Analysis of DTFTs Spectrum Zoom Character and Design of Its Fast Algorithm

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.