Understanding System Stability: BIBO Stability Question Explained

  • Thread starter Thread starter rusty009
  • Start date Start date
  • Tags Tags
    Stability
AI Thread Summary
The discussion focuses on determining the bounded-input bounded-output (BIBO) stability of two functions, y1[n] and y2[n]. It is established that y1[n] = n^2 * x[n] is not stable due to the output being unbounded as n increases. In contrast, y2[n] = x[n]^4 is considered stable because raising a bounded input to the fourth power results in a bounded output. The confusion arises from the assumption that a bounded input raised to any power remains bounded, which is affirmed in the discussion. Understanding these principles is crucial for analyzing system stability effectively.
rusty009
Messages
68
Reaction score
0
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
 
Engineering news on Phys.org
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
 
Thread 'Weird near-field phenomenon I get in my EM simulation'

Thread 'Weird near-field phenomenon I get in my EM simulation'

I recently made a basic simulation of wire antennas and I am not sure if the near field in my simulation is modeled correctly. One of the things that worry me is the fact that sometimes I see in my simulation "movements" in the near field that seems to be faster than the speed of wave propagation I defined (the speed of light in the simulation). Specifically I see "nodes" of low amplitude in the E field that are quickly "emitted" from the antenna and then slow down as they approach the far...
View full post »

Thread 'EMF (Electromagnetic Field) & EHS (Electromagnetic Hyper Sensitivity)'

Hello dear reader, a brief introduction: Some 4 years ago someone started developing health related issues, apparently due to exposure to RF & ELF related frequencies and/or fields (Magnetic). This is currently becoming known as EHS. (Electromagnetic hypersensitivity is a claimed sensitivity to electromagnetic fields, to which adverse symptoms are attributed.) She experiences a deep burning sensation throughout her entire body, leaving her in pain and exhausted after a pulse has occurred...
View full post »

Similar threads

BIBO Stable if and only if impulse response is summable
Replies
2
Views
4K
The apparent stability of a mechanical system: a bike on railroad tracks
Replies
10
Views
2K
LDO voltage regulator stability
Replies
3
Views
2K
Basic Circuit: Why don't these two LEDs light up?
Replies
9
Views
2K
I Kleppner Classical mechanics: Question about stability (p.217)
Replies
2
Views
1K
A Proof of thermodynamic stability condition
Replies
4
Views
3K
Taps for simple IIR Filter in GNU Radio
Replies
1
Views
2K
Electrical Engineering: Is this signal stable?
Replies
7
Views
2K
Comp Sci C++ Reading Data File: Calculating Distances and Finding Closest Point
Replies
14
Views
3K
Can power supplies/adapters be used to clean up dirty generator power?
2
Replies
61
Views
9K

Hot Threads

Recent Insights

Back
Top