orthogonal functions

Orthogonal functions are a set of functions that, when integrated together over a specific interval, produce zero unless they are the same function. Think of them as "perpendicular" in a math sense—like crossed lines at right angles—meaning they don't "overlap" in their behavior. This property allows them to be used as building blocks to represent complex functions, much like how different musical notes combine to create melodies without interfering with each other. In mathematics and engineering, orthogonal functions help simplify analysis and solve problems involving signals, data, or waves.