ifft#
- scipy.fft.ifft(x, n=None, axis=-1, norm=None, overwrite_x=False, workers=None, *, plan=None)[source]#
Compute the 1-D inverse discrete Fourier Transform.
This function computes the inverse of the 1-D n-point discrete Fourier transform computed by
fft
. In other words,ifft(fft(x)) == x
to within numerical accuracy.The input should be ordered in the same way as is returned by
fft
, i.e.,x[0]
should contain the zero frequency term,x[1:n//2]
should contain the positive-frequency terms,x[n//2 + 1:]
should contain the negative-frequency terms, in increasing order starting from the most negative frequency.
For an even number of input points,
x[n//2]
represents the sum of the values at the positive and negative Nyquist frequencies, as the two are aliased together. Seefft
for details.- Parameters:
- xarray_like
Input array, can be complex.
- nint, optional
Length of the transformed axis of the output. 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. See notes about padding issues.
- axisint, optional
Axis over which to compute the inverse DFT. If not given, the last axis is used.
- norm{“backward”, “ortho”, “forward”}, optional
Normalization mode (see
fft
). Default is “backward”.- overwrite_xbool, optional
If True, the contents of x can be destroyed; the default is False. See
fft
for more details.- workersint, optional
Maximum number of workers to use for parallel computation. If negative, the value wraps around from
os.cpu_count()
. Seefft
for more details.- planobject, optional
This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.
Added in version 1.5.0.
- 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.
- Raises:
- IndexError
If axes is larger than the last axis of x.
See also
Notes
If the input parameter n is larger than the size of the input, the input is padded by appending zeros at the end. Even though this is the common approach, it might lead to surprising results. If a different padding is desired, it must be performed before calling
ifft
.If
x
is a 1-D array, then theifft
is equivalent toy[k] = np.sum(x * np.exp(2j * np.pi * k * np.arange(n)/n)) / len(x)
As with
fft
,ifft
has support for all floating point types and is optimized for real input.Examples
>>> import scipy.fft >>> import numpy as np >>> scipy.fft.ifft([0, 4, 0, 0]) array([ 1.+0.j, 0.+1.j, -1.+0.j, 0.-1.j]) # may vary
Create and plot a band-limited signal with random phases:
>>> import matplotlib.pyplot as plt >>> rng = np.random.default_rng() >>> t = np.arange(400) >>> n = np.zeros((400,), dtype=complex) >>> n[40:60] = np.exp(1j*rng.uniform(0, 2*np.pi, (20,))) >>> s = scipy.fft.ifft(n) >>> plt.plot(t, s.real, 'b-', t, s.imag, 'r--') [<matplotlib.lines.Line2D object at ...>, <matplotlib.lines.Line2D object at ...>] >>> plt.legend(('real', 'imaginary')) <matplotlib.legend.Legend object at ...> >>> plt.show()