Abstract: In an exemplary embodiment, a tomography device comprises a scanner that obtains image slices. The device additionally comprises at least one processor configured to: perform a Hermetic Transform on the image slices to obtain hermetically transformed data using; filter and perform an Inverse Hermetic Transform on the Hermetic Transform data to obtain filtered inverse Hermetic Transform data; and perform back projection and angle integration on the filtered inverse Hermetic Transform data.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for communicating signals using a multi-dimensional symbol constellation. In one example, a process for modulating a carrier signal includes the actions of mapping data to symbols of a multi-dimensional symbol constellation that includes at least three dimensions, each dimension of the constellation represented by a respective modulation signal. The dimensions of the constellation include first and second dimensions each of which are represented by respective in-phase modulation values and quadrature phase modulation values of a quadrature amplitude modulation (QAM) signal, and a third dimension represented by a transpositional modulation (TM) signal. The method further includes modulating a carrier signal with the TM signal and the QAM signal.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for modulating and demodulating transpositional modulated (TM) signals. One aspect features a method of modulating a carrier signal that include the actions of generating a TM signal by generating a sinusoidal signal, and modulating the sinusoidal signal based on a data signal to provide the TM signal. Inserting the TM signal into a carrier signal to provide a TM modulated carrier signal. Modulating the TM modulated carrier signal with a non-TM signal to provide a combined signal. Transmitting the combined signal.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for communicating signals using a multi-dimensional symbol constellation. In one example, a process for modulating a carrier signal includes the actions of mapping data to symbols of a multi-dimensional symbol constellation that includes at least three dimensions, each dimension of the constellation represented by a respective modulation signal. The dimensions of the constellation include first and second dimensions each of which are represented by respective in-phase modulation values and quadrature phase modulation values of a quadrature amplitude modulation (QAM) signal, and a third dimension represented by a transpositional modulation (TM) signal. The method further includes modulating a carrier signal with the TM signal and the QAM signal.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for modulating and demodulating transpositional modulated (TM) signals. One aspect features a method of modulating a carrier signal that includes the operations of generating a non-transpositional modulation (non-TM) signal from a first data signal, where the non-TM signal has a frequency spectrum that occupies a bandwidth. Generating a TM signal by generating a modulation from a second data signal, and shifting the modulation signal in frequency to an upper or lower sideband in the frequency spectrum of the non-TM signal which lies within the bandwidth of the non-TM signal, and where the power of the first modulated signal is less than a power of the non-TM signal. Combining the non-TM signal with the TM signal on a common carrier signal to provide a combined signal. Transmitting the combined signal.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for communicating signals using a multi-dimensional symbol constellation. In one example, a process for modulating a carrier signal includes the actions of mapping data to symbols of a multi-dimensional symbol constellation that includes at least three dimensions, each dimension of the constellation represented by a respective modulation signal. The dimensions of the constellation include first and second dimensions each of which are represented by respective in-phase modulation values and quadrature phase modulation values of a quadrature amplitude modulation (QAM) signal, and a third dimension represented by a transpositional modulation (TM) signal. The method further includes modulating a carrier signal with the TM signal and the QAM signal.

Abstract: According to an exemplary embodiment, a method of making a Hermetic transform to mitigate noise comprises: receiving over a channel signal frames comprising predetermined data and gaps comprising noise; framing the predetermined data; constructing a set of linear equations which relate a transfer function matrix of the channel to the predetermined data; determining the transfer function matrix by inverting the linear equations using a first pseudo inverse matrix; incorporating transfer function matrix into linear equations for a hermetic transform; and determining the hermetic transform using a second pseudo inverse matrix based on the predetermined data and the noise.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for modulating and demodulating transpositional modulated (TM) signals. One aspect features a method of modulating a carrier signal that includes the operations of generating a non-transpositional modulation (non-TM) signal from a first data signal, where the non-TM signal has a frequency spectrum that occupies a bandwidth. Generating a TM signal by generating a modulation from a second data signal, and shifting the modulation signal in frequency to an upper or lower sideband in the frequency spectrum of the non-TM signal which lies within the bandwidth of the non-TM signal, and where the power of the first modulated signal is less than a power of the non-TM signal. Combining the non-TM signal with the TM signal on a common carrier signal to provide a combined signal. Transmitting the combined signal.

