Example 7.1 Determining specifications for a discrete-Time Filter Specifications of the continuous-time filter passband1-001<H(g)<1+0010709527(2000 ◆2. stopband|H()<001027(300 IHer(in) 1+61 tolerance scheme 容限图 =0011-4 Passband i transition Stopband 2 =0.001 g2=27(20092,=2(3000
12 Example 7.1 Determining Specifications for a Discrete-Time Filter ◆Specifications of the continuous-time filter: ◆1. passband ◆2. stopband 1− 0.01 H ( j) 1+ 0.01 for 0 2 (2000) eff Heff ( j) 0.001 for 2 (3000) 1 = 0.01 2 = 0.001 2 (2000) = p 2 (3000) = s tolerance scheme 容限图
Example 7.1 Determining Specifications for a discrete-Time Filter H Solution: Specifications of the Same 61 discrete-time filter in tolerance 01 limits: 8=0.01 2=0.001 Passband i Transition Stopband H(Q +61 62 61 O.=0.4丌 0.6丌 Passband i Transition Stopband O=9T=10-49 9p=27(200=2x(3000 T=10
13 Example 7.1 Determining Specifications for a Discrete-Time Filter 4 T s 10− = 4 T 10− = = Specifications of the discrete-time filter in 1 = 0.01 2 = 0.001 2 (2000) = p 2 (3000) = s 0.4 p = 0.6 s = Solution: Same tolerance limits: H j eff ( ) ( ) j H e
Filter Design Constraints Designing iir filters is to find the approximation by a rational function of z The poles of the system function must lie inside the unit circle(stability, causality) Designing FIR filters is to find the polynomial approximation FIR filters are often required to be linear phase
14 Filter Design Constraints ◆Designing IIR filters is to find the approximation by a rational function of z. ◆The poles of the system function must lie inside the unit circle(stability, causality). ◆Designing FIR filters is to find the polynomial approximation. ◆FIR filters are often required to be linearphase
Filter Design Techniques 7. 1 Design of Discrete-Time IIR Filters from continuous-Time filters
15 Filter Design Techniques 7.1 Design of Discrete-Time IIR Filters From Continuous-Time Filters
7.1 Design of Discrete-Time IIR Filters From continuous-Time filters The traditional approach to the design of discrete time iir filters involves the transformation of a continuous-time filter into a discrete filter meeting prescribed specitication 16
16 7.1 Design of Discrete-Time IIR Filters From Continuous-Time Filters ◆The traditional approach to the design of discrete-time IIR filters involves the transformation of a continuous-time filter into a discrete filter meeting prescribed specification