Methods and systems for communicating
Methods and systems for communicating are disclosed. A method includes obtaining input communication symbols selected from a set of communication symbols, converting input communication symbols into transmittable waveforms using non-periodic functions, and transmitting transmittable waveforms over a communication channel. Another method includes receiving transmittable waveforms constructed using non-periodic functions and transmitted over a communication channel, and demodulating transmittable waveforms. A system includes a modulator adapted to obtain input communication symbols selected from a set of communication symbols and adapted to convert input communication symbols into transmittable waveforms using non-periodic functions, and a transmitter or transceiver adapted to transmit transmittable waveforms over a communication channel. Another system includes a receiver or transceiver adapted to receive transmittable waveforms transmitted over a communication channel and constructed using non-periodic functions, and a demodulator adapted to demodulate transmittable waveforms.
1. A method for communicating comprising:
obtaining one or a plurality of input communication symbols selected from a set of communication symbols;
converting the one or a plurality of input communication symbols into one or a plurality of transmittable waveforms using one or a plurality of non-periodic functions selected from a set of non-periodic functions; and
transmitting the one or a plurality of transmittable waveforms over a communication channel,
wherein at least one non-periodic function selected from the set of non-periodic functions has a form of equation
f
m
(
t
)
=
[
κ
0
ⅇ
ⅈω
0
]
ⅇ
[
κ
1
ⅇ
ⅈω
1
]
(
t
+
t
0
)
ⅈ
[
κ
2
ⅇ
ⅈω
2
]
(
2
2
-
m
)
,
wherein κ 0 is a first level amplitude coefficient, ω 0 is a first level frequency constant, i is an imaginary constant square root of minus one, κ 1 is a second level amplitude coefficient, ω 1 is a second level frequency constant, t is a time parameter, t 0 is an initial time, κ 2 is a third level amplitude coefficient, ω 2 is a third level frequency constant, and m is a waveform shape term.
2. The method for communicating of claim 1 , wherein κ 0 modulates an amplitude, ω 0 modulates a phase, κ 1 modulates a frequency, at least one of κ 1 and ω 1 vary a time direction, t 0 vary a time shift, at least one of κ 2 and ω 2 vary a rotational direction, and at least one of m, κ 2 , ω 1 and ω 2 vary a growth.
3. The method for communicating of claim 1 , wherein each non-periodic function in the set of non-periodic functions differs from other non-periodic functions in the set of non-periodic functions by at least one of an amplitude, a phase, a frequency, a time direction, a time shift, a rotational direction, and a growth.
4. The method for communicating of claim 1 , wherein at least one of the one or a plurality of input communication symbols and the set of non-periodic functions is obtained from at least one of a modulator, a computer-readable media, a computer, a satellite communication device and a mobile device.
5. The method for communicating of claim 1 , wherein one or a plurality of portions of at least one of the one or a plurality of transmittable waveforms corresponds to at least one of the one or a plurality of input communication symbols.
6. The method for communicating of claim 1 , wherein the one or a plurality of transmittable waveforms is at least one of generated and transmitted over the communication channel using two-component transmission.
7. The method for communicating of claim 6 , wherein the one or a plurality of transmittable waveforms is at least one of generated and transmitted over the communication channel further using intra-symbol time multiplexing.
8. The method for communicating of claim 1 , wherein at least one of the one or a plurality of transmittable waveforms comprises a head portion and a tail portion, such that the tail portion returns the communication channel to initial conditions.
9. The method for communicating of claim 1 , wherein the one or a plurality of input communication symbols is converted into the one or a plurality of transmittable waveforms using a modulator.
10. The method for communicating of claim 9 , wherein the modulator comprises at least one of an encoder and a pulse-shaping filter.
11. The method for communicating of claim 10 , wherein the encoder obtains amplitude data using a lookup table mapping the set of communication symbols to the set of non-periodic functions.
12. The method for communicating of claim 1 , wherein the one or a plurality of transmittable waveforms is at least one of generated and transmitted over the communication channel using at least one of a transmitter and a transceiver.
13. The method for communicating of claim 1 , wherein the one or a plurality of transmittable waveforms is at least one of generated and transmitted over the communication channel using at least one of a computer, a satellite communication device and a mobile device.
14. The method for communicating of claim 1 , further comprising:
receiving the one or a plurality of transmittable waveforms; and
demodulating the one or a plurality of transmittable waveforms.
15. The method for communicating of claim 14 , further comprising communicating one or a plurality of output communication symbols to at least one of a user, a computer-readable media, a computer, a satellite communication device and a mobile device.
16. The method for communicating of claim 14 , wherein the one or a plurality of transmittable waveforms is received using at least one of a receiver and a second transceiver.
17. The method for communicating of claim 14 , wherein the one or a plurality of transmittable waveforms is received using at least one of a computer, a satellite communication device and a mobile device.
18. The method for communicating of claim 14 , wherein the one or a plurality of transmittable waveforms is demodulated using a demodulator.
