Course title

Course code


Signal Processing on Sphere


Harmonic analysis on the line: Fourier series and transforms (discrete and continuous), orthogonality (discrete and continuous), sampling theorem (uniform sampling), aliasing, convolution, window functions, autocovariance/autocorrelation functions, power spectral densities, computational aspects, periodogram estimation, FFT, least squares spectral analysis.

Global harmonic analysis on the sphere: Orthogonal base functions on the sphere, associated Legendre functions, spherical harmonics, convolution, sampling theorems (uniform), aliasing, filtering, autocovariance/autocorrelation functions, power spectral density, computational aspects.

Localized analysis on the sphere: Space localizing basis functions (radial basis functions, spherical splines, Band-limited spline functions), computational aspects.

Slepian functions: Uncertainty principle of signal processing, uncertainty principle on the sphere, Slepian functions, Shannon number, periodogram estimation,computational aspects.

Empirical orthogonal functions: Spatio-temporal datasets, eigenvalue decomposition, significance testing of modes, signal reconstruction, data compression, computational aspects.



  1. Dahlen, FA and Simons, FJ (2008). Spectral estimation on a sphere in geophysics and cosmology. Geophysical Journal International, 174:774–807. doi:10.1111/j.1365-246X.2008.03854.x.
  2. Devaraju, B (2015). Understanding filtering on the sphere – Experiences from filtering GRACE data. Ph.D. thesis, Universität Stuttgart.
  3. Devaraju, B and Sneeuw, N (2017). The polar form of the spherical harmonic spectrum: implications for filtering GRACE data. Journal of Geodesy, pp. 1–15.        doi:10.1007/s00190-017-1037-7.
  4. Eicker, A (2008). Gravity field refinements by radial basis functions from In-situ satellite data. Ph.D. thesis, University of Bonn.
  5. Hamming, RW (1989). Digital Filters. 3rd edn. Prentice Hall.
  6. Jekeli, C (2018). Spectral methods in geodesy and geophysics. CRC Press
  7. Michel, V (2013). Lectures on Constructive Approximation. Birkhäuser Boston. doi:10.1007/978-0-8176- 8403-7.
  8. Simons, F, Dahlen, F and Wieczorek, M (2006). Spatiospectral concentration on      a sphere. SIAM Review, 48(3):504–536. doi:10.1137/S0036144504445765.