Chapter 7 Filter Design Techniques ◆7.0 Introduction 7. 1 Design of discrete-Time iir Filters from Continuous-Time filters 97.2 Design of FIR Filters by Windowing 7. 3 Examples of FIR Filters design by the Kaiser window method 7.4 Optimum Approximations of FIR Filters 97.5 Examples of FIR Equiripple Approximation 7. 6 Comments on iir and FIr Discrete-Time Filters
2 Chapter 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 ◆7.3 Examples of FIR Filters Design by the Kaiser Window Method ◆7.4 Optimum Approximations of FIR Filters ◆7.5 Examples of FIR Equiripple Approximation ◆7.6 Comments on IIR and FIR Discrete-Time Filters
Filter Design Techniques 7.0 Introduction
3 Filter Design Techniques 7.0 Introduction
7.0 Introduction Frequency-selective filters pass only certain frequencies Any discrete-time system that modifies certain frequencies is called a filter We concentrate on design of causal Frequency-selective filters
4 7.0 Introduction ◆Frequency-selective filters pass only certain frequencies ◆Any discrete-time system that modifies certain frequencies is called a filter. ◆We concentrate on design of causal Frequency-selective filters
Linear time-invariant discrete-time system If input is bandlimited and sampling frequency is high enough to avoid aliasing then overall system behaves as an Lti continuous-time system Hel iQT <兀 H uQ=H(Q >丌 CID H(e/) D/C xa(t) yIn ya(t) effective T continuous-time specifications are converted to discrete time specifications by: a=5l,lejo\= T/ a i
5 ◆If input is bandlimited and sampling frequency is high enough to avoid aliasing, Linear time-invariant discrete-time system continuous-time specifications are converted to discrete time specifications by: ( ) , eff j H H j T e = = T, then overall system behaves as an LTI continuous-time system ( ) ( ) ( ), 0, j T c eff H e T H j H j T = = effective
Stages of Filter Design Determine the specification of the desired properties of the system The approximation of the specifications using(designing) a causal discrete-time system The realization of the system Our focus is on second step Specifications are typically given in the frequency domain
6 Stages of Filter Design ◆Determine the specification of the desired properties of the system. ◆The approximation of the specifications using(designing) a causal discrete-time system. ◆The realization of the system. ◆Our focus is on second step ◆Specifications are typically given in the frequency domain