Understanding System Stability: BIBO Stability Question Explained

[rusty009]

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

 

[MisterX]

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