rfft(a, n=None, axis=-1, norm=None)¶
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).
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 over which to compute the FFT. If not given, the last axis is used.
New in version 1.10.0.
Normalization mode (see
numpy.fft). Default is None.
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
If n is odd, the length is
If axis is larger than the last axis of a.
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.
A = rfft(a) and fs is the sampling frequency,
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;
the largest positive frequency (fs/2*(n-1)/n), and is complex in the
If the input a contains an imaginary part, it is silently discarded.
>>> 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