numpy.fft.rfft#
- fft.rfft(a, n=None, axis=- 1, norm=None)[source]#
Compute the one-dimensional discrete Fourier Transform for real input.
This function computes the one-dimensional n-point discrete Fourier Transform (DFT) of a real-valued array by means of an efficient algorithm called the Fast Fourier Transform (FFT).
- Parameters
- aarray_like
Input array
- nint, 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.
- axisint, optional
Axis over which to compute the FFT. If not given, the last axis is used.
- norm{“backward”, “ortho”, “forward”}, optional
New in version 1.10.0.
Normalization mode (see
numpy.fft
). Default is “backward”. Indicates which direction of the forward/backward pair of transforms is scaled and with what normalization factor.New in version 1.20.0: The “backward”, “forward” values were added.
- Returns
- outcomplex ndarray
The truncated or zero-padded 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 not a valid axis of a.
See also
Notes
When the DFT is computed for purely real input, the output is Hermitian-symmetric, i.e. the negative frequency terms are just the complex conjugates of the corresponding positive-frequency terms, and the negative-frequency 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 zero-frequency 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*(n-1)/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 non-negative frequency terms.