Lesson_23 - Lesson 23 Lesson 23 Challenge 22 Lesson 23...

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Unformatted text preview: Lesson 23 Lesson 23 Challenge 22 Lesson 23 Inverse z-Transform Challenge 23 Lesson 23 Challenge 22 Classify the stability of the displayed filter. w[k] T 1 2 2 w[k] y[k] T 1 2-2 w[k] x[k] 2 From Challenge 21 H(z) 1st_order = z/(z-2). Therefore H(z) 2nd_0rder =( H(z) 1st_order ) 2 = z 2 / (z-2) 2 . Poles at z = 2 and 2. Unstable. Lesson 23 Lesson 23 Inverse z-transform Lesson 23 Lesson 23 The inverse z-transform of some z- transform X ( z ) is theoretically defined to be: -- = = C k dz z z X j z X Z k x 1 1 ) ( 2 1 )) ( ( ] [ Table 1: Primitive Signals and their z-Transform Time-domain z-transform [ k ] 1 [ k m ] z m u [ k ] z /( z 1) ku [ k ] z /( z 1) 2 k 2 u [ k ] z ( z +1)/( z 1) 3 a k u [ k ] z /( z a ) ka k u [ k ] az /( z a ) 2 k 2 a k u [ k ] az ( z + a )/( z a ) 3 sin[ bk ] u [ k ] cos[ bk ] u [ k ] exp[ akT s ]sin[ bkT s ] u [ kT s ] exp[ akT s ]cos[ bkT s ] u [ kT s ] a k sin( bkT s ) u [ kT s ] a k cos( bkT s ) u [ kT s ] Lesson 23 Lesson 23 Long Division Example ... ... ... 1 2 1 1 2 2 1 1 2 2 1 1 +- + + + + + + +----- z a b a b a a b z b z b b z a z a a 1 1 1 ) (-- = az z X ... 1 1 1 ) ( 3 3 2 2 1 1 + + + + =- =---- z a z a az az z X X[k]={1, a, a 2 , a 3 , . . . } Lesson 23 Lesson 23 Partial Fraction (Heaviside) Expansion ) ( ) ( ) ( z D z N z X = ( 29 =- = L i n i i z z D 1 ) ( = = L i i n N 1 (Signal transform or Transfer function) Poles Multiplicity distinct or repeated Filter order Lesson 23 Lesson 23...
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This note was uploaded on 08/21/2010 for the course EEL 3135 taught by Professor ? during the Spring '08 term at University of Florida.

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Lesson_23 - Lesson 23 Lesson 23 Challenge 22 Lesson 23...

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