This book examines applications of Fourier analysis on finite non-Abelian groups, and discusses different methods to determine compact representations for discrete functions providing for their efficient realizations and related applications. Switching functions are included as a particular example of discrete functions in engineering practice. Consideration is given to the polynomial expressions and decision diagrams defined in terms of Fourier transform on finite non-Abelain groups. The book demonstrates how transferring a problem from its original form into the spectral domain may provide major advantages, such as simplifying numerical calculation tasks.