Orthogonal functions are a set of functions that are perpendicular to each other in a specific mathematical sense. This means that when you take the inner product (or integral) of any two different functions in the set, the result is zero. This property is similar to how perpendicular lines in geometry do not intersect. In many applications, such as in signal processing and quantum mechanics, orthogonal functions are useful because they can represent complex signals or states without interference. Common examples include sine and cosine functions, which form the basis of Fourier series, allowing for the analysis of periodic functions.