fft_real_1d_rfmtcalculates 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
- xfloat, array-like, shape
If is declared with bounds in the function from which
fft_real_1d_rfmtis called, must contain , for .
- 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_rfmtis called, then for , is contained in , and for , is contained in . (See also the C06 Introduction.)
- (errno )
On entry, .
No equivalent traditional C interface for this routine exists in the NAG Library.
Given a sequence of real data values , for ,
fft_real_1d_rfmtcalculates 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_rfmtuses the fast Fourier transform (FFT) algorithm (see Brigham (1974)).
Brigham, E O, 1974, The Fast Fourier Transform, Prentice–Hall