Discrete fourier transform

Abstract

In linear algebra, basis vectors span the entire vector space. And any vector of the vector space can be written as the linear combination of the basis vectors. For any vector in vector space, finding the coefficients of basis vectors used for the construction of the vector can be considered as a transformation. Fourier series are used to represent periodic signals. Fourier series are used to construct any periodic signal from sinusoidal signals. The sinusoidal signals can be considered as the basis signals, and linear combination of these signals with complex coefficients produce any periodic signal.