What is the right way to calculate the inverse Z-transform of $zX(z^{-1})$

1. How do you find Z-transform and inverse Z-transform?
2. What is the inverse Z-transform of 1 z?
3. How do you find the inverse Z-transform in Matlab?

How do you find Z-transform and inverse Z-transform?

Long Division Method

X(z)=x(0)+x(1)Z−1+x(2)Z−2+......... The above sequence represents the series of inverse Z-transform of the given signal forn≥0 and the above system is causal. However for n<0 the series can be written as; x(z)=x(−1)Z1+x(−2)Z2+x(−3)Z3+.........

What is the inverse Z-transform of 1 z?

The Z-transform of a sequence an is defined as A(z)=∑∞n=−∞anz−n. In your case, A(z)=1/z=z−1, so this must mean an=0 for all n≠1, and a1=1. We don't need any fancy computations in this example, we just read off the one nonzero coefficient directly from A.

How do you find the inverse Z-transform in Matlab?

iztrans( F ) returns the Inverse Z-Transform of F . By default, the independent variable is z and the transformation variable is n . If F does not contain z , iztrans uses the function symvar . iztrans( F , transVar ) uses the transformation variable transVar instead of n .