DTFT频谱细化特性分析及其快速算法设计

Analysis of DTFT's Spectrum Zoom Character and Design of Its Fast Algorithm

该文介绍了离散时间傅里叶变换(Discrete Time Fourier Transform,DTFT)的一种等价定义式,分析了DTFT与线性调频Z变换(Chirp-Z transform)的联系与区别,推导出DTFT是一种特殊形式的Chirp-Z变换,具有频谱细化特性。设计了DTFT的快速算法,给出了算法实现步骤。算法计算量分析表明:在相同频率分辨率下,DTFT快速算法的计算量比Chirp-Z变换快速算法小。仿真结果验证了理论推导的正确性和DTFT在频率估计方面的优越性。

One equivalent definition of Discrete Time Fourier Transform （DTFT） is introduced in this paper. The relationship and differences between DTFT and Chirp-Z transform are analyzed. It is pointed out that DTFT, with spectrum zoom character, is a special form of Chirp-Z transform. Moreover, one fast algorithm and its detailed process of DTFT are given. Computational complexity analysis shows that fast algorithm of DTFT is less complicated than Chirp-Z with the same frequency resolution. Simulation results prove the validity of the theoretical results and the advantage of DTFT in frequency estimation.