Pulse or digital communications – Synchronizers – Frequency or phase control using synchronizing signal
Reexamination Certificate
1999-02-05
2002-08-27
Pham, Chi (Department: 2631)
Pulse or digital communications
Synchronizers
Frequency or phase control using synchronizing signal
C375S354000
Reexamination Certificate
active
06442224
ABSTRACT:
FIELD OF THE INVENTION
This invention relates to a mixing and separating method for a plurality signals, more particularly, to achieve control circuit for signal processing.
BACKGROUND OF THE INVENTION
The electronic communication has grown more and more prosperous and the problem of available of communication channel becomes even serious. The bandwidth of a specific communication medium is limited, therefore how to most exploit the avail bandwidth is essential. It is the object of the invention to provide a method for transmitting a plurality of signals in a pair of transmission line or a single channel.
SUMMARY OF THE INVENTION
Principles of the Invention I
The present invention is based on the principle of unique solution condition for a set of N linearly equations, i.e., linearly independence. Based on this principle, each of the m signal S
i
(t) within period [T
0
, T
1
] is sampled for n samples S
i
(t
j
), j=1,2 . . . n, wherein t&egr;[T
0
, T
1
], T
0
, T
1
&egr;R, t is time variable. Each sample is multiplied by a coefficient function
i
a
j
(t) which is a linear independent set (i=1,2 . . . m, j=1,2 . . . n), thus obtaining m transformed signals for S
i
(t):
S
i
0
(
t
)
=
∑
j
=
1
n
[
a
j
i
(
t
)
S
i
(
t
j
)
]
summing above m transformed signals obtains the mixed transformed signals:
SM
(
t
)
=
∑
i
=
1
m
[
S
i
0
(
t
)
]
The mixed transformed signals have m×n variables S
i
(t
j
) with coefficient
i
a
j
(t). If party A transmits SM(t) during time [T
0
, T
1
] to party B, party B will obtain message of m×n S
i
(t
j
), (i=1,2 . . . m, j=1,2 . . . n), wherein the bandwidth depends on the max bandwidth of
i
a
j
(t). More particularly, party A can m messages S
i
(t) (i=1,2 . . . m) to party B during time [T
0
, T
1
], if the samples (unknowns) S
i
(t
1
), S
i
(t
2
), S
i
(t
3
) . . . S
i
(t
n
), ((i=1,2 . . . m) are sufficient to represent S
i
(t) (i=1,2 . . . m) during time [T
0
, T
1
].
The party B can resolve S
i
(t
i
) upon receiving SM(t) if m×n−1 differential means are provided to obtain differential signals SM′(t), SM″(t) . . . SM
m×n−1
(t):
∑
i
=
1
m
∑
j
=
1
n
[
a
j
i
(
t
)
S
i
(
t
j
)
]
=
SM
(
t
)
∑
i
=
1
m
∑
j
=
1
n
[
a
j
′
i
(
t
)
S
i
(
t
j
)
]
=
SM
′
(
t
)
⋮
∑
i
=
1
m
∑
j
=
1
n
[
a
j
(
m
×
n
-
1
)
i
(
t
)
S
i
(
t
j
)
]
=
SM
m
×
n
-
1
(
t
)
(
1
)
Eq( 1) is an m×n equation set, wherein functions
i
a
j
(t) (i=1,2 . . . m, j=1,2 . . . n) are linear independent. Therefore, S
i
(t
i
) in Eq(1) has unique solution because the Wronskin (determinant)of functions
i
a
j
(t) is not equal to zero.
Therefore, the S
i
(t
i
) can be calculated by choosing a specific time t
0
within [T
0
, T
1
] and obtain
i
a
j
(u)
(t
0
) and SM
(u)
(t
0
). Moreover, each S
i
(t) can be calculated (i=1,2 . . . m,j=1,2 . . . n, u=0, 1,2 . . . m×n−1).
Principles of the Invention II
The above solving procedure requires m×n−1 differential means to solve S
i
(t), the hardware structure is bulky. However, party B can also take m×n samples after receiving SM(t):
∑
i
=
1
m
∑
j
=
1
n
[
a
j
i
(
t
1
)
S
i
(
t
j
)
]
=
SM
(
t
1
)
∑
i
=
1
m
∑
j
=
1
n
[
a
j
i
(
t
2
)
S
i
(
t
j
)
]
=
SM
(
t
2
)
⋮
∑
i
=
1
m
∑
j
=
1
n
[
a
j
i
(
t
m
×
n
)
S
i
(
t
j
)
]
=
SM
(
t
m
×
n
)
(
2
)
wherein t
1
, t
2
. . . t
m×n
are all within [T
0
, T
1
] and t
u
≠t
v
if u≠v, (u, v=0,1,2 . . . m×n). S
i
(t) has unique solution because
i
a
j
(t) (i=1,2 . . . m, j=1,2 . . . n) are linear independent in [T
0
, T
1
].
