In mathematics, the Balian–Low theorem in Fourier analysis is named for Roger Balian and Francis E. Low. The theorem states that there is no well-localized window function (or Gabor atom) g either in time or frequency for an exact Gabor frame (Riesz Basis).
for integers m and n, and a,b>0 satisfying ab=1. The Balian–Low theorem states that if
The Balian–Low theorem has been extended to exact Gabor frames.
- Gabor filter (in image processing)
- Benedetto, John J.; Heil, Christopher; Walnut, David F. (1994). "Differentiation and the Balian–Low Theorem". Journal of Fourier Analysis and Applications. 1 (4): 355–402. doi:10.1007/s00041-001-4016-5.