Abstract: Systems, devices, software, and methods of the present invention enable frequency-based signal power analyses in software suitable for signal with either stationary and non-stationary spectrums. The methods that may be used throughout various systems including transmitters receivers, repeater, controllers, monitors, etc. and in software simulators to enable various signal power calculations and analyses, such as frequency spectrum analysis, throughout operating systems and that may be consistently applied in system design and operation simulations.

Abstract: Systems, methods and devices for communicating comprise one or more 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 to perform at least one of supplying data as input communication symbols to an encoder, which converts the input communication symbols into transmittable waveforms having a head function and a tail function, which are different. A transmitter transmits transmittable waveforms over a communication channel, which is received by a receiver, then demodulated and output communication symbols carrying the data 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.

Abstract: Systems, devices, and methods of the present invention enhance data transmission through the use of polynomial symbol waveforms (PSW) and sets of PSWs corresponding to a symbol alphabet is here termed a PSW alphabet. Methods introduced here are based on modifying polynomial alphabet by changing the polynomial coefficients or roots of PSWs and/or shaping of the polynomial alphabet, such as by polynomial convolution, to produce a designed PSW alphabet including waveforms with improved characteristics for data transmission.

Abstract: Systems, devices, methods, and computer readable medium for transmitting data using polynomials and instantaneous spectral analysis. In and/or prior to the transmitter, a signal may be formed by fitting the data with a polynomial, which is projected onto Cairns series functions. The Cairns series functions are converted into Cairns exponential functions, which are combined based on frequency information to produce the set of sinusoidals with continuously time-varying amplitude, each of the sinusoidals having a different frequency.

Abstract: Systems, devices, and methods of the present invention enhance data transmission through the use of polynomial symbol waveforms (PSW) and sets of PSWs corresponding to a symbol alphabet is here termed a PSW alphabet. Methods introduced here are based on modifying polynomial alphabet by changing the polynomial coefficients or roots of PSWs and/or shaping of the polynomial alphabet, such as by polynomial convolution, to produce a designed PSW alphabet including waveforms with improved characteristics for data transmission.

Abstract: Systems, devices, and methods of the present invention facilitate secure communication by changing sets of symbol waveforms used transmit data in particular symbol times defined herein as Symbol Waveform Hopping. SWH may be enabled by selecting two or more modulation formats that have sufficiently comparable communication performance (e.g., occupied bandwidth and signal power efficiency) to enable successful sending of data between a transmitter and receiver employing SWH, but characterized by symbol waveform alphabet that include different symbol waveform, so that the overall transmission/communication performance of data stream in a signal transmission channel of the system is not significantly affected by switching between modulation formats, but one symbol waveform alphabet is not reliably able to receive signals sent using the other alphabets. Some or all of the symbol waveforms in each alphabet may not be present in other alphabets.

Abstract: Systems, devices, and methods of the present invention facilitate secure communication by altering the set of symbol waveforms that may be in use in particular symbol times defined herein as Symbol Waveform Hopping. SWH may be enabled by selecting two or more modulation formats that have sufficiently comparable communication performance (e.g., occupied bandwidth and signal power efficiency), but characterized by symbol waveform alphabet that include different symbol waveform, so that the overall transmission/communication performance of data stream in a signal transmission channel of the system is not significantly affected by switching between modulation formats. Some or all of the symbol waveforms in each alphabet may not be present in other alphabets.

Abstract: Systems, devices, software, and methods of the present invention provide for homomorphically encrypted (HE) and other data represented as polynomials of degree K?1 to be transformed in O(K*log(K)) time into ‘unique-spiral’ representations in which both linear-time (O(K)) addition and linear-time multiplication are supported without requiring an intervening transformation. This capability has never previously been available and enables very significant efficiency improvements, i.e., reduced runtimes, for applications such as Fully Homomorphic Encryption (FHE), Post-Quantum Cryptography (PQC) and Artificial Intelligence (AI). Other efficient operations, such as polynomial division, raising to a power, integration, differentiation and parameter-shifting are also possible using the unique-spiral representations. New methods are introduced based on the unique-spiral representation that have applications to efficient polynomial composition, inversion, and other important topics.

Abstract: Systems, devices, methods, and computer readable medium for transmitting data using polynomials and instantaneous spectral analysis. In and/or prior to the transmitter, a signal may be formed by fitting the data with a Taylor series polynomial, which is projected onto Cairns series functions. The Cairns series functions are converted into Cairns exponential functions, which are combined based on frequency information to produce the set of sinusoidals with continuously time-varying amplitude, each of the sinusoidals having a different frequency.

Abstract: Systems, devices, methods, and computer readable medium for transmitting data using polynomials and instantaneous spectral analysis. In and/or prior to the transmitter, a signal may be formed by fitting the data with a polynomial, which is projected onto Cairns series functions. The Cairns series functions are converted into Cairns exponential functions, which are combined based on frequency information to produce the set of sinusoidals with continuously time-varying amplitude, each of the sinusoidals having a different frequency.

