Solved Examples of Z-Transform - Notes | Study Digital Signal Processing - Electrical Engineering (EE)

Example 1

Find the response of the system    when all the initial conditions are zero.

Solution − Taking Z-transform on both the sides of the above equation, we get

Taking the inverse Z-transform of the above equation, we get

Example 2

Find the system function H(z) and unit sample response h(n) of the system whose difference equation is described as under

where, y(n) and x(n) are the output and input of the system, respectively.

Solution − Taking the Z-transform of the above difference equation, we get

This system has a pole at 

Hence, taking the inverse Z-transform of the above, we get

Example 3

Determine Y(z),n≥0 in the following case −

Solution − Applying the Z-transform to the above equation, we get