# maxframe.tensor.fft.ifft

### maxframe.tensor.fft.ifft(a, n=None, axis=-1, norm=None)

Compute the one-dimensional inverse discrete Fourier Transform.

This function computes the inverse of the one-dimensional *n*-point
discrete Fourier transform computed by fft.  In other words,
`ifft(fft(a)) == a` to within numerical accuracy.
For a general description of the algorithm and definitions,
see mt.fft.

The input should be ordered in the same way as is returned by fft,
i.e.,

* `a[0]` should contain the zero frequency term,
* `a[1:n//2]` should contain the positive-frequency terms,
* `a[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, `A[n//2]` represents the sum of
the values at the positive and negative Nyquist frequencies, as the two
are aliased together. See numpy.fft for details.

* **Parameters:**
  * **a** (*array_like*) – Input tensor, can be complex.
  * **n** ([*int*](https://docs.python.org/3/library/functions.html#int) *,* *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.
  * **axis** ([*int*](https://docs.python.org/3/library/functions.html#int) *,* *optional*) – Axis over which to compute the inverse DFT.  If not given, the last
    axis is used.
  * **norm** ( *{None* *,*  *"ortho"}* *,* *optional*) – Normalization mode (see numpy.fft). Default is None.
* **Returns:**
  **out** – The truncated or zero-padded input, transformed along the axis
  indicated by axis, or the last one if axis is not specified.
* **Return type:**
  complex Tensor
* **Raises:**
  [**IndexError**](https://docs.python.org/3/library/exceptions.html#IndexError) – If axes is larger than the last axis of a.

#### SEE ALSO
`mt.fft`
: An introduction, with definitions and general explanations.

[`fft`](maxframe.tensor.fft.fft.md#maxframe.tensor.fft.fft)
: The one-dimensional (forward) FFT, of which ifft is the inverse

[`ifft2`](maxframe.tensor.fft.ifft2.md#maxframe.tensor.fft.ifft2)
: The two-dimensional inverse FFT.

[`ifftn`](maxframe.tensor.fft.ifftn.md#maxframe.tensor.fft.ifftn)
: The n-dimensional inverse FFT.

### 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.

### Examples

```pycon
>>> import maxframe.tensor as mt
```

```pycon
>>> mt.fft.ifft([0, 4, 0, 0]).execute()
array([ 1.+0.j,  0.+1.j, -1.+0.j,  0.-1.j])
```

Create and plot a band-limited signal with random phases:

```pycon
>>> import matplotlib.pyplot as plt
>>> t = mt.arange(400)
>>> n = mt.zeros((400,), dtype=complex)
>>> n[40:60] = mt.exp(1j*mt.random.uniform(0, 2*mt.pi, (20,)))
>>> s = mt.fft.ifft(n)
>>> plt.plot(t.execute(), s.real.execute(), 'b-', t.execute(), s.imag.execute(), 'r--')
...
>>> plt.legend(('real', 'imaginary'))
...
>>> plt.show()
```
