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dft(n, scale=None)

Create the matrix that computes the discrete Fourier transform of a sequence . The nth primitive root of unity used to generate the matrix is exp(-2*pi*i/n), where i = sqrt(-1).

Notes

When scale is None, multiplying a vector by the matrix returned by dft is mathematically equivalent to (but much less efficient than) the calculation performed by scipy.fft.fft.

Parameters

n : int: Size the matrix to create.
scale : str, optional: Must be None, 'sqrtn', or 'n'. If scale is 'sqrtn', the matrix is divided by sqrt(n). If scale is 'n', the matrix is divided by n. If scale is None (the default), the matrix is not normalized, and the return value is simply the Vandermonde matrix of the roots of unity.

Returns

m : (n, n) ndarray: The DFT matrix.

Discrete Fourier transform matrix.

Examples

import numpy as np
from scipy.linalg import dft
np.set_printoptions(precision=2, suppress=True)  # for compact output
m = dft(5)
m

x = np.array([1, 2, 3, 0, 3])
m @ x  # Compute the DFT of x

Verify that ``m @ x`` is the same as ``fft(x)``.

from scipy.fft import fft
fft(x)     # Same result as m @ x

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.linalg._special_matrices:dft

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GitHub : /scipy/linalg/_special_matrices.py#973
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