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10.3 An analogue first-order low-pass filter has the transfer function G(s) = 1+ ts where r is the time constant of the filter. (a) What is the 3 dB bandwidth of the analogue filter? (b) Use the bilinear transformation 2 (1-z AT 1+2 S =- where AT is the sampling interval, to show that an equivalent digital filter has the z-transfer function: M2) _ a, + a,z"! G(z) = F(2) 1- bz where 2r 2r AT ΔΤ (c) Hence show that the corresponding difference equation is: y(i) = a,x(i) + a,x(i – 1) + b,y(i – 1)

10.3 An analogue first-order low-pass filter has the transfer function G(s) = 1+ ts where r is the time constant of the filter. (a) What is the 3 dB bandwidth of the analogue filter? (b) Use the bilinear transformation 2 (1-z AT 1+2 S =- where AT is the sampling interval, to show that an equivalent digital filter has the z-transfer function: M2) _ a, + a,z"! G(z) = F(2) 1- bz where 2r 2r AT ΔΤ (c) Hence show that the corresponding difference equation is: y(i) = a,x(i) + a,x(i – 1) + b,y(i – 1)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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10.3 An analogue first-order low-pass filter has the transfer function G(s) = 1+ ts where z is the time constant of the filter. (a) What is the 3 dB bandwidth of the analogue filter? (b) Use the bilinear transformation 2 (1-z AT 1+z where AT is the sampling interval, to show that an equivalent digital filter has the z-transfer function: G(z) = M2) 4, +a;z"! (2) 1- bz where 2r ΔΤ ao = a1 2r +1 ΔΤ 2r +1 AT (c) Hence show that the corresponding difference equation is: y(i) = a,x(i) + - a;x(i – 1) + b,y(i –- 1)
Transcribed Image Text:10.3 An analogue first-order low-pass filter has the transfer function G(s) = 1+ ts where z is the time constant of the filter. (a) What is the 3 dB bandwidth of the analogue filter? (b) Use the bilinear transformation 2 (1-z AT 1+z where AT is the sampling interval, to show that an equivalent digital filter has the z-transfer function: G(z) = M2) 4, +a;z"! (2) 1- bz where 2r ΔΤ ao = a1 2r +1 ΔΤ 2r +1 AT (c) Hence show that the corresponding difference equation is: y(i) = a,x(i) + - a;x(i – 1) + b,y(i –- 1)
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