Systems

In electrical engineering, a system is a transform that maps an input signal to another signal (an output signal). We say that if $x$ is the input signal, $y$ is the output signal, and $T$ is the transform that describes the system, then:

$$y=T\{x\}$$

The value of the signal at a particular time is given by $y(t)$. We can broadly divide systems into those that are linear and non-linear, and time-invariant and time-varying systems. Linear time-invariant (LTI) systems are pretty important, because many systems are LTI.

Continuous-time systems often model physical phenomena. Discrete-time systems follow the theory of CT systems closely. They are the result of engineering processes: like the discretisation of CT systems, digital signal processing, or financial/economic models.

Basic theory

We can define CT/DT systems with a pointwise definition, i.e., we give a formula for $y(t)$ in terms of all input signal values — this gets us an explicit formula for the output.

DT systems can often also be described in terms of a recursive expression. We can still sometimes express it in a pointwise manner but

Systems may have the following properties:

• Linearity
• Time invariance
• Causality
  • Memorylessness
• Invertibility (not sure if systems are considered maps)
• Stability

Systems design

Systems can be interconnected to create larger systems. Common interconnections include series, parallel, and feedback configurations.

We may be able to design some sub-systems, but not all — but we must understand those that we don’t design to make good decisions, i.e., what frequency may be best to transmit. Broadly systems can be achieved in a few ways, principal of which are circuits (analogue or digital).

Courses

• ECE216 — Signals and Systems
• ECE311 — Introduction to Control Systems

See also

• Similarly-named concepts
  • Systems software