A system is characterized by how it responds to input signals. In general, a system has one or more input signals and one or more output signals. Therefore, one natural characterization of systems is by how many inputs and outputs they have:

- SISO (Single Input, Single Output)
- SIMO (Single Output, Multiple Outputs)
- MISO (Multiple Inputs, Single Output)
- MIMO (Multiple Inputs, Multiple Outputs)

Signals can be continuous or discrete in time, as well as continuous or discrete in the values they take at any given time:

- Signals that are continuous in time and continuous in value are known as analog signals.
- Signals that are discrete in time and discrete in value are known as digital signals.
- Signals that are discrete in time and continuous in value are called discrete-time signals. While important mathematically, systems that process discrete time signals are difficult to physically realize. The methods developed for analyzing discrete time signals and systems are usually applied to digital signals and systems.

- A system that has analog input and analog output is known as an analog system.
- A system that has digital input and digital output is known as a digital system.
- Systems with analog input and digital output or digital input and analog output are possible. However, it is usually easiest to break these systems up for analysis into their analog and digital parts, as well as an analog to digital or digital to analog converter.

- Memoryless systems do not depend on any past input.
- Systems with memory do depend on past input.
- Causal systems do not depend on any future input.
- Non-causal systems do depend on future input. Note: It is not possible to physically realize a non-causal system. However, from the standpoint of analysis, they are important for two reasons. First, the ideal system for a given application is often a noncausal system, which although not physically possible can give insight into the design of a causal system to accomplish a similar purpose. Second, there are instances when a system does not operate in "real time" but is rather simulated "off-line" by a computer.

- A system is linear if it obeys the following relation: For any input signals x
_{1}and x_{2}and their corresponding output signals y_{1}and y_{2}, and any real constants α and β, the output corresponding to αx_{1}+ βx_{2}is αy_{1}+ βy_{2}. In other words, adding two input signals together adds their outputs and multiplying an input signal by a constant multiplies the output by the same constant. - A system that is not linear is non-linear.
- If the output of a system does not depend explicitly on time, the system is said to be time-invariant. This may be expressed mathematically as follows: If the input signal x(t) produces an output y(t), then x(t + a) produces the output y(t + a).
- Any system for which the above relation does not hold is said to be time-varying.
- A system that will always produce the same output for a given input is said to be deterministic.
- A system that will produce different outputs for a given input is said to be stochastic.

Some important concepts in system analysis are the transfer function, feedback and stability, frequency response, steady-state and transient behavior, filters, and noise.