Abstract: Systems, devices, and methods of the present invention facilitate secure communication by altering the set of symbol waveforms that may be in use in particular symbol times defined herein as Symbol Waveform Hopping. SWH may be enabled by selecting two or more modulation formats that have sufficiently comparable communication performance (e.g., occupied bandwidth and signal power efficiency), but characterized by symbol waveform alphabet that include different symbol waveform, so that the overall transmission/communication performance of data stream in a signal transmission channel of the system is not significantly affected by switching between modulation formats. Some or all of the symbol waveforms in each alphabet may not be present in other alphabets.

Abstract: Systems, methods and devices for communicating comprise one or more 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 to perform at least one of supplying data as input communication symbols to an encoder, which converts the input communication symbols into transmittable waveforms having a head function and a tail function, which are different. A transmitter transmits transmittable waveforms over a communication channel, which is received by a receiver, then demodulated and output communication symbols carrying the data 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.

Abstract: Systems, devices, and methods of the present invention enhance data transmission through the use of polynomial symbol waveforms (PSW) and sets of PSWs corresponding to a symbol alphabet is here termed a PSW alphabet. Methods introduced here are based on modifying polynomial alphabet by changing the polynomial coefficients or roots of PSWs and/or shaping of the polynomial alphabet, such as by polynomial convolution, to produce a designed PSW alphabet including waveforms with improved characteristics for data transmission.

Abstract: Systems, transmitters, and methods employing waveform bandwidth compression to transmit information are provided. Transmitters may include an encoder to generate a time-domain amplitude sequence from information in a constant amplitude sinusoidal modulation format; fit a polynomial to the time-domain amplitude sequence, the fitted polynomial spanning at least one transmission time interval; and convert the polynomial to a transmission signal, the transmission signal comprising a sum of sinusoids of differing frequencies, each sinusoid having a continuously time-varying amplitude. A carrier source providing a carrier that is modulated with the transmission signal and transmitted through the system to a receiver, which receives the signal in the constant amplitude sinusoidal modulation format. The sum of sinusoids of differing frequencies having a continuously time-varying amplitude may be generated using instantaneous spectral analysis, to reduce the spectral occupancy of the transmission signal.

Abstract: Systems, devices, software, and methods of the present invention enable frequency-based signal power analyses in software suitable for signal with either stationary and non-stationary spectrums. The methods that may be used throughout various systems including transmitters receivers, repeater, controllers, monitors, etc. and in software simulators to enable various signal power calculations and analyses, such as frequency spectrum analysis, throughout operating systems and that may be consistently applied in system design and operation simulations in a wide range of applications, such as interference and spectrum monitoring or clearance, object tracking, transmission channel and noise analyses, radiated power analysis, signal boundary interference, satellite downlink signal identification, pulsed radar monitoring, audio detection and identification, lidar systems, sonar systems, etc.

Abstract: Systems, methods and devices for communicating comprise one or more 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 to perform at least one of supplying data as input communication symbols to an encoder, which converts the input communication symbols into transmittable waveforms having a head function and a tail function, which are different. A transmitter transmits transmittable waveforms over a communication channel, which is received by a receiver, then demodulated and output communication symbols carrying the data 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.

Abstract: Systems, devices, and methods of the present invention enhance data transmission through the use of polynomial symbol waveforms (PSW) and sets of PSWs corresponding to a symbol alphabet is here termed a PSW alphabet. Methods introduced here are based on modifying polynomial alphabet by changing the polynomial coefficients or roots of PSWs and/or shaping of the polynomial alphabet, such as by polynomial convolution, to produce a designed PSW alphabet including waveforms with improved characteristics for data transmission.

Abstract: Systems, devices, and methods of the present invention facilitate secure communication by altering the set of symbol waveforms that may be in use in particular symbol times defined herein as Symbol Waveform Hopping. SWH may be enabled by selecting two or more modulation formats that have sufficiently comparable communication performance (e.g., occupied bandwidth and signal power efficiency), but characterized by symbol waveform alphabet that include different symbol waveform, so that the overall transmission/communication performance of data stream in a signal transmission channel of the system is not significantly affected by switching between modulation formats. Some or all of the symbol waveforms in each alphabet may not be present in other alphabets.

Abstract: Systems, transmitters, and methods employing waveform bandwidth compression to transmit information are provided. Transmitters may include an encoder to generate a time-domain amplitude sequence from information in a constant amplitude sinusoidal modulation format; fit a polynomial to the time-domain amplitude sequence, the fitted polynomial spanning at least one transmission time interval; and convert the polynomial to a transmission signal, the transmission signal comprising a sum of sinusoids of differing frequencies, each sinusoid having a continuously time-varying amplitude. A carrier source providing a carrier that is modulated with the transmission signal and transmitted through the system to a receiver, which receives the signal in the constant amplitude sinusoidal modulation format. The sum of sinusoids of differing frequencies having a continuously time-varying amplitude may be generated using instantaneous spectral analysis, to reduce the spectral occupancy of the transmission signal.

Abstract: Systems, devices, methods, and computer readable medium for transmitting data using polynomials and instantaneous spectral analysis. In and/or prior to the transmitter, a signal may be formed by fitting the data with a Taylor series polynomial, which is projected onto Cairns series functions. The Cairns series functions are converted into Cairns exponential functions, which are combined based on frequency information to produce the set of sinusoidals with continuously time-varying amplitude, each of the sinusoidals having a different frequency.