tatb06-fft package

tatb06-fft package#

Submodules#

tatb06-fft.dft module#

Contains DFT and inverse DFT algorithms

tatb06_fft.dft.dft(a: numpy.typing.ArrayLike, variant: str = 'explicit') → numpy.typing.NDArray.numpy.complex128[source]#

Computes the Fourier transform of the input data using the DFT-matrix

Parameters:

  • a (ArrayLike) – Input array, can be real or complex

  • variant (str) – The implementation used, can be ‘explicit’ or ‘implicit’. (Default ‘explicit’)

Returns:

The transformed array

Return type:

NDArray[complex128]

tatb06_fft.dft.idft(a: numpy.typing.ArrayLike, variant: str = 'explicit') → numpy.typing.NDArray.numpy.complex128[source]#

Computes the inverse Fourier transform of the input data using the DFT-matrix

Parameters:

  • a (ArrayLike) – Input array, can be real or complex

  • variant (str) – The implementation used, can be ‘explicit’ or ‘implicit’. (Default ‘explicit’)

Returns:

The transformed array

Return type:

NDArray[complex128]

tatb06-fft.fft module#

Contains algorithms for the FFT

tatb06_fft.fft.fft(a: numpy.typing.ArrayLike, variant: str = 'python_iter') → tuple[numpy.typing.NDArray.numpy.complex128, int][source]#

Computes the Fourier transform of the input data using the Cooley–Tukey FFT algorithm.

Pads the input array with zeros at the tail if its length is not a power of two.

Parameters:

  • a (ArrayLike) – Input array, can be real or complex

  • variant (str) – The implementation used, can be ‘python_iter’, ‘python_recur’, ‘rust_iter’, ‘rust_recur’, ‘rust_parallell’. (Default ‘python_iter’).

Returns:

A tuple containing the transformed array and with how many zeros the array was padded.

Return type:

tuple[NDArray[complex128], int]

tatb06_fft.fft.ifft(a: numpy.typing.ArrayLike, variant: str = 'python_iter') → tuple[numpy.typing.NDArray.numpy.complex128, int][source]#

Computes the inverse Fourier transform of the input data using the Cooley–Tukey FFT algorithm

Pads the input array with zeros at the center (i.e. at the high frequencies) if its length is not a power of two.

Parameters:

  • a (ArrayLike) – Input array, can be real or complex

  • variant (str) – The implementation used, can be ‘python_iter’, ‘python_recur’, ‘rust_iter’, ‘rust_recur’, ‘rust_parallell’. (Default ‘python_iter’).

Returns:

A tuple containing the transformed array and with how many zeros the array was padded.

Return type:

tuple[NDArray[complex128], int]

tatb06-fft.tools module#

Contains helper functions for generating signals, plotting, and measuring function execution time

tatb06_fft.tools.generate_cosine_signal(parameters: list[tuple[float, float]], resolution: int) → numpy.typing.NDArray.numpy.float64[source]#

Generates a signal on [0,1] using multiple cosine waves with the given parameters.

Parameters:

  • parameters (list[tuple[float, float]]) – A list containing the amplitudes and frequencies for the different cosine waves. The layout should be [(amp1, freq1), (amp2, freq2), …].

  • resolution (int) – How many samples of the signal to return

Return type:

NDArray[float64]

tatb06_fft.tools.generate_sine_signal(parameters: list[tuple[float, float]], resolution: int) → numpy.typing.NDArray.numpy.float64[source]#

Generates a signal on [0,2*pi] using multiple sine waves with the given parameters.

Parameters:

  • parameters (list[tuple[float, float]]) – A list containing the amplitudes and frequencies for the different sine waves. The layout should be [(amp1, freq1), (amp2, freq2), …].

  • resolution (int) – How many samples of the signal to return

Return type:

NDArray[float64]

tatb06_fft.tools.plot_magnitude_stem(a: numpy.typing.ArrayLike, title: str = '', reorder: bool = True, show: bool = True) → None[source]#

Plots a magnitude stem of the input data in a new figure.

Parameters:

  • a (ArrayLike) – Input array, can be real or complex

  • title (str) – Title of the figure

  • show (bool) – If set to True, run plt.show() after plotting the stem. Should be False if you want to plot multiple plots

Reorder:

If set to True, reorder the data using reorder_frequencies() before plotting.

tatb06_fft.tools.reorder_frequencies(a: numpy.typing.ArrayLike) → numpy.typing.ArrayLike[source]#

Moves the second half of the frequency data to the front for correct visualization.

In the output of the FFT algorithm, the first half of the data corresponds to the frequencies 0 to N/2, and the second half corresponds to -N/2 to just below 0, which is why the reordering is needed.

Parameters:

a (ArrayLike) – Input array, can be real or complex

tatb06_fft.tools.time_function(f, args, n_samples=5)[source]#

Runs the given function a number of times and returns the average execution time.

Parameters:

  • f – The function to measure

  • args (list) – A list containing the positional arguments sent to the function

  • n_samples – The number of samples to take, i.e. how many times the function is run

Returns:

The mean execution time of the function calls

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