| Line 9: | Line 9: | ||
== Time Invariance check == | == Time Invariance check == | ||
| − | Let us check for y[n] = x[n]^2 | + | Let us check for '''y[n] = x[n]^2''' |
*<math>y[x[n-n0]] = x{[n-n0]^2}</math> | *<math>y[x[n-n0]] = x{[n-n0]^2}</math> | ||
Also, | Also, | ||
*<math>y[n-n0] = x{[n-n0]^2}</math> | *<math>y[n-n0] = x{[n-n0]^2}</math> | ||
| − | Thus the above system is time invariant | + | Thus the above system is '''time invariant''' |
| Line 21: | Line 21: | ||
Let us test for | Let us test for | ||
'''y[n]=cos[nQ]*x[n]''' | '''y[n]=cos[nQ]*x[n]''' | ||
| + | |||
| + | *y[x[n-n0]]=cos[nQ]*x[n-n0] | ||
| + | Also, | ||
| + | *y[n-n0]= cos[n-n0]* x[n-n0] | ||
| + | |||
| + | Thus from above we can say that the system is '''time variant''' | ||
Revision as of 11:09, 12 September 2008
Time invariance
A system is called time invariant if the cascade
x[n]----->Time delay ----> System -----> z[n] yields the same output as x[n]----->system----->Time Delay-----> y[n]
Time Invariance check
Let us check for y[n] = x[n]^2
- $ y[x[n-n0]] = x{[n-n0]^2} $
Also,
- $ y[n-n0] = x{[n-n0]^2} $
Thus the above system is time invariant
Time Variance check
Let us test for
y[n]=cos[nQ]*x[n]
- y[x[n-n0]]=cos[nQ]*x[n-n0]
Also,
- y[n-n0]= cos[n-n0]* x[n-n0]
Thus from above we can say that the system is time variant
