Chebyshev Interpolation for Analog Non-Linear Function Generation
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Solution Overview
Problem
Existing analog computing methods, such as continuous-time table lookup, require excessive processing time and system resources, and lack flexibility and accuracy in evaluating non-linear functions, especially in hybrid computing applications.
Innovation Solution
An improved method using Chebyshev interpolation, where interpolation coefficients are computed in the digital domain and used to program adder and multiplier elements in the analog domain for arbitrary non-linear function generation, allowing for flexible accuracy tailored to specific applications.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If continuous-time table lookup method is used for non-linear function generation, then the function can be generated in analog domain, but excessive processing time and system resources are required
Solution Approach 1:
The patent segments the non-linear function evaluation into two distinct parts: (1) digital domain computation of Chebyshev interpolation coefficients, and (2) analog domain evaluation using pre-computed coefficients with adder and multiplier elements. This segmentation allows the complex non-linear function to be broken down into manageable polynomial terms that can be efficiently evaluated in the analog domain, reducing both processing time and system resource requirements compared to continuous-time table lookup methods.
Solution Approach 2:
The patent applies preliminary action by pre-computing the Chebyshev interpolation coefficients in the digital domain before the analog computation occurs. These pre-computed coefficients are then used to program the analog adder and multiplier elements, eliminating the need for real-time table lookup and reducing processing time during the actual analog computation phase.
2Measurement precision
If continuous-time table lookup method is used, then non-linear functions can be generated, but accuracy is limited by storage medium size and converter resolution
Solution Approach 1:
The patent replaces the mechanical/analog storage medium and analog-to-digital converters with a digital computation approach using Chebyshev interpolation. By computing interpolation coefficients digitally and using them to program analog adder and multiplier elements, the system achieves higher accuracy without being constrained by physical storage medium size or converter resolution limitations.
Solution Approach 2:
The patent changes the fundamental parameters of the function generation approach by transitioning from direct analog table lookup to polynomial interpolation with pre-computed coefficients. This parameter change allows the system to achieve arbitrary precision by adjusting the polynomial degree and coefficient precision, independent of storage medium or converter limitations.
3Adaptability or versatility
If arbitrary non-linear functions are to be generated with flexible accuracy, then custom function generation is needed, but this increases device complexity and programming difficulty
Solution Approach 1:
The patent creates a universal framework for generating arbitrary non-linear functions using Chebyshev polynomial interpolation. The same analog circuit architecture with adder and multiplier elements can evaluate any non-linear function by simply changing the pre-computed Chebyshev coefficients, making the system highly adaptable without increasing hardware complexity or programming difficulty for each new function.
Data Source
AI summary
The inventive disclosures described herein pertain to an improved physical analog computer that features the ability to evaluate arbitrary non-linear functions using an interpolation method based on Chebyshev polynomials. What has been developed is an improved method for non-linear-function generation in hybrid computing that relies on Chebyshev interpolation. The method requires an initial computation of the interpolation coefficients, which is to be carried out in the digital domain. These coefficients, along with the domain of definition of the non-linear function to be generated, are used during the programming of the analog domain to set multiplier and summer elements.