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Example 1
Find the response of the system when all the initial conditions are zero.
Solution − Taking Ztransform on both the sides of the above equation, we get
Taking the inverse Ztransform 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 Ztransform of the above difference equation, we get
This system has a pole at
Hence, taking the inverse Ztransform of the above, we get
Example 3
Determine Y(z),n≥0 in the following case −
Solution − Applying the Ztransform to the above equation, we get
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