N2 - This paper presents a simple DFT-based golden section searching algorithm
(DGSSA) for the single tone frequency estimation. Because of truncation
and discreteness in signal samples, Fast Fourier Transform (FFT) and
Discrete Fourier Transform (DFT) are inevitable to cause the spectrum
leakage and fence effect which lead to a low estimation accuracy. This
method can improve the estimation accuracy under conditions of a low
signal-to-noise ratio (SNR) and a low resolution. This method firstly uses
three FFT samples to determine the frequency searching scope, then –
besides the frequency – the estimated values of amplitude, phase and dc
component are obtained by minimizing the least square (LS) fitting error
of three-parameter sine fitting. By setting reasonable stop conditions or
the number of iterations, the accurate frequency estimation can be
realized. The accuracy of this method, when applied to observed
single-tone sinusoid samples corrupted by white Gaussian noise, is
investigated by different methods with respect to the unbiased Cramer-Rao
Low Bound (CRLB). The simulation results show that the root mean square
error (RMSE) of the frequency estimation curve is consistent with the
tendency of CRLB as SNR increases, even in the case of a small number of
samples. The average RMSE of the frequency estimation is less than 1.5
times the CRLB with SNR = 20 dB and N = 512.
JO - Metrology and Measurement Systems
L1 - http://www.czasopisma.pan.pl/Content/90341/PDF/Journal10178-Volume+XXII+Issue3_08paper.pdf
L2 - http://www.czasopisma.pan.pl/Content/90341
IS - No 3
EP - 416
KW - frequency estimation
KW - CRLB
KW - three-parameter sine-fitting
KW - RMSE
KW - golden section
ER -
A1 - Xin Liu
A1 - Yongfeng Ren
A1 - Chengqun Chu
A1 - Wei Fang
PB - Polish Academy of Sciences Committee on Metrology and Scientific Instrumentation
VL - vol. 22
JF - Metrology and Measurement Systems
SP - 403
T1 - Accurate Frequency Estimation Based On Three-Parameter Sine-Fitting With Three FFT Samples
UR - http://www.czasopisma.pan.pl/dlibra/docmetadata?id=90341
DOI - 10.1515/mms-2015-0032