2010Power System Protection and ControlOpen access

An interpolated FFT algorithm based on three-item cosine window

Bai Chun-tao

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Abstract

An interpolated FFT algorithm based on the trinomial cosine exact Blackman window is proposed.This paper first discusses the frequency response of the exact Blackman window,then derives the formulas of interpolated FFT algorithm based on the exact Blackman window in detail.T he cubic spline function is used to calculate correction factors for frequency and complex amplitude. Simulation results demonstrate that by using the cubic spline function,the amplitude error is less than 0.1 % ,the frequency error is less than 0.01Hz,a nd the phase error is less than 5%.T he new interpolated FFT algorithm proposed in this paper can effectively enhance the measuring accuracy of power system harmonics. I t has a good real-time performance with less calculations compared with other interpolated FFT algorithms based on quadrinomial cosine window.

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What this paper is about

An interpolated FFT algorithm based on the trinomial cosine exact Blackman window is proposed.This paper first discusses the frequency response of the exact Blackman window,then derives the formulas of interpolated FFT algorithm based on the exact Blackman window in detail.T he cubic spline function is used to calculate correction factors for frequency and complex amplitude. Simulation results demonstrate that by using the cubic spline function,the amplitude error is less than 0.1 % ,the frequency error is less than 0.01Hz,a nd the phase error is less than 5%.T he new interpolated FFT algorithm proposed in this paper can effectively enhance the measuring accuracy of power system harmonics. I t has a good real-time performance with less calculations compared with other interpolated FFT algorithms based on quadrinomial cosine window.

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Available abstract

An interpolated FFT algorithm based on the trinomial cosine exact Blackman window is proposed.This paper first discusses the frequency response of the exact Blackman window,then derives the formulas of interpolated FFT algorithm based on the exact Blackman window in detail.T he cubic spline function is used to calculate correction factors for frequency and complex amplitude. Simulation results demonstrate that by using the cubic spline function,the amplitude error is less than 0.1 % ,the frequency error is less than 0.01Hz,a nd the phase error is less than 5%.T he new interpolated FFT algorithm proposed in this paper can effectively enhance the measuring accuracy of power system harmonics. I t has a good real-time performance with less calculations compared with other interpolated FFT algorithms based on quadrinomial cosine window.

Key concepts: Fast Fourier transform, Window function, Trigonometric functions, Algorithm, Trinomial, Mathematics, Harmonics, Window (computing)

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