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the cascade | the cascade | ||
| − | x[n]----->Time delay ----> System -----> z[n] | + | *x[n]----->Time delay ----> System -----> z[n] |
| − | + | yields the same output as | |
| − | x[n]----->system----->Time Delay-----> y[n] | + | *x[n]----->system----->Time Delay-----> y[n] |
| + | |||
| + | |||
| + | == Time Invariance check == | ||
| + | Let us check for '''y[n] = x[n]^2''' | ||
| + | |||
| + | *<math>y[x[n-n0]] = x{[n-n0]^2}</math> | ||
| + | Also, | ||
| + | *<math>y[n-n0] = x{[n-n0]^2}</math> | ||
| + | Thus the above system is '''time invariant''' | ||
| + | |||
| + | |||
| + | == Time Variance check == | ||
| + | |||
| + | Let us test for | ||
| + | '''y[n]=cos[nQ]*x[n]''' | ||
| + | |||
| + | *<math>y[x[n-n0]]=cos[nQ]*x[n-n0]</math> | ||
| + | Also, | ||
| + | *<math>y[n-n0]= cos[n-n0]Q* x[n-n0]</math> | ||
| + | |||
| + | Thus from above we can say that the system is '''time variant''' | ||
Latest revision as of 10:11, 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]Q* x[n-n0] $
Thus from above we can say that the system is time variant
