Fourier Transform

A linear integral transform that maps a function of time or space into a function of frequency, representing the original as a superposition of sinusoidal components.

An integral transform that maps a function or distribution on one conjugate domain (for example time or space) to a function on the dual frequency domain by integrating against complex exponentials, converting convolution into pointwise multiplication and relating differentiation to polynomial factors in the dual variable.

An integral transform that maps a function or tempered distribution in the time/spatial domain to a complex-valued function of frequency, decomposing the original into sinusoidal (exponential) frequency components.