(New page: ==Linearity and Time Invariance== For the system Xk[n]=d[n-k] The output is defined as Yk[n]=(k+1)2 d[n-(k+1)] a) Time Invariance This system is not time invariant because it is depe...) |
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This system is not time invariant because it is dependent on the time shift <math>k</math>. If the time is shifted before being put through the system, there will be a different output than if it is put through the system and then time shifted. | This system is not time invariant because it is dependent on the time shift <math>k</math>. If the time is shifted before being put through the system, there will be a different output than if it is put through the system and then time shifted. | ||
| − | b) Looking at the examples on Mimi's homework page[[http://cobweb.ecn.purdue.edu/~mboutin/ECE301/Index.html]], the x[n] to produce the output Y[n]=u[n-1] would be u[n]. | + | b) Linearity |
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| + | Looking at the examples on Mimi's homework page[[http://cobweb.ecn.purdue.edu/~mboutin/ECE301/Index.html]], the x[n] to produce the output Y[n]=u[n-1] would be u[n]. | ||
Latest revision as of 16:29, 12 September 2008
Linearity and Time Invariance
For the system
Xk[n]=d[n-k]
The output is defined as
Yk[n]=(k+1)2 d[n-(k+1)]
a) Time Invariance
This system is not time invariant because it is dependent on the time shift $ k $. If the time is shifted before being put through the system, there will be a different output than if it is put through the system and then time shifted.
b) Linearity
Looking at the examples on Mimi's homework page[[1]], the x[n] to produce the output Y[n]=u[n-1] would be u[n].
