Wbilinear5

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

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Unformatted text preview: 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 = : 005, equation a becomes z = 1 1 : 005 s b Substituting s 1 = 2 into b gives the following value for z 1 : z 1 = 1 1 : 005 2 = 1 1 : 01 = 0.9901 c Substituting s 2 = 2 j 100 into b gives the following values for z 2 : z 2 = 1 1 : 005 2 j 100 = 1 1 : 01 j : 5 = : 7952 j : 3937 d Substituting...
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This note was uploaded on 09/07/2010 for the course ECE 421 taught by Professor Hallen during the Summer '08 term at N.C. State.

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

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