Lesson 31

# 6 z 1 016 z 2 1 1 4 z 1 dconv1 0251 06 016 d

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: orms » n=[1 0 0]; » d=[1 -0.6 -0.16 0]; » [R,P,K]=residue(n,d) R= 0.8000 0.2000 0 P= 0.8000 -0.2000 0 K= Zero input solution Y ( z ) = 0 .2 [ z z + 0.8 z + 0 .2 z − 0 .8 y [k ] = 0.2(−0.2) k + 0.8(0.8) k u[k ] Notice: Eigenvalues provided by the system (only). No contribution from the input. Lesson 31 z-Transforms Zero state solution (z-domain) ( ) ( ) Y ( z ) − 0.6 z −1Y ( z ) − 0.16 z −2Y ( z ) = 5(1 /(1 − 1 / 4 z −1 )) Y ( z )(1 − 0.6 z −1 − 0.16 z − 2 ) = 5(1 /(1 − 1 / 4 z −1 )) Y ( z ) = 5 /((1 − 0.6 z −1 − 0.16 z − 2 )(1 − 1 / 4 z −1 )) d=conv([1 -0.25],[1 -0.6 -0.16]) d = 1.0000 -0.8500 -0.0100 0.0400 Y ( z) = 5 1 − 0.85 z −1 − 0.01z − 2 − 0.04 z −3 ( 5z 3 Y ( z) = 3 z − 0.85 z 2 − 0.01z + 0.04 Y ( z) 5z 2 =3 z z − 0.85 z 2 − 0.01z + 0.04 Lesson 31 % Multiply 2 polynomials ) (Prepare for Heaviside expansion) z-Transforms » n=[5 0 0]; » d=conv([1 -0.25],[1 -0.6 -0.16]) d = 1.0000 -0.8500 -0.0100 0.0400 » [R,P,K]=residue(n,d) R= 5.8182 Zero state solution -1.2626 z z z 0.4444 Y ( z ) = 0.444 + 5.8182 + −1.26 P= z + 0 .2 z − 0.8 z − 0.25 0.8000 0.2500 y [k ] = 0.444( −0.2)k + 5.8(0.9)k − 1.26(0.25)k u[k ] -0.2000 K= Notice: Eigenvalues provided by both the system and input signal (i.e., convolution). [ Lesson 31 Stability Lesson 31 Stability Conditionally Stable Stable s­domain z­domain Unstable Lesson 31 Stability 7th order discrete-time lowpass filter. Stable Poles |H(ejω)| Lesson 31 Continuous to Discrete A first look. A study of mapping continuous-time systems (h(t) or H(s)) into their discretetime equivalent (h[k] or H(z)). H(s) H(z)? Lesson 31 Continuous to Discrete Accepted z-transform forms: • • • • • • • Impulse invariant (standard z-transform) Step invariant Zero order hold Finite difference Matched transform z-transform Bilinear z-transform others … You will only be responsible to the standard z-transform. Le...
View Full Document

## This note was uploaded on 10/29/2013 for the course EEL 3112 taught by Professor Harris during the Spring '07 term at University of Florida.

Ask a homework question - tutors are online