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Determine z-transform of x[n]=(1/4)^n u[-n+3] | Determine z-transform of x[n]=(1/4)^n u[-n+3] | ||
| − | X(z)=sigma x[n]z^(-n)=sigma (1/4)^(n)z^(-n)=sigma (1/4)^(-n)z^(n)=sigma (1/4)^(-n+3)z^(n-3) | + | X(z)=sigma x[n]z^(-n)=sigma (1/4)^(n)z^(-n)=sigma (1/4)^(-n)z^(n)=sigma (1/4)^(-n+3)z^(n-3)=(1/64)z^(-3)/(1-4z) |
| − | =(1/64)z^(-3)/(1-4z) | + | |
=(1/64)z^(-4)/(1-(1/4)z^(-1)), |z|<1/4 | =(1/64)z^(-4)/(1-(1/4)z^(-1)), |z|<1/4 | ||
Latest revision as of 11:07, 3 May 2013
This is problem 10.21 (f) in O+W
Determine z-transform of x[n]=(1/4)^n u[-n+3]
X(z)=sigma x[n]z^(-n)=sigma (1/4)^(n)z^(-n)=sigma (1/4)^(-n)z^(n)=sigma (1/4)^(-n+3)z^(n-3)=(1/64)z^(-3)/(1-4z) =(1/64)z^(-4)/(1-(1/4)z^(-1)), |z|<1/4
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