Abstract: Systems and methods are described using a Hermetic Transform, as well as related transforms, for applications such as directional reception and/or transmit of signals using phased-array devices and systems. The systems and methods an include identifying a direction of arrival for a mobile communicating device. The systems and methods also include the use of a noise conditioning matrix.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for modulating and demodulating transpositional modulated (TM) signals. One aspect features a method of modulating a carrier signal that includes the operations of generating a non-transpositional modulation (non-TM) signal from a first data signal, where the non-TM signal has a frequency spectrum that occupies a bandwidth. Generating a TM signal by generating a modulation from a second data signal, and shifting the modulation signal in frequency to an upper or lower sideband in the frequency spectrum of the non-TM signal which lies within the bandwidth of the non-TM signal, and where the power of the first modulated signal is less than a power of the non-TM signal. Combining the non-TM signal with the TM signal on a common carrier signal to provide a combined signal. Transmitting the combined signal.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for modulating and demodulating transpositional modulated (TM) signals. One aspect features a method of modulating a carrier signal that include the actions of generating a TM signal by generating a sinusoidal signal, and modulating the sinusoidal signal based on a data signal to provide the TM signal. Inserting the TM signal into a carrier signal to provide a TM modulated carrier signal. Modulating the TM modulated carrier signal with a non-TM signal to provide a combined signal. Transmitting the combined signal.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for modulating and demodulating transpositional modulated (TM) signals. One aspect features a method of modulating a carrier signal that includes the operations of generating a non-transpositional modulation (non-TM) signal from a first data signal, where the non-TM signal has a frequency spectrum that occupies a bandwidth. Generating a TM signal by generating a modulation from a second data signal, and shifting the modulation signal in frequency to an upper or lower sideband in the frequency spectrum of the non-TM signal which lies within the bandwidth of the non-TM signal, and where the power of the first modulated signal is less than a power of the non-TM signal. Combining the non-TM signal with the TM signal on a common carrier signal to provide a combined signal. Transmitting the combined signal.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for modulating and demodulating transpositional modulated (TM) signals. One aspect features a method of modulating a carrier signal that include the actions of generating a TM signal by generating a sinusoidal signal, and modulating the sinusoidal signal based on a data signal to provide the TM signal. Inserting the TM signal into a carrier signal to provide a TM modulated carrier signal. Modulating the TM modulated carrier signal with a non-TM signal to provide a combined signal. Transmitting the combined signal.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for communicating signals using a multi-dimensional symbol constellation. In one example, a process for modulating a carrier signal includes the actions of mapping data to symbols of a multi-dimensional symbol constellation that includes at least three dimensions, each dimension of the constellation represented by a respective modulation signal. The dimensions of the constellation include first and second dimensions each of which are represented by respective in-phase modulation values and quadrature phase modulation values of a quadrature amplitude modulation (QAM) signal, and a third dimension represented by a transpositional modulation (TM) signal. The method further includes modulating a carrier signal with the TM signal and the QAM signal.

Abstract: In a direct sequence spread-spectrum (DSSS) systems, such as CDMA, information is encoded in symbols using phase shift keying or quadrature amplitude modulation. Further, a transmitter applied a selected time shifted lag to each symbol to convey additional information. A receiver detects both the symbol data and the lag value. The receiver can use a hermetic matched filter matrix to identify the lag.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for communicating signals using a multi-dimensional symbol constellation. In one example, a process for modulating a carrier signal includes the actions of mapping data to symbols of a multi-dimensional symbol constellation that includes at least three dimensions, each dimension of the constellation represented by a respective modulation signal. The dimensions of the constellation include first and second dimensions each of which are represented by respective in-phase modulation values and quadrature phase modulation values of a quadrature amplitude modulation (QAM) signal, and a third dimension represented by a transpositional modulation (TM) signal. The method further includes modulating a carrier signal with the TM signal and the QAM signal.

Abstract: According to an exemplary embodiment, a method of making a Hermetic transform to mitigate noise comprises: receiving over a channel signal frames comprising predetermined data and gaps comprising noise; framing the predetermined data; constructing a set of linear equations which relate a transfer function matrix of the channel to the predetermined data; determining the transfer function matrix by inverting the linear equations using a first pseudo inverse matrix; incorporating transfer function matrix into linear equations for a hermetic transform; and determining the hermetic transform using a second pseudo inverse matrix based on the predetermined data and the noise.

Abstract: According to an exemplary embodiment, a method of making a Hermetic transform to mitigate noise comprises: receiving over a channel signal frames comprising predetermined data and gaps comprising noise; framing the predetermined data; constructing a set of linear equations which relate a transfer function matrix of the channel to the predetermined data; determining the transfer function matrix by inverting the linear equations using a first pseudo inverse matrix; incorporating transfer function matrix into linear equations for a hermetic transform; and determining the hermetic transform using a second pseudo inverse matrix based on the predetermined data and the noise.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for communicating signals using a multi-dimensional symbol constellation. In one example, a process for modulating a carrier signal includes the actions of mapping data to symbols of a multi-dimensional symbol constellation that includes at least three dimensions, each dimension of the constellation represented by a respective modulation signal. The dimensions of the constellation include first and second dimensions each of which are represented by respective in-phase modulation values and quadrature phase modulation values of a quadrature amplitude modulation (QAM) signal, and a third dimension represented by a transpositional modulation (TM) signal. The method further includes modulating a carrier signal with the TM signal and the QAM signal.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for modulating and demodulating transpositional modulated (TM) signals. One aspect features a method of modulating a carrier signal that include the actions of generating a TM signal by generating a sinusoidal signal, and modulating the sinusoidal signal based on a data signal to provide the TM signal. Inserting the TM signal into a carrier signal to provide a TM modulated carrier signal. Modulating the TM modulated carrier signal with a non-TM signal to provide a combined signal. Transmitting the combined signal.