numpy.fft — Fast Fourier Transform routines

The numpy.fft submodule provides one-dimensional Fast Fourier Transform routines. The length of the input array must be a power of 2; otherwise a ValueError is raised.

When ulab is built without complex support, the real and imaginary parts of the transform are kept in separate numpy.ndarray objects, and the functions return a 2-tuple (real, imag). When ulab is built with the ULAB_SUPPORTS_COMPLEX and ULAB_FFT_IS_NUMPY_COMPATIBLE options enabled, the routines accept and return complex arrays in a numpy-compatible manner.

Functions

numpy.fft.fft(r: ndarray, c: ndarray | None = None) → tuple[ndarray, ndarray]

Compute the one-dimensional discrete Fourier Transform of r.

Parameters:

  • r – a one-dimensional array whose length is a power of two. Holds the real part of the input signal.

  • c – an optional one-dimensional array of the same length as r, containing the imaginary part of the input. If omitted, the imaginary part is assumed to be zero.

Returns:

a 2-tuple (real, imag) of numpy.ndarray objects holding the real and imaginary parts of the transform.

Raises:

ValueError – if the length of the input is not a power of two.

When ulab is compiled with ULAB_SUPPORTS_COMPLEX and ULAB_FFT_IS_NUMPY_COMPATIBLE set to 1, the function instead takes a single (possibly complex) array and returns a complex array, in the same manner as numpy.fft.fft.

numpy.fft.ifft(r: ndarray, c: ndarray | None = None) → tuple[ndarray, ndarray]

Compute the one-dimensional inverse discrete Fourier Transform.

Parameters:

  • r – a one-dimensional array whose length is a power of two. Holds the real part of the spectrum.

  • c – an optional one-dimensional array of the same length as r, containing the imaginary part of the spectrum. If omitted, the imaginary part is assumed to be zero.

Returns:

a 2-tuple (real, imag) of numpy.ndarray objects holding the real and imaginary parts of the inverse transform. The result is normalised by N (the number of samples), so that ifft(fft(x)) reproduces the original input.

Raises:

ValueError – if the length of the input is not a power of two.

When ulab is compiled with ULAB_SUPPORTS_COMPLEX and ULAB_FFT_IS_NUMPY_COMPATIBLE set to 1, the function takes a single (possibly complex) array and returns a complex array.