Hanning self-convolution window and its application to harmonic analysis

Abstract

The Hanning self-convolution window (HSCW) is proposed in this paper. And the phase difference correction algorithm based on the discrete spectrum and the HSCW is given. The HSCW has a low peak side lobe level, a high side lobe roll-off rate, and a simple spectrum representation. Hence, leakage errors and harmonic interferences can be considerably reduced by weighting samples with the HSCW, the parameter estimation by the HSCW-based phase difference correction algorithm is free of solving high order equations, and the overall method can be easily implemented in embedded systems. Simulation and application results show that the HSCW-based phase difference correction algorithm can suppress the impacts of fundamental frequency fluctuation and white noise on harmonic parameter estimation, and the HSCW is advantageous over existing combined cosine windows in terms of harmonic analysis performance.hanning self-convolution window, FFT, phase difference, spectral leakage, frequency fluctuationThe accurate dynamic estimation of signal parameters has been a hot topic in the field of signal processing [1] . 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. Yang, Ding et al. gave a discrete phase difference correction algorithm suitable for all kinds of symmetrical windows, which can calculate signal parameters without relying on the expression of the window spectral function [24] . Yang et al. proposed ...

Frequency Estimation of Distorted and Noisy Signals in Power Systems by FFT-Based Approach

“…Then, from (8) and (9), the variance of can be calculated as (19) where . Based on the above relationships, the expression of variance of the frequency estimation is thus obtained as (see Appendix B) (20) To illustrate the windowing effect on the frequency estimation variance, we can define a coefficient (21) Then, the (20) can be rewritten as (22) It is worth noticing that the variance of the frequency estimation is strictly related to the characteristics of the adopted TSCW. In particular, it is interesting to note that is proportional to the ratio , where is the DFT of the adopted window.…”

“…The WIFFT employs windows to deal with the spectral leakage. Various windows have been constructed by adjusting coefficients of classical windows (e.g., Hanning window, Blackman window, Rife-Vincent window, Nuttall window, et al [20], [21]) or by convolutions of a specific parent window (quasi-synchronous window, extremely flat-top convoluted windows, Hanning self-convolution window, and triangular self-convolution window (TSCW), et al [22]- [24]). Furthermore, spectrum interpolation algorithms can reduce picket fence effects and provide accurate analytical formulas, (e.g., windowed two-point interpolation FFT and windowed multipoint interpolation FFT [18]).…”

Window effects on the performance of matched filtering for linear frequency modulation signal

“…Using these windows can effectively lower the sidelobes but broaden the main lobe at the same time. The hanning window is also known as the raised cosine window [4], defined by…”

Harmonic analysis based on time domain mutual-multiplication window

“…It is well known that the performance of windowed FFT is mainly determined by the window function [8]. A combination of various window functions are proposed to improve the accuracy of power system harmonic analysis, such as Hanning window, Nuttall window, rectangular self-convolution window, Hanning selfconvolution window and Nuttall self-convolution window interpolation FFT algorithm [9][10][11][12][13][14][15][16][17][18][19]. However, all side-lobe characteristics of the above window functions need to be improved particularly in spectrum leakage inhibition.…”