Properties of systems
In early parts of this course, we shall concern ourselves with mainly the first two classes, viz. Continuous-time and Discrete-time systems, but later we shall also deal with Hybrid systems as well. So, we find it worthwhile here to take a look at what properties the systems of various classes can have:
|
Property |
Continuous input - Continuous output |
Discrete input- Discrete output |
Continuous- Discrete input/ Discrete- Continuous output |
|
Memory |
Yes
If input and output are of the same type |
Yes
If input and output are of the same type |
No
However, we can define a restricted version of memory if there is a correspondence in the input and output variables (e.g.: continuous and discrete time) |
|
Causality |
Yes
If input and output are of the same type |
Yes
If input and output are of the same type |
No
A restricted version of causality can be defined: “If the inputs are same upto an instant corresponding to a discrete variable, then the outputs of a causal system are same |
|
Shift invariance (Time invariance) |
Yes
If input and output are of the same type |
Yes
If input and output are of the same type |
No
We can define shift invariance in cases where the inputs are shifted by certain quanta corresponding to the spacing in discrete variables. |
|
Stability |
Yes |
Yes |
Yes |
|
Linearity |
Yes |
Yes |
Yes |
Note that this is a table of properties which the system can have; they are not necessary properties of a system. Hence, we can find a Continuous-time system that is stable (though there may be Continuous-time systems which are unstable), but it is impossible to apply the concept of memory to a discrete-continuous system without modifying the concept itself.
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