Learning Boolean Functions via the Fourier Transform

The importance of using the “right” representation of a function in order to “approximate” it has been widely recognized. The Fourier Transform representation of a function is a classic representation which is widely used to approximate real functions (i.e. functions whose inputs are real numbers). However, the Fourier Transform representation for functions whose inputs are boolean has been far less studied. On the other hand it seems that the Fourier Transform representation can be used to learn many classes of boolean functions.