Apr 3, 2022 #1 B Baidehi Newbie Joined Apr 3, 2022 Messages 1 Helped 0 Reputation 0 Reaction score 0 Trophy points 1 Activity points 12 Can someone please help me out with this Z transform problem? I have just started with this chapter and got stuck here: Find the Z transform of (n-1)u(n-1)
Can someone please help me out with this Z transform problem? I have just started with this chapter and got stuck here: Find the Z transform of (n-1)u(n-1)
Apr 10, 2022 #2 J jjx Full Member level 3 Joined Sep 12, 2008 Messages 172 Helped 40 Reputation 86 Reaction score 56 Trophy points 1,308 Location Scania Activity points 2,687 The key is to note that it contains a "time"-delayed shift. So if you first find the template x[ n ] = n*u[ n ] from the table of transforms: Z{ x [ n ] } = X(z) = (z^-1) / ( 1 - z^-1)^2 A single time shift equals dividing by z thus Z{ x(n-1) } = X(z) / z Then just fill in the template Z{x(n-1)} = (z^-2) / ( 1 - z^-1)^2 = 1 / ( z - 1 )^2 Upvote 0 Downvote
The key is to note that it contains a "time"-delayed shift. So if you first find the template x[ n ] = n*u[ n ] from the table of transforms: Z{ x [ n ] } = X(z) = (z^-1) / ( 1 - z^-1)^2 A single time shift equals dividing by z thus Z{ x(n-1) } = X(z) / z Then just fill in the template Z{x(n-1)} = (z^-2) / ( 1 - z^-1)^2 = 1 / ( z - 1 )^2