# naginterfaces.library.sum.fft_​real_​2d¶

naginterfaces.library.sum.fft_real_2d(m, n, x)[source]

fft_real_2d computes the two-dimensional discrete Fourier transform of a bivariate sequence of real data values.

For full information please refer to the NAG Library document for c06pv

https://support.nag.com/numeric/nl/nagdoc_30.1/flhtml/c06/c06pvf.html

Parameters
mint

, the first dimension of the transform.

nint

, the second dimension of the transform.

xfloat, array-like, shape

The real input dataset , where is stored in , for , for .

Returns
ycomplex, ndarray, shape

The complex output dataset , where is stored in , for , for . Note the first dimension is cut roughly by half to remove the redundant information due to conjugate symmetry.

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

Notes

fft_real_2d computes the two-dimensional discrete Fourier transform of a bivariate sequence of real data values , for , for .

The discrete Fourier transform is here defined by

where and . (Note the scale factor of in this definition.)

The transformed values are complex. Because of conjugate symmetry (i.e., is the complex conjugate of ), only slightly more than half of the Fourier coefficients need to be stored in the output.

A call of fft_real_2d followed by a call of fft_hermitian_2d() will restore the original data.

This function calls fft_realherm_1d_multi_col() and fft_complex_1d_multi_row() to perform multiple one-dimensional discrete Fourier transforms by the fast Fourier transform (FFT) algorithm in Brigham (1974) and Temperton (1983).

References

Brigham, E O, 1974, The Fast Fourier Transform, Prentice–Hall

Temperton, C, 1983, Fast mixed-radix real Fourier transforms, J. Comput. Phys. (52), 340–350