Discrete-Time Systems A discrete-time system processes a given input sequence x[] to generates an output sequencey[n] with more desirable properties In most applications, the discrete-time system is a single-input, single-output system:

Transform-Domain Representation of Discrete-Time Signals Three useful representations of discrete-time sequences in the transform domain: Discrete-time Fourier Transform (DTFT) Discrete Fourier Transform (DFT) z-Transform

The dtft provides a frequency-domain representation of discrete-time signals and lti discrete-time systems Because of the convergence condition, in many cases. the dtft of a sequence may not exist as a result. it is not possible to make use of such frequency-domain characterization in these cases Copyright C 2001, S K. Mitra

The output y[n] of a frequency-selective LTI discrete-time system with a frequency response exhibits some delay relative to the input x[n] caused by the nonzero phase response of the system

It is nearly impossible to design a linear￾phase IIR transfer function It is always possible to design an FIR transfer function with an exact linear-phase response Consider a causal FIR transfer function H(z) of length N+1, i.e., of order N:

The simple filters discussed so far are characterized either by a single passband and/or a single stopband There are applications where filters with multiple passbands and stopbands are required The comb filter is an example of such filters

描述线性非移变系统的方式： 线性常系数差分方程、单位取样响应、频率响应描述、系统函数

2.1，2.2，2.3，2.5，2.7，2.8， 2.12，2.13，2.18，2.20，2.21(3)， 2.22(4)，2.28(2)，2.30，2.32，2.34 交作业时间：第四周周四（9月26日）上课时

有限长序列的傅里叶变换称为离散傅里叶变换，简写为DFT。DFT可以按3个步骤由 DFS推导出来： ①将有限长序列延拓成周期序列； ②求周期序列的DFS； ③从DFS中取出一个周期便得到有限长 序列的DFT

离散傅里叶变换在实际应用中是非常重要的，利用它可以计算信 号的频谱、功率谱和线性卷积等。但是，如果使用定义式(3.20)来 直接计算DFT，当N很大时，即使使用高速计算机，所花的时间也 太多。因此，如何提高计算DFT的速度，便成了重要的研究课题