傅里叶变换的意义（The meaning of the Fourier transform）.doc

傅里叶变换的意义（The meaning of the Fourier transform） 1. The transformation is a time variable function that becomes a variable function of the corresponding transform domain, so that the operation is simple and easy to handle. Transform domain transformation is FT (frequency domain features as the main research object), LT and ZT (focus on the analysis study of poles and zeros), DTFT, DFT and FFT, DTWT, etc. The Fourier transform is a limit of the Fourier series (FST) of periodic signals as periodic signals. Fourier series - periodic signal, Fourier transform - aperiodic signal 3. Non-periodic continuous -- FT -- continuous non-periodic The continuous period - FST - is discrete Non - periodic discrete - DTFT - continuous cycle Discrete period - DFT - periodic dispersion The discrete Fourier transform (DFT) and the sequence Fourier transform (DTFT) are all related to the Z transform, DTFT is the Z transform on the unit circle, and DFT is the uniform sampling of the Z transform in the unit circle. 4, fast Fourier transform (FFT) is the essence of divide and rule, the use of symmetry, periodic and reducibility, will merge some items will DFT decomposition for short sequences, reduce number of operation, improve the operation speed. 5, the application of fast Fourier transform is very extensive, who can make use of the Fourier transform to analyze, integration, transformation, can use FFT algorithm and digital computing technology are used to. FFT is widely used in digital communication, speech analysis, image processing and matching filtering. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Its not clear in the time domain, it might be easy in the frequency domain, because the rec