numpy.fft.rfft¶

numpy.fft.
rfft
(a, n=None, axis=1, norm=None)[source]¶ Compute the onedimensional discrete Fourier Transform for real input.
This function computes the onedimensional npoint discrete Fourier Transform (DFT) of a realvalued array by means of an efficient algorithm called the Fast Fourier Transform (FFT).
Parameters:  a : array_like
Input array
 n : int, optional
Number of points along transformation axis in the input to use. If n is smaller than the length of the input, the input is cropped. If it is larger, the input is padded with zeros. If n is not given, the length of the input along the axis specified by axis is used.
 axis : int, optional
Axis over which to compute the FFT. If not given, the last axis is used.
 norm : {None, “ortho”}, optional
New in version 1.10.0.
Normalization mode (see
numpy.fft
). Default is None.
Returns:  out : complex ndarray
The truncated or zeropadded input, transformed along the axis indicated by axis, or the last one if axis is not specified. If n is even, the length of the transformed axis is
(n/2)+1
. If n is odd, the length is(n+1)/2
.
Raises:  IndexError
If axis is larger than the last axis of a.
See also
Notes
When the DFT is computed for purely real input, the output is Hermitiansymmetric, i.e. the negative frequency terms are just the complex conjugates of the corresponding positivefrequency terms, and the negativefrequency terms are therefore redundant. This function does not compute the negative frequency terms, and the length of the transformed axis of the output is therefore
n//2 + 1
.When
A = rfft(a)
and fs is the sampling frequency,A[0]
contains the zerofrequency term 0*fs, which is real due to Hermitian symmetry.If n is even,
A[1]
contains the term representing both positive and negative Nyquist frequency (+fs/2 and fs/2), and must also be purely real. If n is odd, there is no term at fs/2;A[1]
contains the largest positive frequency (fs/2*(n1)/n), and is complex in the general case.If the input a contains an imaginary part, it is silently discarded.
Examples
>>> np.fft.fft([0, 1, 0, 0]) array([ 1.+0.j, 0.1.j, 1.+0.j, 0.+1.j]) # may vary >>> np.fft.rfft([0, 1, 0, 0]) array([ 1.+0.j, 0.1.j, 1.+0.j]) # may vary
Notice how the final element of the
fft
output is the complex conjugate of the second element, for real input. Forrfft
, this symmetry is exploited to compute only the nonnegative frequency terms.