Transpositional modulation systems and methods
Systems and methods for transpositional modulation and demodulation are provided. One such method for generating a signal includes the steps of providing a look-up table having a plurality of quarter-cycle waveforms, each of said quarter-cycle waveforms associated with a respective input level; receiving an input signal; and outputting quarter-cycle waveforms associated with levels of the received input signal. Systems for transpositional modulation are also provided. One such system for generating a signal includes a look-up table having a plurality of quarter-cycle waveforms. Each of the quarter-cycle waveforms are associated with a respective input level, and the look-up table is configured to receive an input signal, and output quarter-cycle waveforms associated with levels of the received input signal.
1. A method of generating a signal, comprising the steps of:
receiving a carrier signal;
receiving an input signal, wherein said input signal conveys a modulation level;
generating quarter-cycle waveforms based on the input signal; and
assembling the generated quarter-cycle waveforms into a continuous output signal, wherein the output signal includes a first inflection between adjacent quarter-cycles forming a segment of the output signal between a first negative peak and a positive peak, and wherein the output signal includes a second inflection between adjacent quarter-cycles forming a segment of the output signal between the positive peak and a second negative peak, wherein said first and second inflections represent said modulation level.
2. The method of claim 1 , wherein said modulation levels of said adjacent quarter-cycles are different.
3. The method of claim 1 , wherein the quarter-cycle waveforms are generated as cosine segments of 180° length, at twice the carrier signal frequency, and wherein a first quarter-cycle waveform is generated at the equivalent carrier frequency quadrant of 0°-90°, a second quarter-cycle waveform is generated at the equivalent carrier frequency quadrant of 90°-180°, a third quarter-cycle waveform is generated at the equivalent carrier frequency quadrant of 180°-270°, and a fourth quarter-cycle waveform is generated at the equivalent carrier frequency quadrant of 270°-360°.
4. The method of claim 3 , wherein the quarter-cycle waveforms are generated by a waveform generator or by software.
5. The method of claim 3 , further comprising the step of:
frequency-shifting a third harmonic component of the output signal to the carrier signal frequency, and, wherein the third harmonic component preferably is frequency-shifted to the carrier signal frequency by generating a second harmonic and mixing the second and third harmonics.
6. A system for generating a signal, comprising:
a waveform generator configured to generate quarter-cycle waveforms based on a received carrier signal and a received input signal, wherein said input signal conveys a modulation level; and
an analog gate for assembling the generated quarter-cycle waveforms into a continuous output signal, wherein the output signal includes a first inflection between adjacent quarter-cycles forming a segment of the output signal between a first negative peak and a positive peak, and wherein the output signal includes a second inflection between adjacent quarter-cycles forming a segment of the output signal between the positive peak and a second negative peak, wherein said first and second inflections represent said modulation level.
7. The system of claim 6 , wherein said modulation levels of said adjacent quarter cycles are different.
8. The system of claim 6 , wherein the quarter-cycle waveforms are generated as cosine segments of 180° length, at twice the carrier signal frequency, and wherein a first quarter-cycle waveform is generated at the equivalent carrier frequency quadrant of 0°-90°, a second quarter-cycle waveform is generated at the equivalent carrier frequency quadrant of 90° 480°, a third quarter-cycle waveform is generated at the equivalent carrier frequency quadrant of 180°-270°, and a fourth quarter-cycle waveform is generated at the equivalent carrier frequency quadrant of 270°-360°.
9. The system of claim 6 , further comprising:
(a) a frequency-shifter for frequency-shifting a third harmonic component of the output signal to the carrier signal frequency, and/or
(b) a phase-locked loop for generating a second harmonic component; and
a mixer, wherein the third harmonic component is frequency-shifted to the carrier signal frequency by mixing the second and third harmonics.