Combining the Hanning windowed interpolated FFT in both directions

Frequency estimation of the weighted real tones or resolved multiple tones by iterative interpolation DFT algorithm

“…Belega and Dallet [1] further developed the technique into a general form called the multipoint interpolated DFT approach (WMlpDFT). Recently, an average-based lpDFT was explored [29,30], in which the weighted average of two or more estimates, instead of a single estimate, was adopted to obtain the optimal variance of the frequency estimator in noise. An overview of frequency estimation methods was given in [38].…”

Accuracy analysis of the normalized frequency estimation of a discrete-time sine-wave by the average-based interpolated DFT method

“…The accuracy of the normalized frequency estimator provided by the IpDFT method is affected by the spectral interference from the image component and other spectral components and the additive wideband noise [6]. The first contribution can be reduced by using the Linear Interpolation of DFT (LIDFT) methods [9,10] or the Weighted Multipoint IpDFT (WMIpDFT) methods [4,[11][12][13][14][15][16][17]. All the above methods provide accurate estimates.…”

“…A general expression for the variance of the normalized frequency estimator provided by the averagebased IpDFT method with maximum sidelobe decay windows was derived in [11]. In [12] the weighted coefficients which should be applied to the estimates achieved by the IpDFT method based on the two-term maximum sidelobe decay window (known also as the Hann window) to obtain, for a given value of the fractional part of the number of acquired sine-wave cycles, the minimum variance of the normalized frequency estimator were derived. The expression of the minimum variance was also derived in that work.…”

“…Conversely, the WMIpDFT methods are based on the maximum sidelobe decay windows. The normalized frequency estimators provided by these methods use several weighted DFT spectral lines [11][12][13][14][15][16][17]. The weighted coefficients are often achieved by means of analytical expressions [11][12][13][14][15][16][17].…”

Spectral correction method based on improved flat-top convoluted window for parameter estimation of power harmonic

“…The performance of the windowed FFT algorithms is mainly determined by the window function [25]. Consequently, FDMS-FT window [26] is chosen as parent window, and the FDMS-FT convoluted window is subsequently achieved through multiple-time convolution.…”