Lookup Table Signal Mapping for Lower Interpolation Error
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Solution Overview
Problem
Existing signal processing methods using lookup tables (LUTs) suffer from interpolation errors due to the non-linear nature of second main functions, particularly when linear interpolation is used, leading to inaccuracies in the application of pre-functions and LUTs.
Innovation Solution
Applying a monotonously increasing pre-function to the input signal, followed by a piecewise-defined LUT on a transformed grid, and using linear interpolation to minimize LUT application errors, with optional adaptation of the pre-function to match the second main function's curvature.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If linear interpolation is used to apply the LUT to the input signal, then processing speed is improved, but LUT application errors increase due to the non-linear nature of the second main function
Solution Approach 1:
A pre-function is applied to the input signal before the LUT to transform it into a space where linear interpolation is more accurate. This preliminary transformation adjusts the signal distribution so that the subsequent linear interpolation produces results closer to the true non-linear function values, thereby reducing LUT application errors while maintaining fast processing speed
Solution Approach 2:
The patent changes the parameter space by applying a pre-function transformation to the input signal. This parameter transformation modifies the distribution of signal values, making them更适合 for linear interpolation and reducing the interpolation errors that would occur with the original non-linear function
2Device complexity
If the LUT size is limited to reduce memory usage, then device complexity is reduced, but interpolation errors increase
Solution Approach 1:
The pre-function transformation is applied before the LUT to prepare the input signal in a way that maximizes the effectiveness of linear interpolation with limited LUT entries. This preliminary action ensures that even with a small LUT size, the interpolation errors are minimized because the transformed signal values are better distributed for linear approximation
Solution Approach 2:
By transforming the input parameter space through the pre-function, the patent enables accurate function approximation with fewer LUT entries. The parameter transformation effectively redistributes the signal values to regions where linear interpolation is more accurate, allowing reduced LUT size without proportionally increasing interpolation errors
Data Source
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AI summary
A device applies a pre-function w=P(x) to an input signal x to obtain a first result w and applies a LUT to the first result w, wherein the LUT represents a main function f w (w) defined for a second grid of values Gw such that the pre-function P(x) is piecewise defined on a first grid Gx of signal values, where Gw=P(Gx). The device can further obtain the pre-function P(x), piecewise defined on the first grid Gx of the signal x and calculate the LUT with the second grid Gw=P(Gx). The piecewise pre-function P(x) can be obtained from a second pre-function Q(x) by applying Q(x) to signal values x to calculate the second grid Gw=Q(Gx) and defining the pre-function P(x) piecewise on the first grid Gx by linear interpolation of the values of the second grid Gw such that P(Gx)=Q(Gx).