文档介绍：Design of FIR Digital Filters
Y. Zeng
South China University of Technology, Guangzhou
2013
Digital Signal Processing
2017/11/14
1
Design of Discrete-Time FIR Filters
Filter Design Techniques
Windowing Method
Frequency-Sampling Method
2017/11/14
2
1. Filter Design Techniques
(2) Procedure of Filter Design
Define the specifications of the filter
Selection of an appropriate technique for filter’s coefficient evaluation (a set of aks,bks)
Selection of appropriate structure of filter
Analysis of finite word-length effect
Implementation with a structure
(3) FIR数字滤波器的两种逼近设计方法:窗口法(时域逼近法)、频率采样法(频域逼近法)和最优化设计(等波纹逼近)。
最优化设计一般需要大量的计算,所以一般需要依靠计算机进行辅助设计。
(1) 数字滤波器的设计
数字滤波器的设计就是按照给定的滤波处理系统的性能要求,设计一个因果、稳定的数字系统去逼近这个性能要求;并且用一个有限精度的运算去实现这个系统。
(software+ puter), specific system
Question: how to implement
2017/11/14
3
2. Windowing Method
The design techniques for FIR filters are based on directly approximating the desired frequency response of the discrete-time system.
Most techniques for approximating the magnitude response of an FIR system assume a linear phase constraint.
The windowing technique is the simplest method of FIR filter design.
This method generally begins with an ideal desired frequency response, Hd(ejw), and evaluates(估计) its corresponding impulse response, hd[n]. Then, the desired impulse response, h[n], will be obtained by truncating(截断) hd[n] with selected window function, w[n].
Hd(ejw)
hd[n].
hd[n] w[n]
ideal
infinite length
anti-causal
finite length
anti-causal
h[n]
finite length
causal
Question: how h[n] is in fren. domain?
2017/11/14
4
Windowing Algorithm
Step 1: define specifications of desired filter.
Step 2: evaluate the system function Hd(ejw) from step 1.
Step 3: calculate the impulse response sequence hd[n] as
Step 4: obtain finite duration sequence h[n] from hd[n] as
h[n] = hd[n]w[n], 0 n M
0, otherwise
where w[n] is a selective window function to meet the attenuation requirement, so
H(ejw) = [1/2p] -pp Hd(ejq