The last ten years，the digital signal processing technology with digital computers and Large-scale integrated circuits has a Rapid development ,it has become an science and technology subject with immense vitality.
With a variety of electronic devices and information processing technology development,Fourier transform is used widely in the frequency analysis, convolution computing and so on.Fast Fourier Transform is the fast algorithm of DFT transform of the important time-frequency transform in signal analysis and processing , as time moves,this method will be widely used.
In this paper, we have a analysis to the complexity of DFT algorithm. With the basic principles of Cooley-Tukey algorithm ,we hava a introduction to the time and frequency algorithm. By analyzing the reverse and rotation factor modules, this procedures can meet the fast Fourier transform real-time, high-speed practical requirements.
We use C language to achieve this algorithm ,compile,run it by the TC compiler, verifying procedures by MATLAB built function of Fourier transform. The results showed that procedures are correct.on this basis ,we use FFT to analysis its application. Analysis small-signal detection and signal to noise pollution by a spectrum
