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

naginterfaces.library.sum.fft_real_1d_rfmt(x)[source]

fft_real_1d_rfmt calculates the discrete Fourier transform of a sequence of real data values (using a work array for extra speed).

For full information please refer to the NAG Library document for c06fa

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/c06/c06faf.html

Parameters
xfloat, array-like, shape

If is declared with bounds in the function from which fft_real_1d_rfmt is called, must contain , for .

Returns
xfloat, ndarray, shape

The discrete Fourier transform stored in Hermitian form. If the components of the transform are written as , and if is declared with bounds in the function from which fft_real_1d_rfmt is called, then for , is contained in , and for , is contained in . (See also the C06 Introduction.)

Raises
NagValueError
(errno )

On entry, .

Constraint: .

Notes

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

Given a sequence of real data values , for , fft_real_1d_rfmt calculates their discrete Fourier transform defined by

(Note the scale factor of in this definition.) The transformed values are complex, but they form a Hermitian sequence (i.e., is the complex conjugate of ), so they are completely determined by real numbers (see also the C06 Introduction).

To compute the inverse discrete Fourier transform defined by

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

fft_real_1d_rfmt uses the fast Fourier transform (FFT) algorithm (see Brigham (1974)).

References

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