傅立叶变换在工程应用中的演变

Evolution of fourier transform in engineering application

傅立叶变换是分析信号与系统最基本的分析工具,但在工程实际应用中具有很大的局限性,由此产生了多种傅立叶变换的演变形式,常见的包含离散傅立叶变换、快速傅立叶变换、短时傅立叶变换、小波变换、Laplace变换、Z变换等,这些变换形式都与傅立叶变换有关,都可以从傅立叶变换推广得到,它们和傅立叶变换之间以及它们相互之间可以转化.

Fourier transform is the basic tool to analyze signals and systems. But the application of Fourier transform is limited in engineering, and many evolutional formats of Fourier transform have been formed, including discrete Fourier transform, fast Fourier transform, short - time Fourier transform, wavelet transform, Laplace transform and Z transform. Those formats all are correlative with Fourier transform. They can be formed by the extensions of Fourier transform. The evolutional formats can be mutually converted and can be converted between Fourier transform and themselves.