RETRIEVING THE LOW FREQUENCY COMPONENT FROM TWO FFT BINS
Gao Dong · Jixie qiangdu · 2012
Several spectrum correction approaches had been developed,but their improvements deteriorate significantly when they are applied to retrieving a low frequency component(LFC).It is due to that the parameter model underlying the existing approaches neglected the influence of the negative frequency in the real-valued signal.A new approach is proposed to retrieve the LFC parameters from the fast Fourier transform(FFT) spectrum lines,which can take into account the contribution from the negative frequency.This explicit approach makes use of two spectrum lines around the spectrum main lobe.The proposed approach has been validated by three levels of signal-to-noise(SNR),noise free,weak noise,and strong noise.Simulation results demonstrate that,first the proposed estimator is nearly non-biased,and the bias gets worse when the sampling condition is close to the coherent condition.Second,the empirical variance follows the theoretical Cramer-Rao bound(CRB).The empirical variance is about 1~3 times the CRB,with a local maximum at an integer cycles in record(CiR),but a minimum at a half integer of CiR.