1. System with and without Memory
A system is considered as memoryless if its output at a given time is depended on the input at the same time alone . Otherwise , that system has memory . The system specified by equation (1) is memoryless , while the one specified by equation (2) is a system with memory .
2. Causality
A system is causal if the output at any time depends only on the values of the input at the present and the previous time . The system defined by equation (3) is causal , but the system given by equation (4) is not .
For now , we can conclude that all systems without memory are casual.
3.Time Invariance
A system is regarded as time invariant only if the characteristics of the system are fixed all the time . If we conduct a time shift on the input values, the output values are also shifted by the same time units . This is illustrated the following example.
An example of a time invariant system :
if y[n] = a x[n]
then
y [n-n0] = a x[n-n0]
4. Linearity
A system is linear if the input is the weighted sum of several signals , and consequently , the out put is also the weighted sum of the responses of the system to each of those signals .
More specifically , considering the responses of x1(t) and x2(t) are y1(t) and y2(t) respectively, then the system has the linearity when
1) the response to x1(t) + x2(t) is y1(t) + y2(t) ( the additivity property )
2) the response to ax1(t) is ay1(t) ( scaling or homogeneity property )