离散时间信号处理PPT第七章 滤波器及设计.ppt

7 Filter Design Techniques 7.0 Introduction 7.1 Design of Discrete-Time IIR Filters from Continuous-Time Filters 7.2 Design of FIR Filters by Windowing 7.6 Comments on IIR and FIR Discrete-Time Filters 7.7 Summary 7.0 Introduction Filters are a particularly important class of linear time-invariant systems. The design of filters involves the following stages: (1) the specification of the desired properties of the system, (2) the approximation of the specifications using a causal discrete-time system, and (3) the realization of the system. As shown in Section 4.4, if a linear time-invariant discrete-time system is used as in Figure 7.1, and if the input is bandlimited and the sampling frequency is high enough to avoid aliasing, then the overall system behaves as a linear time-invariant continuous-time system with frequency response In such cases,it is straightforward to convert from specifications on the effective continuous-time filter to specifications on the discrete-time filter through the relation . That is is specified over one period by the equation 下面我们总结利用模拟滤波器设计IIR数字低通滤波器的步骤。 (1)确定数字低通滤波器的技术指标：通带截止频率ωc、通带衰减αc、阻带截止频率ωs、阻带衰减αs。 (2)将数字低通滤波器的技术指标转换成模拟低通滤波器的技术指标。 (3)按照模拟低通滤波器的技术指标设计模拟低通滤波器。 (4)将模拟滤波器Ha(s)，从s平面转换到z平面，得到数字低通滤波器系统函数H(z)。 ① 数字低通的技术指标为 ωc=0.2πrad,αc=1dB; ωs=0.3πrad,αs=15dB ② 模拟低通的技术指标为 ③设计巴特沃斯低通滤波器。先计算阶数N及3dB截止频率Ωc。 (4)用查表法 根据阶数N=6，查表5.2.1，得到归一化传输函数为 Example 7.1 Determining Specifications for a Discrete-Time Filter We want the overall system of that figure to have the following properties when the sampling rate is samples/s ( ) 1. The gain should be within±0.01 of unity in the frequency band 2. the gain should be no greater than 0.001 in the frequency band Such a set of lowpass specifications on