Modified Euclidean Algorithm for Periodic Signal Deinterleaving
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Solution Overview
Problem
Current methods for analyzing data from periodic processes, especially in noisy and sparse environments, are ineffective, as they break down when dealing with multiple periodic components, leading to unreliable measurements and difficulties in frequency agility in applications like radar and communication systems.
Innovation Solution
The development of the Modified Euclidean Algorithm (MEA) and Equidistributed Modified Euclidean Algorithm (EQUIMEA) leverages probabilistic interpretations of the Riemann zeta function and Weyl's equidistribution theorem to efficiently extract and deinterleave periodic components from noisy and sparse data, enabling frequency agility and robust signal processing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If standard filtering methods (Lee filter, Gaussian filter, median filter) are used to denoise data, then noise reduction is achieved, but the methods break down when dealing with multiple periodic components and sparse data
Solution Approach 1:
The patent segments the complex problem of analyzing multi-periodic data into separate analysis steps: first identifying individual periodic components using autocorrelation, then separately analyzing each period using the MEA algorithm, and finally deinterleaving the data. This segmentation allows each step to handle specific aspects without being overwhelmed by the complexity of multiple overlapping periods.
Solution Approach 2:
The patent introduces autocorrelation as an intermediary tool to simplify the analysis of multi-periodic data. By computing the autocorrelation function, the complex mixture of multiple periodic signals is transformed into a form where individual periods can be identified and extracted more easily, serving as a mediator between the raw complex data and the final period extraction.
2Reliability
If probabilistic algorithms are used to analyze periodic processes, then robustness in weak signal conditions is improved, but computational complexity increases
Solution Approach 1:
The patent applies partial action by using probabilistic methods selectively - specifically using the MEA algorithm only after initial period identification through autocorrelation, rather than applying complex probabilistic analysis to all data processing steps. This allows robustness where needed while minimizing overall computational complexity.
3Reliability
If frequency agility is implemented to counter jamming and interference, then system reliability is improved, but the ability to locate the radar broadcaster through radio direction finding is enhanced
Solution Approach 1:
The patent implements frequency agility through periodic frequency hopping, where the radar system rapidly changes operating frequencies according to a predetermined pattern. This periodic action allows the system to counter jamming and interference by moving to fresh frequency channels, while the structured nature of the hopping pattern maintains concealment from passive direction finding.
Data Source
AI summary
Methods and Systems to analyze data from multiple periodic processes and deinterleave those periods including providing process data for analysis from at least one periodic generator; identify underlying different periodic processes; providing a Modified Euclidean Algorithm (MEA) to extract a fundamental period from a set of sparse and noisy observations of a periodic process; relying on the probabilistic interpretation of an equidistributed MEA (EQUIMEA) to deinterleave processes with multiple periods; and outputting the deinterleaved data to be applied to desired applications and analyses. The method may converge to the exact value of the period with as few as ten data samples. Desired applications may include communication and signal processing, bio-rhythms, aggregate business data, signal analysis of radar and sonar systems, queuing in business applications, analysis of neuron firing rates in computational neuroscience, bit synchronization in communications, fading communication channels, detecting patterns in spatial point processes, and the like.