EECS20N: Signals and Systems

Function spaces

 The set of all functions from X to Y is denoted [X → Y]. Such a set is called a function space. Examples:
  • [Time → Pressure] is the set of all sound signals with domain Time and range Pressure.
  • [HorizontalSpace × VerticalSpace → Intensity 3] is the set of all color images of a certain domain and intensity range.
Since function spaces are just sets, we can define functions that have function spaces as their domain, range, or both.