- numpy.fft.rfft(a, n=None, axis=-1)¶
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).
a : array_like
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.
out : complex 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.
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.
When A = rfft(a) and fs is the sampling frequency, A 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.
>>> np.fft.fft([0, 1, 0, 0]) array([ 1.+0.j, 0.-1.j, -1.+0.j, 0.+1.j]) >>> np.fft.rfft([0, 1, 0, 0]) array([ 1.+0.j, 0.-1.j, -1.+0.j])