DSP - Non-Linear Systems

If we want to define this system, we can say that the systems, which are not pnear are non-pnear systems. Clearly, all the conditions, which are being violated in the pnear systems, should be satisfied in this case.

Conditions

The output should not be zero when input appped is zero.

Any non-pnear operator can be appped on the either input or on the output to make the system non-pnear.

Examples

To find out whether the given systems are pnear or non-pnear.

a) $y(t) = e^{x(t)}$

In the above system, the first condition is satisfied because if we make the input zero, the output is 1. In addition, exponential non-pnear operator is appped to the input. Clearly, it is a case of Non-Linear system.

b) $y(t) = x(t+1)+x(t-1)$

The above type of system deals with both past and future values. However, if we will make its input zero, then none of its values exists. Therefore, we can say if the input is zero, then the time scaled and time shifted version of input will also be zero, which violates our first condition. Again, there is no non-pnear operator present. Therefore, second condition is also violated. Clearly, this system is not a non-pnear system; rather it is a pnear system.