Discrete Fourier Transform Matrix
Compute the discrete Fourier transform matrix
dftmtx(n)
n |
Size of Fourier transformation matrix, specified as a positive integer. |
A discrete Fourier transform matrix is a complex matrix whose matrix product
with a vector computes the discrete Fourier transform of the vector.
dftmtx takes the FFT of the identity matrix to generate the transform
matrix. For a column vector x, y <- dftmtx(n) * x is the same
as y <- fft(x, postpad(x, n). The inverse discrete Fourier transform
matrix is inv <- Conj(dftmtx(n)) / n.
In general this is less efficient than calling the fft and ifft
functions directly.
Fourier transform matrix.
David Bateman, adb014@gmail.com.
Conversion to R by Geert
van Boxtel, G.J.M.vanBoxtel@gmail.com.
x <- seq_len(256) y1 <- stats::fft(x) n <- length(x) y2 <- drop(x %*% dftmtx(n)) mx <- max(abs(y1 - y2))
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