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== Part a == | == Part a == | ||
| − | <font size="3">System: <math>X_{k}[n-k] \to Y_{k}[n] = (k+1)^2 \delta [n-(k+1)]</math> | + | <font size="3">System: <math>X_{k}[n]=\delta[n-k] \to Y_{k}[n] = (k+1)^2 \delta [n-(k+1)]</math> |
| − | Time-delay: <math>X_{k}[n-k] \to X_{k}[n-N-k]</math> | + | Time-delay: <math>X_{k}[n]=\delta[n-k] \to X_{k}[n-N]=\delta[n-N-k]</math> |
Revision as of 11:29, 11 September 2008
Part a
System: $ X_{k}[n]=\delta[n-k] \to Y_{k}[n] = (k+1)^2 \delta [n-(k+1)] $
Time-delay: $ X_{k}[n]=\delta[n-k] \to X_{k}[n-N]=\delta[n-N-k] $
$ X_{k}[n] \to timedelay \to sys \to Z_{k}[n]=(k+1)^2 \delta [n-N-(k+1)] $
$ X_{k}[n] \to sys \to timedelay \to Z_{k}[n]=(k+1)^2 \delta [n-N-(k+1)] $
Since $ (k+1)^2 \delta [n-N-(k+1)] $ is equal to $ (k+1)^2 \delta [n-N-(k+1)] $, the system is time-invariant.
