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 Impulse Invariance, Bilinear transformation
17 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: Impulse Invariance, Bilinear transformation
Three reasons 1. The art of continuous time iir filter design is highly advanced, and useful results can be achieved it is advantageous to use the design procedures already developed for continuous-time filters
18 Three Reasons 1. The art of continuous-time IIR filter design is highly advanced, and useful results can be achieved, it is advantageous to use the design procedures already developed for continuous-time filters
Three reasons 2. Many useful continuous-time IIr design method have relatively simple closed form design formulas Therefore discrete-time iir filter design methods based on standard continuous-time design formulas are ather simple to carry out 19
19 Three Reasons 2. Many useful continuous-time IIR design method have relatively simple closed form design formulas. Therefore, discrete-time IIR filter design methods based on standard continuous-time design formulas are rather simple to carry out
Three reasons 3. The standard approximation methods that work well for continuous-time IIR filters do not lead to simple closed-form design formulas when these methods are applied directly to the discrete- time iir case because the frequency response of a discrete-time filter is periodic, and that of a continuous-time filter is not
20 Three Reasons 3. The standard approximation methods that work well for continuous-time IIR filters do not lead to simple closed-form design formulas when these methods are applied directly to the discrete-time IIR case, ➢ because the frequency response of a discrete-time filter is periodic, and that of a continuous-time filter is not
Steps of DT filter design by transforming a prototype continuous-time filter ◆① Obtain the specifications for continuous time filter by transforming the specifications for the desired discrete-time filter ◆② Find the system function of the continuous-time filter ◆③ Transform the continuous- time filter to derive the system function of the discrete-time filter 21
21 Steps of DT filter design by transforming a prototype continuous-time filter ◆① Obtain the specifications for continuoustime filter by transforming the specifications for the desired discrete-time filter. ◆② Find the system function of the continuous-time filter. ◆③ Transform the continuous-time filter to derive the system function of the discrete-time filter