Polynomial Temperature Compensation Algorithms for Sub-GHz Preamble Window Minimization
Polynomial compensation reduces sub-GHz receiver preamble listen windows by converting crystal thermal drift into predictable fixed-point timer corrections.
Horner Scheme
Meaning
Polynomial evaluation follows an efficient sequence of nested multiplications and additions. The horner scheme reduces the total number of operations required to find the value of a high degree polynomial. It transforms a standard polynomial form into a recursive calculation that is computationally inexpensive.
Execution Efficiency
Evaluating a polynomial of degree n typically requires many separate powers of the variable. Using the horner scheme reduces this to exactly n multiplications and n additions. This reduction in the instruction count lowers the energy consumption of the processor during complex calculations.
Stability Analysis
Numerical errors are minimized by the specific order of operations used in the calculation. Because the horner scheme processes the coefficients in a specific sequence, it often provides better precision when working with limited bit widths in embedded systems. This characteristic makes it the preferred method for calculating temperature compensation curves in sensor modules where accuracy must be maintained across a wide range of values.
Firmware Pattern
Implementation usually consists of a single loop that iterates through the coefficients from the highest degree to the lowest. In the horner scheme, the running total is multiplied by the input variable and the next coefficient is added in each step. This straightforward logic structure fits well within the restricted memory space of a connectivity module.