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transforms

The DFT, defined and as a matrix transformation

taught

Taught in

Requires

Required by

Local knowledge map

Local knowledge map

Circular convolution and the discrete convolution theorem Recalling the 1D and multidimensional Fourier transform Circulant matrices are diagonalized by the DFT basis The Fast Fourier Transform: divide-and-conquer an… The Fourier transform in several dimensions, and separability The inverse DFT and conjugate symmetry for real signals The DFT, defined and as a matrix transformation Eigenvalue problems from boundary conditions Every operator on a complex space has an eigenvalue Hyperbolicity: real, distinct eigenvalues Linearity, shifting, scaling, and duality of the Fourier… Multivariable first- and second-order optimality conditions Symmetric matrices and orthogonal diagonalization The "impersonation" framing of aliasing The characteristic polynomial The eigenvalue method -- distinct real eigenvalues The power method for eigenvalues The regular Sturm-Liouville problem Aliasing Eigenvalues and the characteristic equation The Nyquist–Shannon sampling theorem The eigenvector question

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Solid arrows are required prerequisites; dashed are recommended or helpful. Lower rows are more foundational. Click any box to jump to that concept.