{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Wbilinear5

# Wbilinear5 - ECE 421 Sum 2010 Detailed Solutions Set 5...

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

ECE 421 - Sum 2010 Detailed Solutions Set 5 : Filter Design by Mappings 1 5-1. Let s 1 s 2 and s 3 be the three points in the s -plane given by s 1 2 s 2 2 j 100, and s 3 2 j 200 . Use the S -to- Z mapping for backward integration to find the corresponding points z 1 z 2 and z 3 in the z -plane. Use the following values of sampling time T s for these map- pings: (a) T s 005, (b) T s 001. In each case, plot the original s i values in the s -plane, and the corresponding z i mapped values in the z -plane. DETAILED SOLUTION: Given points in the s -plane, the backward integration S -to- Z mapping produces points in the z -plane given by equation (19) in the Notes, repeated here for easy reference: z 1 1 sT s a Now substitute the appropriate s -value and T s value into a to find the point in the z -plane. (a) T s 005 : With T s 0 005, equation a becomes z 1 1 0 005 s b Substituting s 1 2 into b gives the following value for z 1 : z 1 1 1 0 005 2 1 1 0 01 0.9901 c Substituting s 2 2 j 100 into b gives the following values for z 2 : z 2 1 1 0 005 2 j 100 1 1 01 j 0 5 0 7952 j 0 3937 d Substituting s 3 2 j 200 into b

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

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

{[ snackBarMessage ]}

### Page1 / 4

Wbilinear5 - ECE 421 Sum 2010 Detailed Solutions Set 5...

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

View Full Document
Ask a homework question - tutors are online