EE 518 Data Analysis and AI on the Sphere

Fall 2022

Syed Babar Ali School of Science and Engineering
Lahore University of Management Sciences

Course Overview


Data defined on the 2-dimensional surface of the 2-sphere arise whenever the underlying configuration of the problem has a spherical geometry. Hence, such data has inherent angular dependence and is encountered in various fields of science and engineering, such as wireless communication, 3D beamforming, computer graphics, medical imaging, acoustics, geodesy, quantum chemistry, cosmology, astronomy and planetary sciences. Examples of data on the sphere include gravitational, topographic and magnetic fields of the planets, cosmic microwave background (CMB), a relic radiation from the Big Bang, pouring down on us from space, electromagnetic radiation pattern of an antenna array in spherical geometry, acoustic signal received using spherical configuration of microphones etc.

As opposed to 1D and multidimensional Euclidean domain data, which are defined on flat Euclidean domains, spherical data is defined on a curved domain due to which extension of Euclidean domain analysis and processing techniques to the spherical domain is not a trivial task. However, over the years, a lot of methods developed for Euclidean domain signals/data have been carefully extended to process data on the sphere to serve the needs of above-mentioned applications and scientific areas.

This course provides a thorough introduction to the theoretical foundations of data analysis, processing and learning on the sphere. Furthermore, the students will also learn to visualize the data in the spatial (spherical) and harmonic domain using Matlab.


  • (Sep. 06) Welcome to EE 518. Course outline has been posted.

Administrative Details

  • Course Outline (Click to download)

  • Suggested Books:

    • R. A. Kennedy and P. Sadeghi, Hilbert Space Methods in Signal Processing, 2013.

    • Lecture Notes will be provided.

  • Office Hours and Contact Information

    • Instructor: Zubair Khalid (, Office hours: Tuesday, Thursday 3 pm -4 pm

Grading Distribution

  • Assignments and Homeworks, 40 %

  • Quizzes, 20 %

  • Mid-Exam, 20 %

  • Final Exam, 20 %


Homework Solutions
Homework 01 Solutions
Homework 02 Solutions
Homework 03 Solutions
Homework 04 Solutions


  • Week 01-02

    • Course Overview, Motivation: Applications of data analysis on the sphere

    • Advanced operations on vectors, norm, angle, inner product

    • 2-sphere domain, Inner product , Hilbert space

    • Spherical harmonics, spectral domain characterization

    • Subspaces: Space-limited, band-limited, azimuthally symmetric and order-limited subspaces