理解DFT如何逼近FT的实例教学法

An Example-Based Illustration of the Connection between DFT and FT

本文结合一个离散傅里叶变换DFT计算实例,分析了DFT与连续时间傅里叶变换FT之间的联系,以较为直观的方式阐述了由FT到DFT的演变过程,以及该过程关键环节对最终结果的影响,主要包括谱泄漏,折叠效应,栅栏效应以及谱折移等。教学实践表明,通过该实例讲述DFT对FT的逼近问题,能有效加深学生对DFT的认识和理解。

The connection relationship between the discrete Fourier transform （DFT） and the continuous time Fourier transform （FT） is analyzed in this paper based on an example. The main contents of the relationship are spectral leakage, aliasing problem, grating phenomenon, and spectral shift. Teaching practice shows that this examplebased method is very helpful for student to understand how DFT works.