Dynamics of the frequency estimation in the frequency domain

A novel approach for harmonic parameters estimation under nonstationary situations

“…The most common one is simple windowing using nonrectangular window [5][6][7][8][9][10][11][12][13][14][15] prior to DFT, and can in some degree suppress the spectral leakage and increase the accuracy of the HPE. To reduce the picket fence effect, algorithms based on multi-spectrum-line interpolation DFT were presented and applied [16][17][18][19]. The estimation errors of amplitude [16,17], frequency [18] and phase [19] decrease as the number of interpolation points increases.…”

“…To reduce the picket fence effect, algorithms based on multi-spectrum-line interpolation DFT were presented and applied [16][17][18][19]. The estimation errors of amplitude [16,17], frequency [18] and phase [19] decrease as the number of interpolation points increases. However, the computational complexity is greater at the same time, which not so well suit to implement in embedded systems.…”

Hanning self-convolution window and its application to harmonic analysis

“…The estimation can provide an information basis for power measurment [2] , fault diagnosis [3] , electrical harmonic compensation [4] , and orthogonal frequency-division multiplexing [5] . Compared with wavelet transforms, the fast Fourier transform (FFT) is more computationally efficient and easier for implementations in embedded systems such as DSP and ARM, and is by now the most widely used in various signal parameter estimation algorithms [6,7] .For dynamic signals, it is difficult to achieve strict synchronous sampling even if frequency tracking technologies are adopted [8,9] . When using FFT to estimate signal parameters with asynchronous sampling, estimation error due to the spectral leakage and picket fence effect introduced by the asynchronous sampling and signal cutoff is relatively large [10] .…”

“…Various kinds of windows, e.g., the rectangular window [11] , the Hanning window [12] , the Hamming window [13] , the Blackman window [14] , the Blackman-Harris window [15] , the RifeVincent window [16] , the Nuttall window [17] , the polynomial windows [18] , the flat-top window [19] , and the rectangular convolution window [20] , have been proposed and used in the windowed interpolation FFT algorithms, and they can in some degree suppress spectral leakage and increase the accuracy of the signal parameter estimation. The use of the FFT algorithms with dual-spectrum-line [7,12,14] or multi-spectrum-line [6,8] interpolation based on high order combined cosine windows in fundamental and harmonics parameter estimation involves, however, solving high order equations, which is computationally expensive [21][22][23] . Different approaches have been proposed to solve the problem.…”

“…For dynamic signals, it is difficult to achieve strict synchronous sampling even if frequency tracking technologies are adopted [8,9] . When using FFT to estimate signal parameters with asynchronous sampling, estimation error due to the spectral leakage and picket fence effect introduced by the asynchronous sampling and signal cutoff is relatively large [10] .…”