Three reasons 1 The art of continuous-time iir filter design is highly advanced, and since useful results can be achieved it is advantageous to use the design procedures already developed for continuous-time filters
17 Three Reasons 1. The art of continuous-time IIR filter design is highly advanced, and since 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 such standard continuous-time design formulas are rather simple to carry out 18
18 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 such standard continuous-time design formulas are rather simple to carry out
Three reasons 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 19
19 Three Reasons ◆ 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 The specifications for the continuous time filter are obtained by a transformation of the specifications for the desired discrete-time filter Find the system function of the continuous-time filter Transform the continuous-time filter to derive the system function of the discrete-time filter
20 Steps of DT filter design by transforming a prototype continuous-time filter ◆The specifications for the continuoustime filter are obtained by a transformation of the specifications for the desired discrete-time filter. ◆Find the system function of the continuous-time filter. ◆ Transform the continuous-time filter to derive the system function of the discrete-time filter
Constraints of transformation Cto preserve the essential properties of the frequency response, the imaginary axis of the S-plane is mapped onto the unit circle of the Z-plane. S=j2分>z=e m plane lane e Re 21
21 Constraints of Transformation ◆to preserve the essential properties of the frequency response, the imaginary axis of the s-plane is mapped onto the unit circle of the z-plane. j w s = j z = e s − plane z − plane Im Im Re Re