What is the partial fraction expansion of X(z)=1/((1+z-1 )(1-z-1)2)?
A. z/(4(z+1)) + 3z/(4(z-1)) + z/(2〖(z+1)〗2 )
B. z/(4(z+1)) + 3z/(4(z-1)) – z/(2〖(z+1)〗2 )
C. z/(4(z+1)) + 3z/(4(z-1)) + z/(2〖(z-1)〗2 )
D. z/(4(z+1)) + z/(4(z-1)) + z/(2〖(z+1)〗2 )
Answer:A
What is the partial fraction expansion of X(z)=1/((1+z-1 )(1-z-1)2)?
A. z/(4(z+1)) + 3z/(4(z-1)) + z/(2〖(z+1)〗2 ) B. z/(4(z+1)) + 3z/(4(z-1)) – z/(2〖(z+1)〗2 ) C. z/(4(z+1)) + 3z/(4(z-1)) + z/(2〖(z-1)〗2 ) D. z/(4(z+1)) + z/(4(z-1)) + z/(2〖(z+1)〗2 )
Explanation: First we express X(z) in terms of positive powers of z, in the form X(z)=z3/((z+1)〖(z-1)〗2 )