A Improved Apfft Algorithm And Its Application In Mfeit System

Fast Fourier Transform (FFT) is the basis of digital spectrum analysis,which is an important tool of digital signal processing. APFFT(All Phase Fast Fourier Transform)is a good algorithm with low spectral leakage and phase invariance in all the frequency domain. The dissertation studied APFFT algorithm inspired by Welch method, and the computation amount of APFFT was reduced at last.Firstly, all the 3 different forms of all-phase data preprocessing, all-phase spectrum analysis and other basic principles were expounded. FFT and APFFT were compared through theoretical analysis and simulation to verify the merit of APFFT. It was pointed out that APFFT has a lackage of adjustable parameter which lead to a large amount of computation.Secondly, the results of changing the number of overlapping elements of the APFFT algorithm were studied. For the N-order APFFT algorithm, when the number of overlapping data between segments being reduced from N-1 to N-d, the computation amount of complex multiplication and complex addition remains unchanged, and the real number addition operation in all phase data preprocessing nearly reduces to the 1/d of the original. Then, the results of changing the segment length of APFFT algorithm were studied .When the data segment length of N -order APFFT decreases from N to L, original APFFT's complex multiplication and complex addition of the computation reduces quickly as Llog2L. Meanwhile, the change of spectral leakage is not obvious. In some particular values, the phase has approximate invariance. The direction of piecewising was also changed. The original direction is from back to front. We proved that it is better to piecewise from front to back.Finally, based on the studies and simulations of APFFT, MPFFT (Multi-Phase Fast Fourier Transform) algorithm and multi-phase spectrum analysis were proposed. MPFFT uses a special segment length L = ( N? 1) / 2r and piecewises from front to back. When r=1, the spectrum leakage is just as low as APFFT along with similar phase invariance, while the computation is only 1/3 ~ 1/2 of APFFT. At last MPFFT algorithm was realized in a demodulation module in EIT system.