# naginterfaces.library.sum.fft_​complex_​1d_​sep¶

naginterfaces.library.sum.fft_complex_1d_sep(x, y)[source]

fft_complex_1d_sep calculates the discrete Fourier transform of a sequence of complex data values (using a work array for extra speed).

For full information please refer to the NAG Library document for c06fc

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/c06/c06fcf.html

Parameters
xfloat, array-like, shape

If is declared with bounds in the function from which fft_complex_1d_sep is called, must contain , the real part of , for .

yfloat, array-like, shape

If is declared with bounds in the function from which fft_complex_1d_sep is called, must contain , the imaginary part of , for .

Returns
xfloat, ndarray, shape

The real parts of the components of the discrete Fourier transform. If is declared with bounds in the function from which fft_complex_1d_sep is called, for , is contained in .

yfloat, ndarray, shape

The imaginary parts of the components of the discrete Fourier transform. If is declared with bounds in the function from which fft_complex_1d_sep is called, then for , is contained in .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

Notes

No equivalent traditional C interface for this routine exists in the NAG Library.

Given a sequence of complex data values , for , fft_complex_1d_sep calculates their discrete Fourier transform defined by

(Note the scale factor of in this definition.)

To compute the inverse discrete Fourier transform defined by

this function should be preceded and followed by the complex conjugation of the data values and the transform (by negating the imaginary parts stored in ).

fft_complex_1d_sep uses the fast Fourier transform (FFT) algorithm (see Brigham (1974)).

References

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