Causality Checker for S-Parameter Tabulated Data
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Solution Overview
Problem
Existing methods for testing causality of tabulated S-parameters face challenges due to unaccounted interpolation errors, leading to false positives and limited resolution, especially when dealing with highly nonuniformly spaced frequencies.
Innovation Solution
The system employs a global rational function approximation for tabulated frequency responses, allowing both positive and negative real parts, which improves resolution and avoids unbounded values by using nonpiecewise functions, and computes the discretization error using different interpolation functions to accurately assess causality.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If piecewise polynomial interpolation (cubic splines) is used to evaluate the generalized Hilbert transform, then the discretization error can be calculated in closed-form, but unbounded values are produced when tabulated frequencies are highly nonuniformly spaced
Solution Approach 1:
The patent changes the functional form from piecewise polynomials to rational functions, allowing the system to handle highly nonuniform frequency spacing without producing unbounded values while maintaining closed-form error calculation capability
Solution Approach 2:
The patent creates an equivalent test formulation using rational function approximation that avoids numerical integration, similar to how piecewise polynomials avoided integration but without the boundedness problem
2Ease of operation
If numerical integration is used to evaluate the generalized Hilbert transform, then the method works for uniform frequency spacing, but interpolation error is not accounted for leading to underestimated discretization error bounds
Solution Approach 1:
The patent introduces rational function approximation as an intermediary that bridges the gap between tabulated frequency data and the continuous integration required by the generalized Hilbert transform, enabling accurate error accounting without direct numerical integration
Solution Approach 2:
The patent replaces the mechanical numerical integration process with an analytical closed-form evaluation using rational function approximation, eliminating the need for iterative numerical methods while improving accuracy
3Reliability
If the Triverio method is used to bound truncation error, then the bound can control truncation error, but the discretization error bound is underestimated due to unaccounted interpolation error
Solution Approach 1:
The patent merges the truncation error bounding approach with rational function approximation, combining the strengths of both methods to achieve accurate total error accounting that includes both truncation and discretization errors
Data Source
AI summary
A system. The system includes a computing device having a processor, and a causality checker module communicably connected to the processor. The causality checker module is configured to utilize a rational function approximation to a frequency response to determine if a transfer function of a linear time invariant system is causal.