fft_hermitian_1d_rfmtcalculates 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
- 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_rfmtis called, then for , is contained in , and for , is contained in . (See also the C06 Introduction.)
- xfloat, ndarray, shape
The components of the discrete Fourier transform . If is declared with bounds in the function from which
fft_hermitian_1d_rfmtis called, is stored in , for .
- (errno )
On entry, .
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_rfmtcalculates 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_rfmtuses the fast Fourier transform (FFT) algorithm (see Brigham (1974)).
Brigham, E O, 1974, The Fast Fourier Transform, Prentice–Hall