Abstract: 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.