Fast Fourier Transformation with Python and Numpy

In this Github Repository you can see how a Fast Fourier Transformation is implement via using the numpy library for faster array and matrix calculations. The code contains a couple of examples for transforming arrays and matrices. The implementations of the FFTs are based on the explanations of the Book "Introduction to Numerical Analysis"[1}.

The code contains:

FFT for arrays
iFFT for arrays
FFT2D for matrices
iFFT2D for matrices

Local Installation

Clone the repo

git clone https://github.com/JanMarcelKezmann/Fast-Fourier-Transformation-with-Python-and-Numpy.git

Install requirements

(navigate into the new folder)

pip install -r requirements.txt

Make sure you have the following installed:

keras
numpy
matplotlib

Run with JupyterNotebook or JupyterLab

Just open the .ipynb code in a Notebook of your choice and run it.

Results

The code always compares the received transformation with the correct one given by Numpy. For all implemented FFTs the code works just as well as it should. Anyway it is clearly visible in the last example that the code is lacking speed. This is due to the slow speed of Python as well as the used algortihm.

References

[1] Introduction to Numerical Analysis, J. Stoer & R. Bullisch, Springer, 2nd edition

JanMarcelKezmann / Fast-Fourier-Transformation-with-Python-and-Numpy