Challenge07_inverse-z

# Challenge07_inverse-z - Digital Signal Processing Dr Fred J...

This preview shows pages 1–2. Sign up to view the full content.

Digital Signal Processing Dr. Fred J. Taylor, Professor Lesson Title: Inverse z-Transform Challenge Lesson Number: 07 Challenge Problem A signal having a z-transform: ( 29 ( 29 ( 29 2 2 3 1 1 1 3 11 - + + + = z z z z z X has a partial fraction expansion: ( 29 ( 29 ( 29 ( 29 2 3 2 1 0 1 1 1 - + - + + + = z z K z z K z z K K z X Q: What are the value of the 4-tuple { K 0 , K 1 , K 2 , K 3 }? Answer: First convert X ( z ) into X ( z )/z resulting in: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 = - + - + + + = - + + + = = 2 3 2 1 0 2 2 3 1 1 1 1 1 1 3 11 ' z K z K z K z K z z z z z z z X z X Solving for the individual terms yields: ( 29 ( 29 ( 29 1 1 1 1 3 11 0 2 2 3 0 0 = - + + + = = = = z z z z z z z z X z K ( 29 ( 29 ( 29 75 . 1 4 9 1 1 3 11 1 1 2 2 3 1 1 = = - + + = + = - = - = z z z z z z z z X z K ( 29 ( 29 ( 29 5 . 7 2 15 1 1 3 11 1 1 2 3 1 2 3 = = + + + = - = = = z z z z z z z z X z K ( 29 ( 29 ( 29 ( 29 25 . 8 4 33 1 1 2 3 22 11 1 1 3 11 1 1 2 2 2 3 4 1 2 3 1 2 2 = = + - - + + = + + + = - = = = = z z z z z z z z z dz z z z z d dz z z X z d K Therefore INVERSE_Z 1

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

View Full Document
Digital Signal Processing
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 08/21/2010 for the course EEL 5525 taught by Professor Yang during the Summer '09 term at University of Florida.

### Page1 / 2

Challenge07_inverse-z - Digital Signal Processing Dr Fred J...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online