:mod:`ulab.numpy.fft`
=====================

.. py:module:: ulab.numpy.fft

.. autoapi-nested-parse::

   Frequency-domain functions






.. py:function:: fft(r: ulab.numpy.ndarray, c: Optional[ulab.numpy.ndarray] = None) -> Tuple[ulab.numpy.ndarray, ulab.numpy.ndarray]

   :param ulab.numpy.ndarray r: A 1-dimension array of values whose size is a power of 2
   :param ulab.numpy.ndarray c: An optional 1-dimension array of values whose size is a power of 2, giving the complex part of the value
   :return tuple (r, c): The real and complex parts of the FFT

   Perform a Fast Fourier Transform from the time domain into the frequency domain

   See also ~ulab.extras.spectrum, which computes the magnitude of the fft,
   rather than separately returning its real and imaginary parts.


.. py:function:: ifft(r: ulab.numpy.ndarray, c: Optional[ulab.numpy.ndarray] = None) -> Tuple[ulab.numpy.ndarray, ulab.numpy.ndarray]

   :param ulab.numpy.ndarray r: A 1-dimension array of values whose size is a power of 2
   :param ulab.numpy.ndarray c: An optional 1-dimension array of values whose size is a power of 2, giving the complex part of the value
   :return tuple (r, c): The real and complex parts of the inverse FFT

   Perform an Inverse Fast Fourier Transform from the frequeny domain into the time domain