19. The method for communicating of claim 18 , wherein the demodulator comprises a decoder.
20. A method for communicating comprising:
receiving one or a plurality of transmittable waveforms transmitted over a communication channel; and
demodulating the one or a plurality of transmittable waveforms,
wherein the one or a plurality of transmittable waveforms are constructed using one or a plurality of non-periodic functions selected from a set of non-periodic functions, and
wherein at least one non-periodic function selected from the set of non-periodic functions has a form of equation
f
m
(
t
)
=
[
κ
0
ⅇ
ⅈω
0
]
ⅇ
[
κ
1
ⅇ
ⅈω
1
]
(
t
+
t
0
)
ⅈ
[
κ
2
ⅇ
ⅈω
2
]
(
2
2
-
m
)
,
wherein κ 0 is a first level amplitude coefficient, ω 0 is a first level frequency constant, i is an imaginary constant square root of minus one, κ 1 is a second level amplitude coefficient, ω 1 is a second level frequency constant, t is a time parameter, t 0 is an initial time, κ 2 is a third level amplitude coefficient, ω 2 is a third level frequency constant, and m is a waveform shape term.
21. The method for communicating of claim 20 , further comprising communicating one or a plurality of output communication symbols to at least one of a user, a computer-readable media, a computer, a satellite communication device and a mobile device.
22. The method for communicating of claim 20 , wherein κ 0 modulates an amplitude, ω 0 modulates a phase, κ 1 modulates a frequency, at least one of κ 1 and ω 1 vary a time direction, t 0 vary a time shift, at least one of κ 2 and ω 2 vary a rotational direction, and at least one of m, κ 2 , ω 1 and ω 2 vary a growth.
23. The method for communicating of claim 20 , wherein each non-periodic function in the set of non-periodic functions differs from other non-periodic functions in the set of non-periodic functions by at least one of an amplitude, a phase, a frequency, a time direction, a time shift, a rotational direction, and a growth.
24. The method for communicating of claim 20 , wherein one or a plurality of portions of at least one of the one or a plurality of transmittable waveforms corresponds to at least one of one or a plurality of input communication symbols.
25. The method for communicating of claim 20 , wherein the one or a plurality of transmittable waveforms is at least one of generated and transmitted over the communication channel using two-component transmission.
26. The method for communicating of claim 25 , wherein the one or a plurality of transmittable waveforms is at least one of generated and transmitted over the communication channel further using intra-symbol time multiplexing.
27. The method for communicating of claim 20 , wherein at least one of the one or a plurality of transmittable waveforms comprises a head portion and a tail portion, such that the tail portion returns the communication channel to initial conditions.
28. The method for communicating of claim 20 , wherein the one or a plurality of transmittable waveforms is received using at least one of a receiver and a transceiver.
29. The method for communicating of claim 20 , wherein the one or a plurality of transmittable waveforms is received using at least one of a computer, a satellite communication device and a mobile device.
30. The method for communicating of claim 20 , wherein the one or a plurality of transmittable waveforms is demodulated using a demodulator.
31. The method for communicating of claim 30 , wherein the demodulator comprises a decoder.
32. A system for communicating comprising:
a modulator adapted to obtain one or a plurality of input communication symbols selected from a set of communication symbols, and to convert the one or a plurality of input communication symbols into one or a plurality of transmittable waveforms using one or a plurality of non-periodic functions selected from a set of non-periodic functions; and
at least one of a transmitter and a first transceiver adapted to transmit the one or a plurality of transmittable waveforms over a communication channel,
wherein at least one non-periodic function selected from the set of non-periodic functions has a form of equation
f
m
(
t
)
=
[
κ
0
ⅇ
ⅈω
0
]
ⅇ
[
κ
1
ⅇ
ⅈω
1
]
(
t
+
t
0
)
ⅈ
[
κ
2
ⅇ
ⅈω
2
]
(
2
2
-
m
)
.
wherein κ 0 is a first level amplitude coefficient, ω 0 is a first level frequency constant, i is an imaginary constant square root of minus one, κ 1 is a second level amplitude coefficient, ω 1 is a second level frequency constant, t is a time parameter, t 0 is an initial time, κ 2 is a third level amplitude coefficient, ω 2 is a third level frequency constant, and m is a waveform shape term.
33. The system for communicating of claim 32 , wherein κ 0 modulates an amplitude, ω 0 modulates a phase, κ 1 modulates a frequency, at least one of κ 1 and ω 1 vary a time direction, t 0 vary a time shift, at least one of κ 2 and ω 2 vary a rotational direction, and at least one of m, κ 2 , ω 1 and ω 2 vary a growth.
34. The system for communicating of claim 32 , wherein each non-periodic function in the set of non-periodic functions differs from other non-periodic functions in the set of non-periodic functions by at least one of an amplitude, a phase, a frequency, a time direction, a time shift, a rotational direction, and a growth.
35. The system for communicating of claim 32 , wherein at least one of the one or a plurality of input communication symbols and the set of non-periodic functions is obtained from at least one of a modulator, a computer-readable media, a computer, a satellite communication device and a mobile device.
