This function computes the 1-D 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
.
When X = rfft(x)
and fs is the sampling frequency, X[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.
Input array
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 :None:None:`axis` is used.
Axis over which to compute the FFT. If not given, the last axis is used.
Normalization mode (see fft
). Default is "backward".
If True, the contents of x can be destroyed; the default is False. See fft
for more details.
Maximum number of workers to use for parallel computation. If negative, the value wraps around from os.cpu_count()
. See ~scipy.fft.fft
for more details.
This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.
If :None:None:`axis` is larger than the last axis of a.
The truncated or zero-padded input, transformed along the axis indicated by :None:None:`axis`, or the last one if :None:None:`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
.
Compute the 1-D discrete Fourier Transform for real input.
fft
The 1-D FFT of general (complex) input.
fftn
The N-D FFT.
irfft
The inverse of :None:None:`rfft`.
rfft2
The 2-D FFT of real input.
rfftn
The N-D FFT of real input.
>>> import scipy.fft
... scipy.fft.fft([0, 1, 0, 0]) array([ 1.+0.j, 0.-1.j, -1.+0.j, 0.+1.j]) # may vary
>>> scipy.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. For rfft
, this symmetry is exploited to compute only the non-negative frequency terms.
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.fft._basic.hfft
scipy.fft._basic.irfft
scipy.fft._basic.hfftn
scipy.fft._basic.ihfft
scipy.fft._basic.irfftn
scipy.fft._helper.next_fast_len
scipy.fft._basic.rfftn
scipy.fft._basic.fft
scipy.fft._basic.rfft
scipy.fft._basic.ihfftn
scipy.fft._basic.rfft2
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