The DFT as a change of basis

Related lectures (30)

Page 2 of 3

Covers mathematical concepts from number theory to probability and statistics.

Covers scalar products, orthogonal vectors, norms, and projections in vector spaces, emphasizing orthonormal families of vectors.

Explores the history and efficiency of the fast Fourier transform algorithm, demonstrating its practical applications and computational advantages.

Covers Fourier series, analysis, the heat equation, Gibbs phenomenon, and Fourier transform properties.

Explores Fourier series, DFT, FFT, and their applications in signal processing and spectroscopy.

Covers Dirac's notation in linear algebra and the tensor product concept in Hilbert spaces.

Explores frequency periodicity in the discrete Fourier transform for signal reconstruction.

Explains the practical use of the Discrete Fourier Transform (DFT) for digital signal processing.

Explains the Fast Fourier Transform, a fast algorithm for calculating the Discrete Fourier Transform.

Covers the main properties of the Discrete Fourier Transform and convolution methods.