Estimation of the Power Quantities Below One Signal Period Using DFT Coefficients

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

“…If this is not the case [Fig. 5(c)], an additional correction algorithm with median filtering is required [13].…”

“…The use of parametric methods requires a good signal model [8] and the uncertainty of the evaluation is typically reduced iteratively, which costs a lot of computing time. The nonparametric methods use the DFT to transform the sampled real signal into frequency space [9], [10], [11], [12], [13], where a basic image of the signal by components is obtained. The application of DFT involves two steps, namely, coarse search and fine search [14].…”

“…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.…”

Uncertainty of the Energy Measurement Function deriving from Distortion Power Terms for a 16.7 Hz Railway

“…The DFT is calculated on each 60 ms cycle of vp and ip (the fundamental being 50/3 Hz). The calculation of power quantities based on time records accounting for a single cycle or less are described well in [37]. A standard tapering window may be used to limit the effects of spectral leakage, which in such applications is caused by two factors: i) vp and ip waveforms suffer from slow fluctuations caused by the load changes and the reaction of active loads, causing a slight low-frequency modulation effect so that a slight difference between the two ends of the record may occur and ii) the instantaneous frequency of the fundamental varies as a result of various types of instabilities [31] [32].…”