# Solved Problems-8

Problems-8

Determine whether the following systems are invertible:

*y*(*t*) =*x*(*t*â€“*n*)*y*(*t*) =*x*(2*t*)

Solution

*y*(*t*) = 10*x*(*t*)

For this system, the inverse system will be,

Therefore, the system is an

*invertible*system.The inverse system would be,

Here, two outputs are possible: =
This implies that there is no unique output for unique input.
Therefore, the system is a

*x*(*t*) or â€“*x*(*t*).*non-invertible*system.Here, the output is the delayed input, by â€˜
Clearly, the system is
These can be another system for which the output is the advanced input by â€˜
The inverse system is,

*n*â€™ samples.*invertible*.*n*â€™ samples.*y*(*t*) =*x*(2*t*)

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
The inverse system is,

*invertible*.