三阶离散chirp傅里叶变换研究

多项式信号的参数估计是信号处理领域的重要问题,利用三阶离散chirp傅里叶变换可以对三阶多项式信号进行参数估计。研究三阶离散chirp傅里叶变换。给出了三阶离散chirp傅里叶表达式,分析了三阶离散chirp傅里叶变换和三阶连续chirp傅里叶变换的关系。提出了把三阶离散chirp傅里叶变换分解为频率线性chirp率平面、频率二次chirp率平面、线性chirp率二次chirp率平面的方法。利用此方法分析了三个平面内的主瓣、旁瓣的大小。讨论了不同采样率对三阶离散chirp傅里叶变换性能的影响。计算机仿真结果证明了分析的正确性。

Research on the three-order discrete chirp-Fourier transform

Estimating the parameters of polynomial signal is an important problem in the domain of signal processing. The three-order discrete chirp-Fourier transform (DCFT) can estimate the parameters of three-order polynomial signals. The three-order discrete chirp-Fourier transform is studied. The expression of three-order DCFT is introduced and the relationship between three-order DCFT and three-order analog chirp-Fourier transform (ACFT) is analyzed. A method for analyzing the three-order DCFT is presented, which decomposes the three-order DCFT into three planes. These three planes are frequency-linear chirp rate plane, frequency-quadratic chirp rate plane and linear chirp rate-quadratic chirp rate plane. By using this method, the magnitude of mainlobe and sidelobe in three planes is analyzed respectively. Different characteristics of three-order DCFT due to different sampling rates are also discussed. The computer simulation proves the validity of the analysis.