Signals defined only at discrete instants of time
If the samples are uniformly distributed, we further simplify this notation to
Discrete signals naturally occur in scenarios where the input is inherently discrete. They can also result from sampling continuous-time signals. For example, in digital filtering, a continuous signal
Discrete System Representation
Instead of differential equations, we can use difference equations to represent a discrete system. For example,
An alternative is a block diagram like the following:
Difference equations are mathematically precise and concise. However, since difference equation is declarative, it does not show the signal flow path. On the other hand, the block diagram is imperative, and can directly translate into a hardware implementation or an algorithm. 2
Another alternative representation that combines the strength of difference equations and block diagrams are the operator notation. For example, let
Footnotes
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Linear Systems and Signals, 3rd Edition, 1.7.5 ↩
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Lecture 2: Discrete-time systems | Signals and Systems | MIT OpenCourseWare ↩