ECE634S09_L2_PartialFraction

ECE634S09_L2_PartialFraction - ECE634 Signals and Systems...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
ECE634 Signals and Systems II, Spring 2009 - Lecture 2, January 23 Daniel S. Brogan 1 B.5 Partial Fraction Expansion: B.5-1 Method of Clearing Fractions () ( ) 32 1 22 41 61 4 12 3 3 2 sss AB C D Ts ss s s s ++ == + + + + + + Clear fractions by multiplying by denominator… ( )( )( ) ( )( )() ( ) 2 2 4 2 3 1 2 3 1 3 1 2 A s s B C D =+ + ++++ +++ ( )( ) 2 2 4 4 4 3 3 2 3 43 1 44 A s B s Cs s Ds s s = + + + + + + ( ) ( ) 3 2 3 2 23 2 4 16 14 7 16 12 6 11 6 5 84 A s B s s s s = + + + + + + + + + + + + ( ) ( ) 3 2 4 76 5 16 11 4 8 12 6 3 4 A B D sA B C D s C D s A B C D = + + + + + + + + + + 4( 1 ) 51 6 ( 2 ) 16 11 4 8 14 (3) 12 6 3 4 0 (4) ABD CD C D ABCD ++ = + = + = = Multiply Eq. (2) by 4 and subtract Eq. (3) from it, and multiply Eq. (2) by 3 and subtract Eq. (4) from it to remove C . Then subtract equation (6) from Eq. (5) to obtain Eq. (7). Finally, subtract Eq. (1) from Eq. (7) and divide by 2 to find A . 1 ) 12 13 12 50 (5) 91 21 1 4 8 ( 6 ) = ++= 1 ) 12 13 12 50 (5) ( 7 ) = A =− 1 A = − Substitute in A and combine Eq. (1) and Eq. (5) to find B and D . 14 ( 1 ) 12 13 12 50 (5) BD −+ + = −+ + = 5( 1 ) 13 12 62 (5) += 2 B = 3 D =
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
ECE634 Signals and Systems II, Spring 2009 - Lecture 2, January 23 Daniel S. Brogan 2
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 5

ECE634S09_L2_PartialFraction - ECE634 Signals and Systems...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online