Principles of the Invention III
In above scheme, party requires to take m×n samples within [T
0
, T
1
] even thought the differential means can be saved. The sample frequency will increase when the number of signal (m) increases. Therefore, the sampling rate of the A/D should be considered to determine the number of signal m.
To increase m and keep hardware compact, a compromise is to use m−1 differential means to get m differential signals (including original SM(t)), and to take n samples for each signal within [T
0
, T
1
] thus obtaining following equation set:
∑
i
=
1
m
∑
j
=
1
n
[
a
j
i
(
t
1
)
S
i
(
t
j
)
]
=
SM
(
t
1
)
∑
i
=
1
m
∑
j
=
1
n
[
a
j
i
(
t
2
)
S
i
(
t
j
)
]
=
SM
(
t
2
)
⋮
∑
i
=
1
m
∑
j
=
1
n
[
a
j
i
(
t
n
)
S
i
(
t
j
)
]
=
SM
(
t
n
)
∑
i
=
1
m
∑
j
=
1
n
[
a
j
′
i
(
t
1
)
S
i
(
t
j
)
]
=
SM
′
(
t
1
)
∑
i
=
1
m
∑
j
=
1
n
[
a
j
′
i
(
t
2
)
S
i
(
t
j
)
]
=
SM
′
(
t
2
)
⋮
∑
i
=
1
m
∑
j
=
1
n
[
a
j
′
i
(
t
n
)
S
i
(
t
j
)
]
=
SM
′
(
t
n
)
⋮
∑
i
=
1
m
∑
j
=
1
n
[
a
j
(
m
-
1
)
i
(
t
n
)
S
i
(
t
j
)
]
=
SM
(
m
-
1
)
(
t
n
)
(
3
)
i
a
j
(t) (i=1,2 . . . m, j=1,2 . . . n) are linear independent. Therefore, S
i
(t
i
) in Eq(3) has unique solution because the Wronskin (determinant) of functions
i
a
j
(t) is not equal to zero.
Party B has a plurality of ways to create m×n linear independent equation set form SM(t) as will be described below.
∑
i
=
1
m
∑
j
=
1
n
[
a
j
i
(
t
1
)
S
i
(
t
j
)
]
=
SM
(
t
1
)
∑
i
=
1
m
∑
j
=
1
n
[
a
j
i
(
t
2
)
S
i
(
t
j
)
]
=
SM
(
t
2
)
⋮
∑
i
=
1
m
∑
j
=
1
n
[
a
j
i
(
t
n
)
S
i
(
t
j
)
]
=
SM
(
t
n
)
∑
i
=
1
m
∑
j
=
1
n
[
1
D
a
j
i
(
t
1
)
S
i
(
t
j
)
]
=
1
D
SM
(
t
1
)
∑
i
=
1
m
∑
j
=
1
n
[
1
D
a
j
i
(
t
2
)
S
i
(
t
j
)
]
=
1
D
SM
(
t
2
)
∑
i
=
1
m
∑
j
=
1
n
[
1
D
a
j
′
i
(
t
n
)
S
i
(
t
j
)
]
=
1
D
SM
(
t
n
)
⋮
∑
i
=
1
m
∑
j
=
1
n
[
1
D
m
-
1
a
j
i
(
t
n
)
S
i
(
t
j
)
]
=
1
D
m
-
1
SM
(
t
n
)
(
4
)
wherein
1
D
u
a
j
i
(
t
v
)
and
1
D
u
SM
(
t
v
)
is uth integration of
i
a
j
(t) and SM(t) from 0 to t
v
., u=1,2 . . . m−1, v=1,2 . . . n.
Another alternative is:
∑
i
=
1
m
∑
j
=
1
n
[
a
j
i
(
t
1
)
S
i
(
t
j
)
]
=
SM
(
t
1
)
∑
i
=
1
m
∑
j
=
1
n
[
a
j
i
(
t
2
)
S
i
(
t
j
)
]
=
SM
(
t
2
)
⋮
∑
i
Pham Chi
Tran Khai
LandOfFree
Mixing and separating method for a plurality signals does not yet have a rating. At this time, there are no reviews or comments for this patent.
If you have personal experience with Mixing and separating method for a plurality signals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Mixing and separating method for a plurality signals will most certainly appreciate the feedback.
Profile ID: LFUS-PAI-O-2916128