System and method for detecting and characterizing gaussian pulses

A method for characterizing a modulated Gaussian pulse in a signal, the method comprising:

• receiving the signal, wherein the signal comprises a first sequence of values, and wherein the signal comprises the Gaussian pulse;
• determining an estimation of N parameters of the Gaussian pulse, where N is greater than or equal to one, and wherein the estimation corresponds to an estimation waveform of the Gaussian pulse;
• generating M permutations of the estimation of the N parameters, wherein the M permutations and the estimation comprises M+1 parameter sets corresponding to M+1 estimation waveforms;
• generating M+1 linear equations from the M+1 parameter sets, wherein each linear equation is a function of a respective one of the parameter sets and corresponding N parameter variables of the Gaussian pulse;
• and
• determining the N parameter variables of the Gaussian pulse by solving the M+1 linear equations, wherein the determined parameters characterize the Gaussian pulse.

A system for characterizing a modulated Gaussian pulse in a signal, the system comprising:

• a computer, wherein the computer comprises a CPU and a memory, wherein the memory is operable to store one or more software programs, and wherein the CPU is operable to execute the one or more software programs;
• and
• an input for receiving the signal, wherein the signal comprises a first sequence of values;
• wherein said one or more software programs are executable to perform:
• determining an estimation of N parameters of the Gaussian pulse in the signal, where N is greater than or equal to one, and wherein the estimation corresponds to an estimation waveform of the Gaussian pulse;
• generating a plurality of permutations of the estimation of the N parameters, wherein the plurality of permutations comprises a corresponding plurality of parameter sets corresponding to a plurality of estimation waveforms;
• generating a plurality of linear equations from the plurality of parameter sets, wherein each linear equation is a function of a respective one of the parameter sets and at least a subset of the N parameter variables of the Gaussian pulse;
• and
• determining the N parameter variables of the Gaussian pulse by solving the plurality of linear equations, wherein the determined parameters characterize the Gaussian pulse.

A system for characterizing a modulated Gaussian pulse in a signal, the system comprising:

• a computer, wherein the computer comprises a CPU and a memory, wherein the memory is operable to store one or more software programs, and wherein the CPU is operable to execute the one or more software programs;
• and
• an input for receiving the signal, wherein the signal comprises a first sequence of values;
• wherein said one or more software programs are executable to perform:
• determining an estimation of N parameters for the Gaussian pulse in the signal, wherein N is greater than or equal to one;
• generating M permutations of the estimation of the N parameters, wherein the M permutations and the estimation comprise M+1 parameter sets corresponding to M+1 estimation waveforms;
• generating M+1 linear equations from the M+1 parameter sets, wherein each linear equation is a function of a respective one of the parameter sets and corresponding N parameter variables for the Gaussian pulse;
• and
• determining the N parameter variables of the Gaussian pulse by solving the M+1 linear equations, wherein the determined parameters characterize the Gaussian pulse.

A memory medium operable to store program instructions to analyze a signal, wherein the signal comprises a first sequence of values, and wherein the signal comprises the Gaussian pulse, wherein the program instructions are executable to perform:

• determining an estimation of N parameters of the Gaussian pulse, where N is greater than or equal to one, and wherein the estimation corresponds to an estimation waveform of the Gaussian pulse;
• generating a plurality of permutations of the estimation of the N parameters, wherein the plurality of permutations comprises a corresponding plurality of parameter sets corresponding to a plurality of estimation waveforms;
• generating a plurality of linear equations from the plurality of parameter sets, wherein each linear equation is a function of a respective one of the parameter sets and at least a subset of the N parameter variables of the Gaussian pulse;
• and
• determining the N parameter variables of the Gaussian pulse by solving the plurality of linear equations, wherein the determined parameters characterize the Gaussian pulse.

A memory medium operable to store program instructions to analyze a signal, wherein the signal comprises a first sequence of values, wherein the signal comprises a modulated Gaussian pulse, wherein the program instructions are executable to perform:

• determining an estimation of N parameters of the Gaussian pulse in the signal, where N is greater than or equal to one, and wherein the estimation corresponds to an estimation waveform of the Gaussian pulse;
• generating M permutations of the estimation of the N parameters, wherein the M permutations and the estimation comprise M+1 parameter sets corresponding to M+1 estimation waveforms;
• generating M+1 linear equations from the M+1 parameter sets, wherein each linear equation is a function of a respective one of the parameter sets and corresponding N parameter variables of the Gaussian pulse;
• and
• determining the N parameter variables of the Gaussian pulse by solving the M+1 linear equations, wherein the determined parameters characterize the Gaussian pulse.