Analysis and Improvement on Discrete Fourier Transform for Frequency Estimation of Complex Sinusoid

• Main Authors: Sheng-Kai Wen, 溫勝凱
• Other Authors: 廖俊睿
• Format: Others
• Language: zh-TW
• Published: 2014
• Online Access: http://ndltd.ncl.edu.tw/handle/27839980600353846562

碩士 === 國立中興大學 === 通訊工程研究所 === 102 === The frequency estimation of a complex sinusoid under the influence of white noise is usually divided into two stages. The first stage is called “coarse search”. It searches the maximum magnitude of the Discrete Fourier Transform (DFT) coefficients. The second stage is called “fine search”. It searches around the peak magnitude found from the coarse search. A popular way of fine search is to interpolate the DFT coefficients around the peak magnitude. There are four commonly used interpolators in fine search. They are proposed by Quinn, Jacobsen, MacLeod, and Candan. These interpolators exhibit estimation bias because of the approximation in the derivation. In this regard, Candan proposed a constant scaling factor to reduce the bias and has shown that their estimator provides the lowest bias among these estimators. Two methods, phase correction and polynomial root correction, have also been proposed to reduce the estimation bias. Phase correction method multiplies a phase correction term to each DFT coefficient to eliminate bias caused by phase inconsistency. On the other hand, polynomial root correction uses Taylor series expansion to derive a third-order polynomial equation for the estimated frequency. Then, a more accurate estimation can be obtained from the root of the third-order polynomial. In this thesis, we apply the polynomial root correction method to the phase correction method. In the experiments, we show that the two methods combined can achieve the best performance as compared to the previous methods.