Continuous and Discontinuous Linear Approximation of the Window Spectrum by Least Squares Method

Abstract

This paper presents the general solution of the least-squares approximation of the frequency characteristic of the data window by linear functions combined with zero padding technique. The approximation characteristic can be discontinuous or continuous, what depends on the value of one approximation parameter. The approximation solution has an analytical form and therefore the results have universal character. The paper presents derived formulas, analysis of approximation accuracy, the exemplary characteristics and conclusions, which confirm high accuracy of the approximation. The presented solution is applicable to estimating methods, like the LIDFT method, visualizations, etc.

Metrology and Measurement Systems

“…Typical example is spectrum leakage in the DFT algorithm where changes of fundamental frequency cause misadjustment to the length of the measuring window. In such cases, spectrum interpolation methods are used [24][25][26][27]. This variability of biosignals complicates the selection of informative parameters unique to a particular person and it also provides higher fraud resistance since biosignal is more difficult to fake.…”

Fast and Accurate Frequency Estimation for Renewable Energy Systems Using Maximum Decay Sidelobes Windows

“…An important group of methods are the methods of DFT interpolation, which account, in their equations, for the phenomenon of spectral leakage. These methods include the group of multi-point weighted interpolations of DFT methods (MWIDFT) [19], [20], [24] and a linear interpolation of the DFT (LIDFT) [25]- [27], based on an approximation of the unit circle by a polygon. This paper presents a generalization of the interpolation method MWDIFT [28] for maximum decay sidelobes windows at an arbitrary order, which allows to estimate the frequency of the fundamental sinusoidal component of a multi-frequency signal in a short measurement time (measurement of 0.5-2.5 measured signal cycles).…”