| Line 10: | Line 10: | ||
== Question 6a == | == Question 6a == | ||
| + | <math>x[n] \rightarrow \mbox{Time Delay} \rightarrow y[n]=x[n-n_0] \rightarrow System \rightarrow Y_k[n-n_0]=(k+1)^2 \delta [n-n_0-(k+1)]</math> | ||
| + | |||
| + | <math>x[n] \rightarrow System \rightarrow Y_k[n]=(k+1)^2 \delta [n-(k+1)] \rightarrow \mbox{Time Delay}\rightarrow Y_k[n-n_0]=(k+1)^2 \delta [n-n_0-(k+1)]</math> | ||
| + | |||
| + | So the system is time invariant. | ||
== Question 6b == | == Question 6b == | ||
Revision as of 15:27, 11 September 2008
System
Input: $ X_k[n]=\delta [n-k] $
Output: $ Y_k[n]=(k+1)^2 \delta [n-(k+1)] $
For any non-negative integer k
Question 6a
$ x[n] \rightarrow \mbox{Time Delay} \rightarrow y[n]=x[n-n_0] \rightarrow System \rightarrow Y_k[n-n_0]=(k+1)^2 \delta [n-n_0-(k+1)] $
$ x[n] \rightarrow System \rightarrow Y_k[n]=(k+1)^2 \delta [n-(k+1)] \rightarrow \mbox{Time Delay}\rightarrow Y_k[n-n_0]=(k+1)^2 \delta [n-n_0-(k+1)] $
So the system is time invariant.
