BM661 - Module 1: Introduction to Signals and Systems

Lecture 1B

Systems

Any process or set of processes that can affect a signal may be called a system. A system can have one or more inputs and generate one or more outputs. We shall consider simple systems that accept one input and produce one output.

Properties of systems

• Memory: Any system whose present output depends on present and past inputs is said to have memory. Most systems have some form of memory.
• Causality: A system whose present output depends only on present and/or past inputs and does not depend on future inputs is said to be causal. All real-world physical systems are causal. Non-causal or acausal systems exist not only in theory but can also be simulated by shifting the time reference.
• Invertibility: Consider a system that given an input, x(t), produces an output y(t). If this system is invertible then an inverse system can be devised that will take y(t) as its input and produce x(t) as its output.
• Stability: A system is said to be stable if for any finite input the output is always finite.
• Time-Invariance: A system whose properties and behaviour do not change over time is said to be time-invariant.
• Linearity: A system is linear if it has the following two properties:
  • Additivity: If an input, x₁(t), produces an output y₁(t) and an input x₂(t) produces an output y₂(t), then for an input x₁(t)+x₂(t) if the output is y₁(t)+y₂(t) the system is said to have the property of additivity.
  • Scaling: Consider a system that given an input, x(t), produces an output y(t). When the input is scaled by any factor K and given to the system, if the output is scaled by the same factor K, the system is said to have the property of scaling.

Examples of Systems

The following interactive example gives a few systems that operate on time signals. Use it and see which properties are present in each.

Look particularly for these: