EasyCalculusca-154

Z-Transform of Geometric Sequence

Problem

The z-transform of x[n] = a^n for n >= 0 is X(z) = sum of a^n * z^(-n) = z / (z - a), converging for |z| > |a|.

Given a and z with z != a, return X(z).

Hint

This is a geometric series in a / z; sum it in closed form.

case 1

in: [0.5,2]

expected: 1.3333333333333333

case 2

in: [0,3]

expected: 1

case 3

in: [2,4]

expected: 2

case 4

in: [0.5,-1]

expected: 0.6666666666666666

Starter codePython

def z_transform_geometric(a, z):
    # Your code here
    pass

4 test cases · run your code against them in the editor