Replaces the columns of a dense complex matrix with their discrete Fourier transforms: if X has n rows,
![n∑-1 √--
X [k,:] := e-2πjk -1∕nX[j,:], k = 0,...,n - 1.
j=0](cvxopt94x.png)
dft(X)
Replaces the columns of a dense complex matrix with their discrete Fourier transforms: if X has n rows,
idft(X)
Replaces the columns of a dense complex matrix with their inverse discrete Fourier transforms: if X has n rows,
![n∑-1 √--
X [k,:] := 1 e2πjk -1∕nX [j,:], k = 0,...,n - 1.
n j=0](cvxopt95x.png)
The module also includes a discrete N-dimensional Fourier transform. The input matrix is interpreted as an N-dimensional matrix stored in column-major order. The discrete N-dimensional Fourier transform computes the corresponding one-dimensional transform along each dimension. For example, the two-dimensional transform applies a one-dimensional transform to all the columns of the matrix, followed by a one-dimensional transform to all the rows of the matrix.
dftn(X[, dims=X.size])
Replaces a dense complex matrix with its N-dimensional discrete Fourier transform. The dimensions of the N-dimensional matrix are given by the N-tuple dim. The two-dimensional transform is computed as dftn(X, X.size).
idftn(X[, dims=X.size])
Replaces a dense complex N-dimensional matrix with its inverse N-dimensional discrete Fourier transform. The dimensions of the matrix are given by the tuple dim. The two-dimensional inverse transform is computed as idftn(X, X.size).