More generally, if T and W are subsets of the integers modulo N, let L T , R W : ℓ ℓ 2 ( Z / N Z ) → → ℓ ℓ 2 ( Z / N Z ) denote the time-limiting operator and band-limiting operators, respectively. Then ‖ ‖ L T R W ‖ ‖ 2 ≤ ≤ | T | | W | | G | where the norm is the operator norm of operators on the Hilbert space ℓ ℓ 2 ( Z / N Z ) of functions on the integers modulo N. This inequality has implications for signal reconstruction.