fourier.md

3. Fourier Transformations

3.1 DFT

The fourier.dft_slow function is a plain implementation of discrete Fourier transformation.

The fourier.fft_vectorized function depends on this function.

3.1.1 Parameters

Parameter	Description
input_data	Array containing the values to be transformed.

Returns an array containing the transformed values.

3.1.2 Example usage

>>> from Asteria import fourier
>>> fourier.dft_slow([1,2,3,4])
array([10.+0.00000000e+00j, -2.+2.00000000e+00j, -2.-9.79717439e-16j, -2.-2.00000000e+00j])

3.2 FFT

The fourier.fft_vectorized function is a vectorized, non-recursive version of the Cooley-Tukey FFT

Gives the same result as fourier.dft_slow but is many times faster.

3.2.1 Parameters

Parameter	Description
input_data	Array containing the values to be transformed.

Returns an array containing the transformed values.

3.2.2 Example usage

>>> from Asteria import fourier
>>> fourier.fft_vectorized([1,2,3,4])
array([10.+0.00000000e+00j, -2.+2.00000000e+00j, -2.-9.79717439e-16j, -2.-2.00000000e+00j])

3.3 IFFT

This function computes the inverse of the one-dimensional n-point discrete Fourier transform computed by fft

3.3.1 Parameters

Parameter	Description
input_data	Input array, can be complex.

3.3.2 Example usage

>>> from Asteria import fourier
>>> fourier.ifft([0,4,0,0])
array([ 1.+0.j,  0.+1.j, -1.+0.j,  0.-1.j])

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