Understanding System Stability: BIBO Stability Question Explained

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The discussion focuses on determining the BIBO (Bounded Input, Bounded Output) stability of two discrete-time systems defined by the functions y1[n]=n²*x[n] and y2[n]=x⁴[n]. It is established that y1[n] is unstable due to its output being proportional to n², which is unbounded as n approaches infinity. Conversely, y2[n] is confirmed to be stable because raising a bounded input x[n] to the fourth power results in a bounded output, as demonstrated by the inequality A⁴ < (x[n])⁴ < B⁴.

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rusty009
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Hi,

I am trying to find out if a system is bounded (stable) or not, and I don't understand the process, I basically have these two functions,

y1[n]=n2*x[n]

y2[n]=x4[n]

According to my notes, y1[n] is not stable, as the output is proportional to n2 which is not bounded, I understand this part. My notes also state that y2[n] is stable, this is what I don't understand, you have the input to the power of 4, why is this not-bounded ? Thanks in advance for any help
 
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A bounded quantity raised to the power of 4 would also be bounded. To me it is obvious why.

A < x[n] < B

A4 < (x[n])4 < B4
 

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