Waveforms comprising a plurality of elements and transmission thereof
Systems and/or methods are disclosed for generating a waveform that comprises a plurality of elements by using a Fourier transform and/or an inverse Fourier transform. The waveform that comprises the plurality of elements may be transmitted by transmitting, sequentially in time, the plurality of elements. In some embodiments, the Fourier transform and/or inverse Fourier transform comprises a Fast Fourier Transform and/or Inverse Fast Fourier Transform and the waveform that comprises the plurality of elements may be transmitted by using, sequentially in time, the plurality of elements to modulate a sinusoidal waveform.
1. A communications method comprising:
providing a frequency content for a waveform by Fourier transforming a signal;
forming a desired spectrum shape for the waveform, that differs from the frequency content, responsive to the frequency content;
generating the waveform by inverse Fourier transforming the desired spectrum shape; and
transmitting the waveform by using a plurality of elements thereof, sequentially one after another, to modulate a single carrier frequency;
wherein generating the waveform by inverse Fourier transforming the desired spectrum shape comprises:
generating a discrete time-domain waveform U(nT); wherein n denotes a discrete time index of U(nT), wherein n=1, 2, . . . , N; and NT≦τ; wherein τ denotes a time span of the discrete time-domain waveform U(nT); and
wherein transmitting the waveform by using a plurality of elements thereof, sequentially one after another, to modulate a single carrier frequency comprises:
using substantially all of the elements of U(nT) sequentially to modulate the single carrier frequency by using U(T), followed by using U(2T), . . . , followed by using U(NT).
2. The communications method according to claim 1 , wherein said forming a desired spectrum shape for the waveform is performed at a transmitter.
3. The communications method according to claim 1 , wherein said forming a desired spectrum shape for the waveform is performed at a distance from a transmitter and is then relayed to the transmitter.
4. The communications method according to claim 1 , wherein said forming a desired spectrum shape for the waveform further comprises using a first plurality of frequencies over a first time interval and using a second plurality of frequencies over a second time interval; wherein the first plurality of frequencies differs from the second plurality of frequencies in at least one frequency.
5. The communications method according to claim 1 , wherein said forming a desired spectrum shape for the waveform comprises forming the desired spectrum shape to include a first frequency interval comprising a first spectral level that is non-zero and to include a second frequency interval comprising a second spectral level that is also non-zero and different from the first spectral level.
6. The communications method according to claim 5 , wherein the desired spectrum shape further includes a third frequency interval that is situated between the first and second frequency intervals and comprises a spectral level that is substantially zero.
7. The communications method according to claim 1 , wherein said generating the waveform further comprises:
requiring that a maximum amplitude value at an output of the inverse Fourier transform be limited in order to reduce non-linear distortion effects in an amplification stage of a transmitter.
8. A communications method comprising:
providing a frequency content for a waveform by Fourier transforming a signal;
forming a desired spectrum shape for the waveform, that differs from the frequency content, responsive to the frequency content;
generating the waveform by inverse Fourier transforming the desired spectrum shape; and
transmitting the waveform by using a plurality of elements thereof, sequentially one after another, to modulate a single carrier frequency;
wherein forming a desired spectrum shape for the waveform comprises:
selecting a frequency interval over which the waveform is to exist;
allowing at least one frequency that is included in the selected frequency interval to provide a frequency content to the waveform; and
excluding at least one frequency that is included in the selected frequency interval from providing a frequency content to the waveform.
9. The communications method according to claim 8 , wherein said forming a desired spectrum shape for the waveform is performed at a transmitter.
10. The communications method according to claim 8 , wherein said forming a desired spectrum shape for the waveform is performed at a distance from a transmitter and is then relayed to the transmitter.
11. The communications method according to claim 8 , wherein said forming a desired spectrum shape for the waveform further comprises using a first plurality of frequencies over a first time interval and using a second plurality of frequencies over a second time interval; wherein the first plurality of frequencies differs from the second plurality of frequencies in at least one frequency.
12. The communications method according to claim 8 , wherein said forming a desired spectrum shape for the waveform comprises forming the desired spectrum shape to include a first frequency interval comprising a first spectral level that is non-zero and to include a second frequency interval comprising a second spectral level that is also non-zero and different from the first spectral level.
