Signals in Natural Domain
Chapter 3 :  Discrete-Time Systems
 
Invertibility:
A system is said to be invertible if the input signal {x[n]} can be recovered from the output signal {yk[n]}. For this to be true two different input signals should produce two different outputs. If some different input signal produce same output signal then by processing output we can not say which input produced the output.
Example of an invertible system is                   $\displaystyle y[n]=\sum\limits_{k=- \infty}^{n}x[k]$

then                                                                $\displaystyle x[n]=y[n]-y[n-1]$
Example if a non-invertible system is                      $\displaystyle y[n]=0$
That is the system produces an all zero sequence for any input sequence. Since every input sequence gives all zero sequence, we can not find out which input produced the output.
The system which produces the sequence {x[n]} from sequence {yk[n]} is called the inverse system. In communication system, decoder is an inverse of the encoder.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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