Nonparametric Frequency Estimation Below Two Signal Periods Using Two Windows and DFT

An Improvement of the Nonparametric Frequency Estimation Below Two Signal Periods Using Two Windows

“…If the number of cycles of the fundamental component in the measurement interval lies between 0.5 < θ 1 < 2, the largest amplitude DFT coefficients are at i = 1 and 2 and can be used for nonparametric frequency estimation [15]. It is possible to remove the influence of amplitude and phase in the same way as for one-point estimation (15) by using two points interpolation of DFT at bins i + 1 and i (in our case, i = 1) and two windows (P = 0, 1) on the same set of signal points.…”

“…In the following analyses (Figs. The behavior of the estimation errors shows that the onepoint estimation by (15) [Fig. 4(c)] is only useful below one period θ 1 < 1.…”

“…One way to estimate the relative frequency under these measurement conditions is to use the weights of two windows (a rectangular window and a Hann window) for the same set of samples and then combine the two consecutive DFT coefficients into a quotient that depends only on the relative frequency used in the proposed estimates. This is a further development of the article [13], in which only dc DFT coefficients or zero frequency DFT components were used, and of the proceedings paper [15], in which two coefficients were used. This article is organized in five main sections and an Appendix with detailed derivations of the most important estimation equations.…”

“…Curve b: Two-point estimation according to(11). Curve c: One-point estimation according to(15). Curve d: Two-point estimation according to(23) with two windows; A 1 = 1.0, 0.8 < θ 1 < 2.4, θ 1 = 0.1, −π/2 < ϕ 1 < π/2, and ϕ 1 < π/22.…”