Order Markov Source; p
t
= 0.7 ,
42