13. The communications method according to claim 12 , wherein the desired spectrum shape further includes a third frequency interval that is situated between the first and second frequency intervals and comprises a spectral level that is substantially zero.
14. The communications method according to claim 8 , wherein said generating the waveform further comprises:
requiring that a maximum amplitude value at an output of the inverse Fourier transform be limited in order to reduce non-linear distortion effects in an amplification stage of a transmitter.
15. A communications system comprising:
a processor that is configured to provide a frequency content for a waveform by Fourier transforming a signal, to form a desired spectrum shape for the waveform, that differs from the frequency content, responsive to the frequency and to generate the waveform by inverse Fourier transforming the desired spectrum shape; and
a transmitter that is configured to transmit the waveform, comprising a plurality of elements, by using the plurality of elements, sequentially one after another, to modulate a single carrier frequency;
wherein the waveform comprises a discrete time-domain waveform U(nT); wherein n denotes a discrete time index of U(nT), wherein n=1, 2, . . . , N; and NT≦τ; wherein τ denotes a time span of the discrete time-domain waveform U(nT); and
wherein the transmitter is further configured to use substantially all of the elements of U(nT) sequentially to modulate the single carrier frequency by using U(T), followed by using U(2T), . . . , followed by using U(NT).
16. The communications system according to claim 15 , wherein the processor and the transmitter are co-located.
17. The communications system according to claim 15 , wherein the processor is located a distance from the transmitter.
18. The communications system according to claim 15 , wherein said desired spectrum shape for the waveform comprises a first plurality of frequencies over a first time interval and a second plurality of frequencies over a second time interval; wherein the first plurality of frequencies differs from the second plurality of frequencies in at least one frequency.
19. The communications system according to claim 15 , wherein said desired spectrum shape for the waveform includes a first frequency interval comprising a first spectral level that is non-zero and a second frequency interval comprising a second spectral level that is also non-zero and different from the first spectral level.
20. The communications system according to claim 19 , wherein the desired spectrum shape further includes a third frequency interval that is situated between the first and second frequency intervals and comprises a spectral level that is substantially zero.
21. The communications system according to claim 15 , wherein the processor is further configured to require that a maximum amplitude value at an output of the inverse Fourier transform be limited in order to reduce non-linear distortion effects in an amplification stage of the transmitter.
22. A communications system comprising:
a processor that is configured to provide a frequency content for a waveform by Fourier transforming a signal, to form a desired spectrum shape for the waveform, that differs from the frequency content, responsive to the frequency content and to generate the waveform by inverse Fourier transforming the desired spectrum shape; and
a transmitter that is configured to transmit the waveform, comprising a plurality of elements, by using the plurality of elements, sequentially one after another, to modulate a single carrier frequency;
wherein the processor is further configured to:
select a frequency interval over which the waveform is to exist;
allow at least one frequency that is included in the selected frequency interval to provide a frequency content to the waveform; and
exclude at least one frequency that is included in the selected frequency interval from providing a frequency content to the waveform.
23. The communications system according to claim 22 , wherein the processor is further configured to use the frequency interval that is selected over a first time interval and then to change the frequency interval that is selected and to use the changed frequency interval over a second time interval.
24. The communications system according to claim 22 , wherein the processor and the transmitter are co-located.
25. The communications system according to claim 22 , wherein the processor is located a distance from the transmitter.
26. The communications system according to claim 22 , wherein said desired spectrum shape for the waveform comprises a first plurality of frequencies over a first time interval and a second plurality of frequencies over a second time interval; wherein the first plurality of frequencies differs from the second plurality of frequencies in at least one frequency.
27. The communications system according to claim 22 , wherein said desired spectrum shape for the waveform includes a first frequency interval comprising a first spectral level that is non-zero and a second frequency interval comprising a second spectral level that is also non-zero and different from the first spectral level.
28. The communications system according to claim 27 , wherein the desired spectrum shape further includes a third frequency interval that is situated between the first and second frequency intervals and comprises a spectral level that is substantially zero.
29. The communications system according to claim 22 , wherein the processor is further configured to require that a maximum amplitude value at an output of the inverse Fourier transform be limited in order to reduce non-linear distortion effects in an amplification stage of the transmitter.