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: 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: 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: 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: 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: 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: Systems and methods are described using a Hermetic Transform and inverse Hermetic Transform for transmitting and receiving OFDM signal by replacing a FFT and IFFT with the Hermetic Transform and inverse Hermetic Transform. In an exemplary embodiment, an OFDM transmitter comprises a processor configured to receive a serial signal, divide the serial signal into multiple parallel signals, modulate each of the multiple parallel signals, perform an inverse Hermetic Transform on the multiple parallel signals and provide an output from the inverse Hermetic Transform to RF circuitry for transmission.

Abstract: According to one or more exemplary embodiments, a receiver comprises one or more first metamaterial circuit elements configured to receive a signal; one or more second metamaterial circuit elements configured to perform a hermetic transform on the signal to output a hermetic transform output; and one or more third metamaterial circuit elements configured to perform a summation on the hermetic transform output. Additionally, according to one or more exemplary embodiments, a transmitter comprises a metamaterial waveguide configured to guide a signal and allow the signal to exit the metamaterial waveguide; one or more first metamaterial circuit elements coupled to the metamaterial waveguide and configured to perform a hermetic transform on the signal; and one or more second metamaterial elements configured to transmit the 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: In one or more exemplary embodiments, a method comprises applying one or more first hermetic filters to an interval of data to produce one or more first filtered subintervals of data, wherein the one or more first hermetic filters are constructed from a hermetic function for the interval; and applying one or more second hermetic filters to the one or more first filtered subintervals of data to produce one or more second filtered subintervals of data, wherein the one or more second hermetic filters are constructed from a hermetic function for the one or more first filtered subintervals.

Abstract: The systems and methods use Hermetic Transform processing to achieve higher resolution in space, time, and frequency measurements, leading to enhanced object detection, localization, and classification, and can improve several aspects of RADAR, including: phased-array beamforming, Doppler filter processing, pulse compression/replica correlation, and in the creation of higher resolution ambiguity function measurements for both multi-static active and passive RADAR.