数字信号处理课程中的傅里叶变换教学探索  

Teaching Research of the Fourier Transform in the Digital Signal Processing

作　　者：姜恩华[1] 杨一军[1] 窦德召[1] 汪徐德[1] 陈得宝[1] 

机构地区：[1]淮北师范大学,安徽淮北235000

出　　处：《廊坊师范学院学报（自然科学版）》2017年第1期52-56,共5页Journal of Langfang Normal University(Natural Science Edition)

基　　金：安徽省高校自然科学研究重点项目(KJ2016A628);安徽省教育厅名师工作室(2015msgzs138);安徽省高等教育振兴计划项目(2014zdjy060)

摘　　要：详细分析了非周期信号的傅里叶变换和周期信号的傅里叶级数。借助时域采样定理和频域采样定理,推导了连续非周期信号的傅里叶变换、序列的傅里叶变换和离散傅里叶变换X(k)之间的关系。借助X(k)计算非周期信号的频谱,分析了连续周期信号的傅里叶级数和周期序列的傅里叶级数的差别。借助频域采样定理,推导了周期序列傅里叶级数与离散傅里叶变换X(k)之间的关系。借助X(k)计算周期序列的频谱,在CCStudio v3.3软件开发环境下,编写C语言程序,实现快速傅里叶变换(FFT)算法,计算出X(k)。以矩形序列和正弦序列为例,借助X(k),求得矩形脉冲信号和正弦序列的频谱结构。In the paper,the Fourier transformation of the Non-periodic signal and the Fourier series of periodic signal were analyzed in detail.By using the time domain sampling theorem and the frequency domain sampling theorem,the relationship of the Fourier transformation of the Non-periodic signal,the sequences Fourier transform and the discrete Fourier transform X（k） were deduced.The frequency spectrum of the non-periodic signal was calculated by using X（k）.The difference between the Fourier series of the continuous periodic signal and the Fourier series of the periodic sequences is analyzed.By using the frequency domain sampling theorem,the relationship of the Fourier series of the periodic sequences and the discrete Fourier transform X（k） were deduced.The frequency spectrum of the periodic sequences was calculated by using X（k）.Using the CCStudio v3.3 software,the fast Fourier transform algorithm（FFT） was implemented by the C language program,the X（k） was calculated by the FFT algorithm.Using the example of the Rectangular sequence and the Sine sequence,the frequency spectrum of Rectangular pulse signal and the Sine sequence were obtained by using X（k）.

关 键 词：傅里叶变换 序列的傅里叶变换 离散傅里叶变换 傅里叶级数 

分 类 号：TN911.6[电子电信—通信与信息系统]