# US 11,310,090 B2 · Systems, transmitters, and methods employing waveform bandwidth compression to transmit information > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 11,310,090 B2 - Document ID: US11310090B2 - Status: Granted - Kind: B2 - Application number: 17/227,365 - Filed: 2021-04-11 - Published: 2021-07-29 - Granted: 2022-04-19 - Earliest claimed: 2016-05-23 - Assignees: Astrapi Corporation - Applicants: Astrapi Corporation - Inventors: Jerrold Prothero - Web page: https://patentgrep.com/patent/US11310090B2 ## CPC - H04L 27/2639: {Modulators using other transforms, e.g. discrete cosine transforms, Orthogonal Time Frequency and Space [OTFS] or hermetic transforms} - H04L 27/34: Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems - G06F 17/141: {Discrete Fourier transforms} - H04L 27/10: Frequency-modulated carrier systems, i.e. using frequency-shift keying (H04L27/32 takes precedence) - H04L 27/18: Phase-modulated carrier systems, i.e. using phase-shift keying (H04L27/32 takes precedence) - H04L: TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION (arrangements common to telegraphic and telephonic communication H04M) - G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N) ## 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. ## Claims ### Claim 1 A transmitter comprising: 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; 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; and a carrier source providing a carrier that is modulated with the transmission signal. ### Claim 2 (depends on 1) The transmitter of claim 1, where the carrier source is directly modulated. ### Claim 3 (depends on 1) The transmitter of claim 1, where the carrier is a wireless carrier. ### Claim 4 (depends on 1) The transmitter of claim 1, where the transmitter is for use in one of a satellite and a terrestrial wireless network. ### Claim 5 (depends on 1) The transmitter of claim 1, where the constant amplitude sinusoidal modulation format is at least one of phase-shift keying (PSK) modulation, frequency-shift keying (FSK) modulation, quadrature amplitude modulation (QAM), or orthogonal frequency-division multiplexing (OFDM) modulation. ### Claim 6 (depends on 1) The transmitter of claim 1, where the encoder converts the polynomial to the transmission signal using instantaneous spectral analysis. ### Claim 7 (depends on 6) The transmitter of claim 6, where instantaneous spectral analysis comprises projecting the polynomial onto Cairns series functions; converting the polynomial from a function described by the Cairns series functions to Cairns exponential functions; and combining, into the transmission signal, the Cairns exponential functions into the sinusoids of differing frequencies. ### Claim 8 (depends on 1) The transmitter of claim 1, where the encoder encodes the information in the transmission signal in a plurality of stages. ### Claim 9 (depends on 1) The transmitter of claim 1, where the encoder fits the polynomial to the time-domain amplitude sequence over a plurality of transmission time intervals. ### Claim 10 (depends on 1) The transmitter of claim 1, where the encoder including at least one processor and computer readable storage medium. ### Claim 11 A non-transitory computer readable medium storing instructions, the instructions comprising: one or more instructions which, when executed by one or more processors, cause the one or more processors to: generate a time-domain amplitude sequence of information using 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; 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 to be received in the constant amplitude sinusoidal modulation format; and transmit, via a transmitter, the transmission signal. ### Claim 12 (depends on 11) The non-transitory computer readable medium of claim 11, where the constant amplitude sinusoidal modulation format is at least one of phase-shift keying (PSK) modulation, frequency-shift keying (FSK) modulation, quadrature amplitude modulation (QAM), or orthogonal frequency-division multiplexing (OFDM) modulation. ### Claim 13 (depends on 11) The non-transitory computer readable medium of claim 11, wherein the non-transitory computer readable medium and the at least one processor are included in the transmitter. ### Claim 14 (depends on 11) The non-transitory computer readable medium of claim 11, where the one or more instructions, that cause the one or more processors to convert the polynomial, cause the one or more processors to: convert the polynomial using instantaneous spectral analysis. ### Claim 15 (depends on 11) The non-transitory computer readable medium of claim 11, where the one or more instructions, that cause the one or more processors to convert the polynomial using instantaneous spectral analysis, cause the one or more processors to: project the polynomial onto Cairns series functions; convert the polynomial from a function described by the Cairns series functions to Cairns exponential functions; and combine, into the transmission signal, frequency information contained in the Cairns exponential functions. ### Claim 16 (depends on 11) The non-transitory computer readable medium of claim 11, where the one or more instructions, when executed by the one or more processors, further cause the one or more processors to: receive, at a receiver, the transmission signal as a time- domain amplitude sequence; and convert the received time-domain amplitude sequence into the constant amplitude sinusoidal modulation format. ### Claim 17 An information transmission system comprising: a transmitter including 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; 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; and a carrier source providing a carrier that is modulated with the transmission signal; and a receiver including a decoder to receive the transmission signal as a time- domain amplitude sequence, and convert the received time-domain amplitude sequence into the constant amplitude sinusoidal modulation format. ### Claim 18 (depends on 17) The system of claim 17, where the transmitter is one of a plurality of transmitter, where at least one of the plurality of transmitters transmits information using the constant amplitude sinusoidal modulation format. ### Claim 19 (depends on 17) The system of claim 17, where the transmitter is a replacement for a traditional transmit that transmits information to a traditional receiver using the constant amplitude sinusoidal modulation format. ### Claim 20 (depends on 17) The system of claim 17, where a Fourier transformation is performed on the received time-domain amplitude sequence.