- #1
Bipolarity
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Not sure if this is the right subforum.
This is technically a signal processing question, but it edges on proving whether a certain mapping is linear or non-linear, so I thought I'd post it here.
Say a digital system is defined in the following way:
## y[n] = 5*y[n-2] ##
How might I prove that this system is linear?
In algebra, one usually proves it by showing that:
## L(x[n]+c*z[n]) = L(x[n]) + c*L(z[n]) ##
The problem here is that since the system is defined recursively, there are no input functions x, or rather the input to the system is the output. So how might this work?
Also, similarly, how might I prove time-invariance (I'm not sure if this system is even time-invariant by the way, but I think it is!).
Thanks!
BiP
This is technically a signal processing question, but it edges on proving whether a certain mapping is linear or non-linear, so I thought I'd post it here.
Say a digital system is defined in the following way:
## y[n] = 5*y[n-2] ##
How might I prove that this system is linear?
In algebra, one usually proves it by showing that:
## L(x[n]+c*z[n]) = L(x[n]) + c*L(z[n]) ##
The problem here is that since the system is defined recursively, there are no input functions x, or rather the input to the system is the output. So how might this work?
Also, similarly, how might I prove time-invariance (I'm not sure if this system is even time-invariant by the way, but I think it is!).
Thanks!
BiP