Digital signal processing technology over the last decade with the digital computer, large scale integrated circuits and other advanced technologies, with rapid advances, has formed a strong technical and scientific vitality. Because it itself has a range of advantage, so effective in promoting the field of engineering technology transformation and subject development, more extensive application fields, in-depth, more and more people's attention. First, the fast Fourier transform (FFT) digital signal processing is the most basic computing, this article describes the beginning of the fast Fourier transform definition and the most widely used types. Then, the definition of parallel algorithms and matrix operations and matrix multiplication parallel algorithms parallel algorithms, parallel algorithms are also introduced performance metrics. Finally, a practical application, reflects the fast Fourier transform algorithm used in parallel, through the main parallel FFT algorithm is studied, expect that the parallel Fast Fourier Transform algorithm has a clear understanding.