Fourier analysis

Fourier series, the fast Fourier transform and fast convolution, the Hilbert transform and the discrete cosine transform.

Gibbs’s phenomenon (1899)

Gibbs's phenomenon (1899)

Cooley and Tukey’s fast Fourier transform (1965)

Cooley and Tukey's fast Fourier transform (1965)

Hilbert’s conjugate functions and the analytic signal (1905)

Hilbert's conjugate functions and the analytic signal (1905)

Stockham’s high-speed convolution (1966)

Stockham's high-speed convolution (1966)

Ahmed, Natarajan and Rao’s discrete cosine transform (1974)

Ahmed, Natarajan and Rao's discrete cosine transform (1974)