What is the system function for a two pole band pass filter that has the centre of its pass band at ω=π/2, zero its frequency response characteristic at ω=0 and at ω=π, and its magnitude response is 1/√2 at ω=4π/9?
A. 0.15(1-z-2)/(1+0.7z-2 )
B. 0.15(1+z-2)/(1-0.7z-2 )
C. 0.15(1-z-2)/(1-0.7z-2 )
D. 0.15(1+z-2)/(1+0.7z-2 )
Answer:A
What is the system function for a two pole band pass filter that has the centre of its pass band at ω=π/2, zero its frequency response characteristic at ω=0 and at ω=π, and its magnitude response is 1/√2 at ω=4π/9?
A. 0.15(1-z-2)/(1+0.7z-2 ) B. 0.15(1+z-2)/(1-0.7z-2 ) C. 0.15(1-z-2)/(1-0.7z-2 ) D. 0.15(1+z-2)/(1+0.7z-2 )
Explanation: Clearly, the filter must have poles at P1,2=re±jπ/2 and zeros at z=1 and z=-1. Consequently the system function is