Fast Fourier Transform is widely used in the signal spectrum analysis. However, it usually gets interesting in a part of the whole signal spectrum in engineering, so it needs spectrum zoom analysis. It is the common method for spectrum zoom which including complex modulation Zoom-FFT (ZFFT) and Chirp-Z Transform (CZT). After the calculating methods of two kinds spectrum zoom are given, both ZFFT and CZT can improve the measurement accuracy by simulation in MATLAB. Lastly, this paper gives the realization steps of the two methods in FPGA engineering.