naginterfaces.library.sum.fft_​hermitian_​1d_​rfmt

naginterfaces.library.sum.fft_hermitian_1d_rfmt(x)[source]

fft_hermitian_1d_rfmt calculates the discrete Fourier transform of a Hermitian sequence of complex data values (using a work array for extra speed).

For full information please refer to the NAG Library document for c06fb

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/c06/c06fbf.html

Parameters
xfloat, array-like, shape

The sequence to be transformed stored in Hermitian form. If the data values are written as , and if is declared with bounds in the function from which fft_hermitian_1d_rfmt is called, then for , is contained in , and for , is contained in . (See also the C06 Introduction.)

Returns
xfloat, ndarray, shape

The components of the discrete Fourier transform . If is declared with bounds in the function from which fft_hermitian_1d_rfmt is called, is stored in , for .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

Notes

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

Given a Hermitian sequence of complex data values (i.e., a sequence such that is real and is the complex conjugate of , for ), fft_hermitian_1d_rfmt calculates their discrete Fourier transform defined by

(Note the scale factor of in this definition.) The transformed values are purely real (see also the C06 Introduction).

To compute the inverse discrete Fourier transform defined by

this function should be preceded by forming the complex conjugates of the ; that is, , for .

fft_hermitian_1d_rfmt uses the fast Fourier transform (FFT) algorithm (see Brigham (1974)).

References

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