数字滤波器的响应.docVIP

第8章 数字滤波器的响应 一个数字滤波器是一个处理离散时间信号的系统。在这章，我们研究这种脉冲和频率响应的线性定常系统。 预期的学习成果包括: 理解在塑造一个LTI系统时脉冲响应之间的关系、频率响应、差分方程和传递函数; 能够识别无限脉冲响应(IIR)和有限脉冲响应(FIR)滤波器，注意一个数据响应是一个可以进行离散时间信号的系统; 计算系统频率响应的能力。 Response of digital filters A digital filter is a system which processes discrete-time signals.In this chapter,the impulse and frequency responses of linear time-invariant (LTI) systems are studied.The intended learning outcomes include:(i)Understanding the relationships between impulse response ,frequency response ,difference equation and transfer function in characterizing a LTI system; (ii)Ability to identify infinite impulse response (IIR) and finite impulse response (FIR) filters;and (iii)Ability to compute system frequency response. 8.1 线性定常系统特性 图8.1显示了框图数字处理的一个模拟信号与使用一个配置线性定常能控系统。在这一章,研究脉冲响应和频率响应的过滤器处理离散LTI输入x[n]产生输出序列y[n]是我们研究的重点。 X[t] x[n] y[n] y[t] 通过前面章节,我们已经知道LTI系统可以以其脉冲响应、频率响应、差分方程和传递函数。快速回顾,如下： 8.1 linear time-invariant system characterization Figure 8.1 shows the block diagram for digital processing of an analog signal with the use of a LTI system.In this chapter,our focus is to study the impulse response and frequency response of the LTI filter which processes the discrete-time input x[n] to produce the output sequence y[n].From previous chapters,we have learned that the FTI system can be characterized by its impulse response,frequency response,difference equation and transfer function. A quick review is given as follows 脉冲响应 让h[n]是LTI过滤器的脉冲响应。回想一下(3.17),它通过卷积来构建系统: （8.1） h[n]是LTI过滤器的主导时间回应。 也就是说,如果h[n]是可用的,我们可以通过使用x[n] 来产生y[n]。事实上，脉冲响应是时域响应的过滤器。 Impulse Response Let h[n] be the impulse response of the FTI filter.Recall from(3.17),it characterizes the system via the convolution: That is if h[n] is avaliable,we can produce y[n] * 频率响应 这个配置线性定常能控系统也可以特征的频率响应, 我们可根据（6.17）知道：这是离散傅里叶变换的H[n]。让x和y分别是DTFTsof x和y[n][n]。 这确实是如8.1所表示的频率。即,在时域卷积中对应于多样的频域。 * 差分方程 一个LIT系统可以满足了不同方程的形式: 也就是