Probability Density Function Separation for Signal Component Analysis
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Solution Overview
Problem
Current methods for separating deterministic and random components from a probability density function are inefficient, leading to inaccurate bit error rate measurements due to difficulty in distinguishing between components, especially when dealing with signals with multiple deterministic components or sine waves, resulting in measurement errors and long observation times for small bit error rates.
Innovation Solution
A probability density function separating apparatus that transforms the function into a frequency domain, computes standard deviation of the random component based on spectral levels, and separates the deterministic component using peak-to-peak values, allowing for precise identification and convolution of components.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional methods are used to separate deterministic and random components from a probability density function, then the separation process can be performed, but the measurement precision is insufficient due to inability to accurately distinguish between components
Solution Approach 1:
The patent segments the probability density function into distinct deterministic and random components by analyzing different regions of the function. The deterministic component is extracted from the peak region while the random component is extracted from the tail regions, enabling precise separation and accurate bit error rate measurement.
Solution Approach 2:
The patent transforms the problem from time domain analysis to frequency domain analysis by examining the probability density function in terms of its statistical moments and spectral characteristics. This dimensional transformation enables clear distinction between deterministic periodic components and random stochastic components.
2Measurement precision
If observation time is extended to measure extremely small bit error rates, then measurement accuracy improves, but the measurement time becomes excessively long
Solution Approach 1:
The patent performs preliminary separation of deterministic and random components before bit error rate calculation. By pre-processing the probability density function to extract component characteristics, the method enables accurate extrapolation to extremely low bit error rates without requiring prohibitively long observation times.
Solution Approach 2:
The patent introduces an intermediary mathematical model that relates the separated deterministic and random components to bit error rate performance. This intermediary model enables accurate prediction of bit error rates at extremely low levels based on measurements taken at higher error rates, significantly reducing required observation time.
3Measurement precision
If the probability density function is convolved to separate components, then component identification improves, but the computational complexity increases
Solution Approach 1:
The patent extracts the deterministic component from the probability density function by identifying and removing the peak region contribution. This extraction process simplifies the remaining function to primarily contain the random component, enabling efficient separation without requiring complex iterative convolution operations.
Solution Approach 2:
The patent changes the parameter representation of the probability density function by using statistical moments (mean, variance, skewness) and spectral parameters instead of direct time-domain convolution. This parameter transformation simplifies the computational complexity while maintaining accurate component separation.
Data Source
AI summary
There is provided a probability density function separating apparatus that separates a predetermined component in a given probability density function, including: a domain transforming section that is supplied with the probability density function and transforms the probability density function into a spectrum in a frequency domain; and a standard deviation computing section that computes standard deviation of a random component included in the probability density function based on the spectrum.