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

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Example 1

Find the response of the system  Solved Examples of Z-Transform - Notes | Study Digital Signal Processing - Electrical Engineering (EE)  when all the initial conditions are zero.

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

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

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

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

Example 2

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

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

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

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

This system has a pole at  Solved Examples of Z-Transform - Notes | Study Digital Signal Processing - Electrical Engineering (EE)

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

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

Example 3

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

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

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

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

The document Solved Examples of Z-Transform - Notes | Study Digital Signal Processing - Electrical Engineering (EE) is a part of the Electrical Engineering (EE) Course Digital Signal Processing.
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