1、目 录 摘 要 I Abstract . II 1 离散傅里叶变换 1 1.1 理论分析 . 1 1.2 设计原理 . 1 1.3 Matlab 程序设计 2 1.4 结果与分析 . 3 2 周期信号傅里叶变换 4 2.1 理论分析 . 4 2.2 设计原理 . 4 2.3 Matlab 程序设计 5 2.4 结果与分析 . 6 3 数字滤波器 9 3.1 理论分析 . 9 3.2 设计原理 . 9 3.3 Matlab 程序设计 . 10 3.4 结果与分析 11 4 心得体会 . 12 参考文献 . 13 I 摘 要 信号处理有一段悠久的历史，高级信号处理算法和硬件广泛见于各种系统，从专用
2、的 军事系统到各式各样廉价大宗的日用电子产品的工业应用都是如此。随着通信系统的日益 无线化、移动式和多功能性，在这些系统中高级信号处理手段的重要性在继续不断地增长 着。当我们凝视未来时，信号在我们社会中的作用正在日益加速的增长。 DFT 是数字信号处理中最重要的数学工具之一。其实质是对有限长序列频谱的离散 化，即通过 DFT 使时域有限长序列与频域有限长序列相对应，从而可在频率域用计算机进 行信号处理。更重要的是 DFT 有快速算法，可使信号处理速度提高好几倍，使数字信号的 实时处理得以实现。因此，DFT 既有重要的理论意义，又有广泛的实际应用价值。通过 Matlab 实现 DFT 算法对理论
3、的理解和实际应用的学习都有非常重大的作用。 关键词：信号处理；DFT；Matlab II Abstract Signal processing for some long history, advanced signal processing algorithms and hardware widely seen in a variety of systems, from dedicated military systems to a wide range of household electronic products cheap bulk industrial application ar
4、e true. As communications systems increasingly wireless, mobile and versatility, in these systems the importance of senior signal processing means to continue growing all. When we gaze the future, the signal role in our society is increasingly accelerated growth. DFT is a digital signal processing i
5、s the most important mathematical tools. Its essence is a finite-length sequence of discrete spectrum, namely through the DFT for the time domain finite-length sequence and frequency-domain finite-length sequence corresponding to the frequency domain using a computer in signal processing. More impor
6、tantly, a fast DFT algorithm, can increase the signal processing speed several times, the digital real-time signal processing can be achieved. Therefore, DFT both theoretical significance, but also a wide range of practical value. DFT algorithm through Matlab understanding of the theory and practical application of learning have a very significant role. Keywords: Signal processing; DFT; Matlab 1 1 离散傅里叶变换 1.1 理论分析 已知序列 xn=1 1 1 1,试用 MATLAB 编写程序，计算该序列的离散傅里叶变换及 逆离散傅里叶反变换。 由题目可知我们要对一个有限长离散时间序列进行离