36. The system for communicating of claim 32 , wherein one or a plurality of portions of at least one of the one or a plurality of transmittable waveforms corresponds to at least one of the one or a plurality of input communication symbols.
37. The system for communicating of claim 32 , wherein the one or a plurality of transmittable waveforms is at least one of generated and transmitted over the communication channel using two-component transmission.
38. The system for communicating of claim 37 , wherein the one or a plurality of transmittable waveforms is at least one of generated and transmitted over the communication channel further using intra-symbol time multiplexing.
39. The system for communicating of claim 32 , wherein at least one of the one or a plurality of transmittable waveforms comprises a head portion and a tail portion, such that the tail portion returns the communication channel to initial conditions.
40. The system for communicating of claim 32 , wherein the modulator comprises an encoder and a pulse-shaping filter.
41. The system for communicating of claim 40 , wherein the encoder obtains amplitude data using a lookup table mapping the set of communication symbols to the set of non-periodic functions.
42. The system for communicating of claim 32 , further comprising:
at least one of a receiver and a second transceiver adapted to receive the one or a plurality of transmittable waveforms; and
a demodulator adapted to demodulate the one or a plurality of transmittable waveforms.
43. The system for communicating of claim 32 , further comprising at least one of a computer-readable media, a computer, a satellite communication device and a mobile device,
wherein the at least one of a computer-readable media, a computer, a satellite communication device and a mobile device is adapted to at least one of:
supply the one or a plurality of input communication symbols;
obtain the one or a plurality of input communication symbols;
convert the one or a plurality of input communication symbols into the one or a plurality of transmittable waveforms;
transmit the one or a plurality of transmittable waveforms over the communication channel;
receive the one or a plurality of transmittable waveforms;
demodulate the one or a plurality of transmittable waveforms; and
communicate one or a plurality of output communication symbols to at least one of a user, a secondary computer-readable media, a secondary computer, a secondary satellite communication device and a secondary mobile device.
44. The system for communicating of claim 42 , wherein the demodulator comprises a decoder.
45. A system for communicating comprising:
at least one of a receiver and a transceiver adapted to receive one or a plurality of transmittable waveforms transmitted over a communication channel; and
a demodulator adapted to demodulate the one or a plurality of transmittable waveforms,
wherein the one or a plurality of transmittable waveforms are constructed using one or a plurality of non-periodic functions selected from a set of non-periodic functions, and
wherein at least one non-periodic function selected from the set of non-periodic functions has a form of equation
f
m
(
t
)
=
[
κ
0
ⅇ
ⅈω
0
]
ⅇ
[
κ
1
ⅇ
ⅈω
1
]
(
t
+
t
0
)
ⅈ
[
κ
2
ⅇ
ⅈω
2
]
(
2
2
-
m
)
.
wherein κ 0 is a first level amplitude coefficient, ω 0 is a first level frequency constant, i is an imaginary constant square root of minus one, κ 1 is a second level amplitude coefficient, ω 1 is a second level frequency constant, t is a time parameter, t 0 is an initial time, κ 2 is a third level amplitude coefficient, ω 2 is a third level frequency constant, and m is a waveform shape term.
46. The system for communicating of claim 45 , wherein κ 0 modulates an amplitude, ω 0 modulates a phase, κ 1 modulates a frequency, at least one of κ 1 and ω 1 vary a time direction, t 0 vary a time shift, at least one of κ 2 and ω 2 vary a rotational direction, and at least one of m, κ 2 , ω 1 and ω 2 vary a growth.
47. The system for communicating of claim 45 , wherein each non-periodic function in the set of non-periodic functions differs from other non-periodic functions in the set of non-periodic functions by at least one of an amplitude, a phase, a frequency, a time direction, a time shift, a rotational direction, and a growth.
48. The system for communicating of claim 45 , wherein one or a plurality of portions of at least one of the one or a plurality of transmittable waveforms corresponds to at least one of one or a plurality of input communication symbols.
49. The system for communicating of claim 45 , wherein the one or a plurality of transmittable waveforms is at least one of generated and transmitted over the communication channel using two-component transmission.
50. The system for communicating of claim 49 , wherein the one or a plurality of transmittable waveforms is at least one of generated and transmitted over the communication channel further using intra-symbol time multiplexing.
51. The system for communicating of claim 45 , wherein at least one of the one or a plurality of transmittable waveforms comprises a head portion and a tail portion, such that the tail portion returns the communication channel to initial conditions.
52. The system for communicating of claim 45 , further comprising at least one of a computer-readable media, a computer, a satellite communication device and a mobile device,
wherein the at least one of a computer-readable media, a computer, a satellite communication device and a mobile device is adapted to at least one of:
receive the one or a plurality of transmittable waveforms;
demodulate the one or a plurality of transmittable waveforms; and
communicate one or a plurality of output communication symbols to at least one of a user, a secondary computer-readable media, a secondary computer, a secondary satellite communication device and a secondary mobile device.
53. The system for communicating of claim 45 , wherein the demodulator comprises a decoder.