numpy.fft.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).
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,
A contains the zero-frequency term 0*fs, which is real due to Hermitian symmetry.
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]) # may vary >>> np.fft.rfft([0, 1, 0, 0]) array([ 1.+0.j, 0.-1.j, -1.+0.j]) # may vary
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