Modeling Toolkit for Time Series Analysis AstroML Notebook Demo

This repository contains Python code for analyzing and visualizing Fourier series, signal processing, and convolution using scientific computing libraries. It leverages libraries such as numpy, scipy, matplotlib, astroML, and arviz to compute and display signal processing operations like Fourier Transforms, window functions, and convolutions.

Features

• Fourier Transform and Series: Fit Fourier series to data using FFT (Fast Fourier Transform) and plot the results.

• Signal Processing: Compute and display convolution of data with window functions.

• Gaussian Convolutions: Analyze Gaussian functions and their Fourier Transforms.

• Aliasing Demonstration: Show how undersampling impacts signal reconstruction.

• Power Spectral Density (PSD): Compute and plot PSDs for windowed and observed data.

• Visualization: Multiple plotting utilities for better understanding of the signal processing steps.

  Example Outputs

Here are some examples of the visual outputs produced by the code:

• Fourier Series Approximation:

  

• Convolution with Window Function:

  

• Power Spectral Density (PSD):

  

License

This project is licensed under the MIT License. See the LICENSE file for details.

Acknowledgements

• Data sourced from astroML.datasets.
• Special thanks to scipy, numpy, and matplotlib developers for the core scientific computing libraries.

Requirements

To run this code, you'll need the following Python packages installed:

pip install numpy scipy matplotlib astroML arviz