Hi-Accuracy Method for Spectrum Shift Determination

Abstract

A new hi-accuracy method for slight-shift determination of low-resolution spectra is proposed. The method allows determining a spectrum shift with an accuracy exceeding the spectrum analyzer resolution to more than three orders of magnitude due to the mathematical post-processing. The method is based on representing the spectrum as a continuous and everywhere differentiable function; expanding it into the Taylor series; approximating all the function derivatives by finite differences of a given order. Thereafter, the spectrum shift is determined using the least-squares method. The method description, its mathematical foundation and the simulation results are given. The advantages of the application of the proposed method are shown.