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Solved Problems-8

Problems-8
Determine whether the following systems are invertible:
  1. Description: Description: Description: 2952.png
  2. Description: Description: Description: 2962.png
  3. y(t) = x(t – n)
  4. y(t) = x(2t)
Solution
  1. y(t) = 10x(t)
For this system, the inverse system will be,
 
Description: Description: Description: 3355.png
Description: Description: Description: 1676.png
 
Therefore, the system is an invertible system.
  1. Description: Description: Description: 2857.png
The inverse system would be,
 
Description: Description: Description: 2863.png
 
Here, two outputs are possible: = x(t) or –x(t).
 
This implies that there is no unique output for unique input.
 
Therefore, the system is a non-invertible system.
  1. Description: Description: Description: 2869.png
Here, the output is the delayed input, by ‘n’ samples.
 
Clearly, the system is invertible.
 
These can be another system for which the output is the advanced input by ‘n’ samples.
 
The inverse system is, Description: Description: Description: 2875.png
  1. y(t) = x(2t)
Here, the input is compressed by a factor 2.
 
Hence, there can be another system which will expand the input by the same factor.
 
Hence the system is invertible.
 
The inverse system is,
Description: Description: Description: 3108.png
 




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