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Solved Problems-5

Problems-5
Consider a discrete-time system whose output y[n] is the average of the three most recent values of the input signal, x[n], given as,
 
Description: Description: Description: 3063.png
 
Show that the system is BIBO stable.
Solution
Let us assume that, Description: Description: Description: 3059.png for all n,
 
Description: Description: Description: 3055.png
 
Hence, the absolute value of the output signal y[n] is always less than the maximum absolute value of the input signal x[n] for all n; which shows that the system is stable.
 




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